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Unformatted text preview: 8 August 2007 Homework Service Book Physics Chapters 23 to 64 High School Questions Contact homework computer at World Wide Web URL https://hw.utexas.edu/ information: https://hw.utexas.edu/bur/overview.html signup: https://hw.utexas.edu/bur/instrGuestEID.html contact: homework@physics.utexas.edu Homework Service Book — Physics 00 Editing Examples 00-01 Basic Templates 00-02 User-Defined Macros 00-03 Figure Files 00-04 Basic Control Structures 00-05 Advanced Control Structures 00-06 Special Purpose Templates 00-07 Basic Functions 00-08 Special Functions 00-09 Basic TEX Techniques 00-10 Basic Tables 00-11 Special Use Tables 00-12 Using Macros in TEX 00-13 Basic PSTricks Techniques 00-14 Basic Graphs 00-15 Using Figure Files in PSTricks 00-16 Special Figures 00-17 Using Macros in PSTricks 00-18 Basic PPCHTeX Techniques 00-19 PPCHTeX and PSTricks 00-20 Basic Biology Templates 00-21 Basic Chem Templates 00-22 Basic PPCHTeX Structures 00-23 Electron Dot Templates 00-24 Complicated Chem Structures 00-25 Basic CS Templates 00-26 CS Structures 00-27 Basic Math Templates 00-28 Math Graphs 00-29 Basic Physics Templates 00-30 Physics Figures 00-99 Associated problems in Chapter 00 01 Physics and Measurement 01-01 The SI System 01-02 Standard Unit for Length, Mass, and Time 01-03 Derived Units 01-04 The Building Blocks of Matter 01-05 Density and Atomic Mass 01-06 Dimensional Analysis 01-07 Conversion of Units 01-08 Order-of-Magnitude Calculations 01-09 Significant Digits and Measurements 01-10 Elementary Error Analysis 01-11 Mathematical and Scientific Notation 01-12 Coordinate Systems 01-13 Mathematics Overview 01-14 Scientific Method 01-15 Scaling -2- 01-16 Problem Solving Strategy 01-17 Measurement Tools 01-99 Associated problems in Chapter 01 02 Motion in One Dimension 02-01 Displacement 02-02 Velocity and Speed 02-03 Average Velocity for Motion along a Straight Line 02-04 Instantaneous Velocity and Speed 02-05 Acceleration 02-06 One-Dimensional Motion with Constant Acceleration 02-07 Freely Falling Objects 02-08 One-Dimensional Motion: Calculus Techniques 02-09 Relative Velocities 02-10 Frame of Reference 02-99 Associated problems in Chapter 02 03 Vectors 03-01 Coordinate Systems and Frames of Reference 03-02 Vector and Scalar Quantities 03-03 Some Properties of Vectors 03-04 Methods of Solving Triangles 03-05 Graphical Addition of Vectors 03-06 Components of a Vector 03-07 Adding Vector Components 03-08 Unit Vectors 03-09 Vector Kinematics 03-10 The Vector Dot (Scalar) Product 03-11 The Vector Cross Product 03-99 Associated problems in Chapter 03 04 Motion in Two Dimensions 04-01 Position and Displacement 04-02 Average and Instantaneous Velocity 04-03 Average and Instantaneous Acceleration 04-04 Two-Dimensional Motion with Constant Acceleration 04-05 Graphical Solutions 04-06 Projectile Motion 04-07 Uniform Circular Motion 04-08 Tangential and Radial Acceleration 04-09 Relative Velocity 04-10 Relative Acceleration 04-11 Relative Motion at High Speeds 04-99 Associated problems in Chapter 04 05 The Laws of Motion 05-01 The Concept of Force Homework Service Book — Physics 05-02 Newton’s First Law and Inertial Frames 05-03 Inertial Mass 05-04 Newton’s Second Law 05-05 Weight 05-06 Contact and Normal Forces 05-07 Hooke’s Law 05-08 Combining Forces 05-09 Newton’s Third Law 05-10 Free Body Diagrams in Problem Solving 05-11 Static Applications of Newton’s Law 05-12 Dynamic Applications of Newton’s Law 05-13 Friction 05-14 Other Resistive Forces (Terminal Velocity) 05-15 The Fundamental Forces of Nature 05-99 Associated problems in Chapter 05 06 Circular Motion and Newton’s Laws 06-01 Newton’s Second Law Applied to Uniform Circular Motion 06-02 Banked and Unbanked Curves 06-03 Nonuniform Circular Motion 06-04 Circular Motion in Accelerated Frames 06-05 Circular Motion in the Presence of Resistive Forces 06-06 Numerical Modeling (Euler’s Method) in Particle Dynamics 06-99 Associated problems in Chapter 06 07 Work and Energy 07-01 Forms of Energy 07-02 Kinetic Energy 07-03 Work 07-04 Work: a General Constant Force 07-05 Work: the Gravitational Force 07-06 Work: a Spring Force 07-07 Work: a General Varying Force 07-08 Kinetic Energy and the Work-Energy Theorem 07-09 The Nonisolated System – Conservation of Energy 07-10 Kinetic Friction 07-11 Power 07-12 Work and Energy in Three Dimensions 07-13 Energy and the Automobile 07-14 Kinetic Energy at High Speeds 07-15 Simple and Compound Machines 07-99 Associated problems in Chapter 07 -3- 08 Potential Energy and Conservation of Energy 08-01 Potential Energy 08-02 Spring Potential Energy 08-03 Conservative and Nonconservative Forces 08-04 Conservative Forces and Potential Energy 08-05 Conservation of Mechanical Energy 08-06 Changes in Mechanical Energy 08-07 Relationship Between Conservative Forces and Potential Energy 08-08 Energy Diagrams and the Equilibrium of a System 08-09 Work Done on a System by an External Force 08-10 Conservation of Energy in General 08-11 Mass-Energy Equivalence 08-12 Quantization of Energy 08-99 Associated problems in Chapter 08 09 Linear Momentum and Collisions 09-01 Linear Momentum 09-02 Impulse and Momentum 09-03 Conservation of Linear Momentum 09-04 Elastic Collisions 09-05 Inelastic Collisions 09-06 One-Dimensional Collisions 09-07 Two- and Three-Dimensional Collisions 09-08 The Center of Mass 09-09 Finding the Center of Mass by Integration 09-10 Motion of a System of Particles (Explosions) 09-11 Energy of a System of Particles 09-12 Energy and Momentum Conservation in Collisions 09-13 Center of Mass Reference Frame 09-14 Rocket Propulsion 09-99 Associated problems in Chapter 09 10 Rotation of a Rigid Object About a Fixed Axis 10-01 Angular Position, Velocity and Acceleration 10-02 Kinematic Equations for Uniformly Accelerated Rotational Motion 10-03 Vector Nature of Angular Quantities 10-04 Relationships Between Angular and Linear Quantities Homework Service Book — Physics 10-05 10-06 10-07 10-08 Rotational Kinetic Energy Calculation of Moments of Inertia Torque Relationship Between Torque and Angular Acceleration 10-09 Work, Power, and Energy in Rotational Motion 10-10 Problem Solving in Rotational Dynamics 10-99 Associated problems in Chapter 10 11 Rolling Motion, Angular Momentum, and Torque 11-01 Rotational Plus Translational Motion: Rolling 11-02 The Kinetic Energy of Rolling 11-03 The Forces of Rolling 11-04 The Yo-Yo 11-05 The Torque Vector 11-06 Angular Momentum of a Particle 11-07 General Motion: Angular Momentum, Torque of a System of Particles 11-08 Rotation of a Rigid Body About a Fixed Axis 11-09 Rotational Imbalance 11-10 Conservation of Angular Momentum 11-11 Precession: Gyroscopes and Tops 11-12 Rotating Frames of Reference: Inertial Forces 11-13 Coriolis Effect 11-14 Quantization of Angular Momentum 11-99 Associated problems in Chapter 11 12 Static Equilibrium and Elasticity 12-01 The Conditions for Equilibrium of a Rigid Object 12-02 Solving Statics Problems 12-03 Stability and Balance: Center of Gravity 12-04 Levers and Pulleys 12-05 Bridges and Scaffolding 12-06 Arches and Domes 12-07 Couples 12-08 Other Objects in Static Equilibrium 12-09 Static Equilibrium in an Accelerated Frame 12-10 Elasticity: Stress and Strain 12-11 Fracturing 12-99 Associated problems in Chapter 12 13 Oscillatory Motion 13-01 Simple Harmonic Motion 13-02 13-03 13-04 13-05 13-06 -4- Mass Attached to a Spring Forces in Simple Harmonic Motion Energy in Simple Harmonic Motion The Simple Pendulum The Physical Pendulum and Torsion Pendulum 13-07 Simple Harmonic Motion Related to Uniform Circular Motion 13-08 Damped Oscillations 13-09 Forced Oscillations: Resonance 13-99 Associated problems in Chapter 13 14 The Law of Gravity 14-01 Newton’s Law of Gravity 14-02 Gravitational Force Due to a System of Particles 14-03 Free Fall Acceleration and the Gravitational Force 14-04 Gravitation Inside the Earth 14-05 Kepler’s Laws: Planetary and Satellite Motion 14-06 The Gravitational Field 14-07 Gravitational Potential Energy 14-08 Escape Velocity 14-09 Energy: Planetary and Satellite Motion 14-10 Gravitational Force: Extended Object & Particle 14-11 Gravitational Force: Particle & Spherical Mass 14-12 Principle of Equivalence 14-99 Associated problems in Chapter 14 15 Fluid Mechanics 15-01 States of Matter 15-02 Density and Specific Gravity 15-03 Pressure 15-04 Fluids at Rest: Variation of Pressure with Depth 15-05 Pressure Measurements (Atmospheric, Gauge) 15-06 Pascal’s Principle (Hydraulics) 15-07 Buoyant Forces and Archimedes’ Principle 15-08 Fluid Dynamics 15-09 Streamlines and the Equation of Continuity 15-10 Bernoulli’s Equation 15-11 Transport Phenomena 15-12 Other Applications of Fluid Dynamics 15-13 Energy from the Wind Homework Service Book — Physics 15-14 Viscosity 15-15 Surface Tension and Capillarity 15-16 Pumps: the Heart 15-99 Associated problems in Chapter 15 16 Wave Motion 16-01 Wave Characteristics and Propagation 16-02 Transverse and Longitudinal Waves 16-03 Speed of a Traveling Wave 16-04 Energy Conservation 16-05 One-Dimensional Traveling Waves 16-06 Periodic Waves (Harmonic, Electromagnetic) 16-07 Superposition and Interference of Waves 16-08 The Speed of Waves on Strings 16-09 Reflection and Transmission of Waves 16-10 Refraction of Waves 16-11 Diffraction of Waves 16-12 Sinusoidal Waves 16-13 Energy Transmitted by Waves on Strings 16-14 The Linear Wave Equation 16-15 Phasors 16-99 Associated problems in Chapter 16 17 Sound Waves 17-01 Characteristics of Sound Waves 17-02 Speed of Sound Waves 17-03 Periodic Sound Waves 17-04 Energy and Intensity of Sound Waves 17-05 The Doppler Effect 17-06 Quality of Sound (Noise) 17-07 The Ear 17-08 Sources of Musical Sound 17-09 Digital Sound Recording 17-10 Motion Picture Sound 17-11 Sonar, Ultrasound, and Ultrasound Imaging 17-99 Associated problems in Chapter 17 18 Superposition and Standing Waves 18-01 Superposition of Sinusoidal Waves 18-02 Interference of Sinusoidal Waves 18-03 Standing Waves in General 18-04 Standing Waves in a String Fixed at Both Ends 18-05 Forced Vibrations and Resonance 18-06 Standing Waves in Air Columns 18-07 Standing Waves in Rods, Plates, and Membranes 18-08 Complex Waves -5- 18-09 Beats: Interference in Time 18-10 Shock Waves and the Sonic Boom 18-11 Harmonic Analysis and Synthesis 18-12 Wave Packets and Dispersion 18-99 Associated problems in Chapter 18 19 Temperature 19-01 Atomic Theory of Matter 19-02 The Zeroth Law of Thermodynamics: Thermal Equilibrium 19-03 Celsius and Fahrenheit Temperature Scales 19-04 The Constant-Volume Gas Thermometer and the Kelvin Scale 19-05 Thermal Expansion of Solids and Liquids 19-06 Macroscopic Description of an Ideal Gas 19-07 Problem Solving: Ideal Gas Law 19-99 Associated problems in Chapter 19 20 Heat and the First Law of Thermodynamics 20-01 Heat and Thermal Energy 20-02 Internal Energy 20-03 Heat Capacity and Specific Heat 20-04 Heat Capacity of Gases 20-05 Heat Capacity of Solids 20-06 Latent Heat 20-07 Phase Diagrams 20-08 Calorimetry 20-09 Work and Heat in Thermodynamic Processes 20-10 The First Law of Thermodynamics 20-11 Work and the P V Diagram for a Gas 20-12 Some Applications of the First Law of Thermodynamics 20-13 Heat and Energy Transfer 20-14 Global Warming and Greenhouse Gases 20-99 Associated problems in Chapter 20 21 The Kinetic Theory of Gases 21-01 Molecular Model of an Ideal Gas 21-02 Specific Heat of an Ideal Gas 21-03 Adiabatic Processes for an Ideal Gas 21-04 The Equipartition of Energy 21-05 The Boltzmann Distribution Law 21-06 Pressure, Temperature, and RMS Speed 21-07 Distribution of Molecular Speeds 21-08 Translational Kinetic Energy Homework Service Book — Physics 21-09 Mean Free Path 21-10 Van der Waals’ Equation of State 21-11 Vapor Pressure and Humidity 21-12 Diffusion 21-13 Failure of the Equipartition Theorem 21-99 Associated problems in Chapter 21 22 Heat Engines, Entropy, & Thermodynamics 22-01 The Second Law of Thermodynamics 22-02 Heat Engines 22-03 Reversible and Irreversible Processes 22-04 The Carnot Engine 22-05 Gasoline and Deisel Engines 22-06 Heat Pumps and Refrigerators 22-07 Entropy 22-08 Entropy Changes in Irreversible Processes 22-09 Entropy on a Microscopic Scale 22-10 Human Metabolism 22-11 Energy Availability: Heat Death 22-12 Statistical Interpretation of Entropy and the Second Law 22-13 Third Law: Maximum Efficiencies 22-99 Associated problems in Chapter 22 23 Electric Fields 23-01 Static Electricity: Electric Charge 23-02 Quantized Charge 23-03 Insulators and Conductors 23-04 Induced Charge: the Electroscope 23-05 Coulomb’s Law 23-06 Conserved Charge 23-07 The Electric Field 23-08 Electric Field Due to a Point Charge 23-09 Electric Field Due to an Electric Dipole 23-10 Electric Field Due to a Line of Charge 23-11 Electric Field Due to a Charged Sheet 23-12 Electric Field Due to a Continuous Charge Distribution 23-13 Electric Field Lines 23-14 Electric Fields and Conductors 23-15 A Point Charge in a Electric Field 23-16 A Dipole in a Electric Field 23-17 Motion of Charged Particles in a Uniform Electric Field 23-18 The Oscilloscope 23-99 Associated problems in Chapter 23 24 Gauss’s Law 24-01 Electric Flux 24-02 Gauss’s Law -6- 24-03 Application: Charged Insulators 24-04 Application: Charged Isolated Conductors 24-05 Application: Cylindrical Symmetry 24-06 Application: Planar Symmetry 24-07 Application: Spherical Symmetry 24-08 Conductors in Electrostatic Equilibrium 24-09 Experimental Proof of Gauss’ Law and Coulomb’s Law 24-99 Associated problems in Chapter 24 25 Electric Potential 25-01 Electric Potential Energy 25-02 Potential Difference and Electric Potential 25-03 Equipotential Surfaces 25-04 Calculating the Potential from the Field 25-05 Potential & Energy: Point Charges 25-06 Potential & Energy: Systems of Point Charges 25-07 Potential & Energy: Electric Dipoles 25-08 Potential & Energy: Continuous Charge Distributions 25-09 Potential & Energy: Charged Conductor 25-10 Calculating the Field from the Potential 25-11 Electrostatic Potential Energy: the Electron Volt 25-12 The Millikan Oil Drop Experiment 25-13 Cathode Ray Tube: TV, Computer Monitors, and Oscilloscopes 25-14 The Van de Graaff Generator and Other Applications 25-99 Associated problems in Chapter 25 26 Capacitance and Dielectrics 26-01 Definition of Capacitance 26-02 Calculation of Capacitance 26-03 Combinations of Capacitors 26-04 Energy Stored in a Charged Capacitor 26-05 Capacitors with Dielectrics 26-06 Dielectrics from a Molecular Level 26-07 Dielectrics and Gauss’ Law 26-08 Electric Dipole in an External Electric Field 26-09 Electrostatic Applications 26-99 Associated problems in Chapter 26 27 Current and Resistance Homework Service Book — Physics 27-01 Electric Current 27-02 Current Density and Drift Speed 27-03 Resistance and Resistivity 27-04 Ohm’s Law 27-05 Microscopic View of Ohm’s Law 27-06 Resistance and Temperature 27-07 Semiconductors 27-08 Superconductors 27-09 Electrical Energy and Power 27-10 Power in Household Circuits 27-11 Electrical Hazards: Leakage Currents 27-12 Electrical Energy in the Heart 27-99 Associated problems in Chapter 27 28 Direct Current Circuits 28-01 Electromotive Force and Terminal Voltage 28-02 Work, Energy, and EMF 28-03 Resistance: Series Circuits 28-04 Resistance: Series/Parallel Combinations 28-05 Potential Difference Between Two Points 28-06 Complicated Circuits: Kirchoff’s Rules 28-07 RC Circuits 28-08 Electrical Instruments: Ammeter and Voltmeter 28-09 Household Wiring and Electrical Safety 28-10 Conduction of Electrical Signals by Neurons 28-11 Transducers and the Thermocouple 28-99 Associated problems in Chapter 28 29 Magnetic Fields 29-01 Magnetic Fields and Forces 29-02 Magnetism from Electric Currents 29-03 Magnetic Force on a Current-Carrying Conductor 29-04 Torque on a Current Loop in a Uniform Magnetic Field 29-05 Motion of a Charged Particle in a Magnetic Field 29-06 Applications of the Motion of Charged Particles in a Magnetic Field 29-07 Crossed Fields: Discovery of the Electron 29-08 The Hall Effect 29-09 Galvanometers, Motors, Loudspeakers 29-10 Cyclotrons and Synchrotrons 29-11 Mass Spectrometer -7- 29-99 Associated problems in Chapter 29 30 Sources of the Magnetic Field 30-01 The Biot-Savart Law 30-02 Magnetic Field Due to a Straight Wire 30-03 Magnetic Force Between Two Parallel Conductors 30-04 Ampere’s Law 30-05 The Magnetic Field of Current Loops 30-06 The Magnetic Field Along the Axis of a Solenoid 30-07 A Current-Carrying Coil as a Magnetic Dipole 30-08 Magnetic Flux 30-09 Gauss’s Law in Magnetism 30-10 Displacement Current and the Generalized Ampere’s Law 30-11 Magnetism and Electrons: Spin 30-12 Magnetism in Matter 30-13 Diamagnetism 30-14 Paramagnetism 30-15 Ferromagnetism 30-16 Magnetic Field of the Earth 30-99 Associated problems in Chapter 30 31 Faraday’s Law 31-01 Faraday’s Law of Induction 31-02 Motional EMF 31-03 Lenz’s Law 31-04 Induced EMF in a Moving Conductor 31-05 Induced Electric Fields 31-06 Electric Field from a Changing Magnetic Flux 31-07 Generators and Motors 31-08 Eddy Currents 31-09 Maxwell’s Equations 31-10 Sound Systems, Computer Memory, the Seismograph 31-99 Associated problems in Chapter 31 32 Inductance 32-01 Inductors and Inductance 32-02 Self-Inductance, Self-Induced EMF 32-03 RL Circuits 32-04 Energy in a Magnetic Field 32-05 Energy Density of a Magnetic Field 32-06 Mutual Inductance 32-07 Oscillations in an LC Circuit 32-08 The RLC Circuit 32-09 Critical Magnetic Fields 32-10 Magnetic Properties of Superconductors Homework Service Book — Physics 32-99 Associated problems in Chapter 32 33 Alternating Current Circuits 33-01 AC Sources 33-02 Phasors 33-03 Resistors in an AC Circuit 33-04 Inductors in an AC Circuit 33-05 Capacitors in an AC Circuit 33-06 LC and RLC Circuits Without a Generator 33-07 The RLC Series Circuit 33-08 Damped Oscillations in an RLC Circuit 33-09 Power in an AC Circuit 33-10 Resonance in a Series RLC Circuit 33-11 Impedance Matching 33-12 Filter Circuits 33-13 The Transformer and Power Transmission 33-14 Three-Phase AC 33-99 Associated problems in Chapter 33 34 Electromagnetic Waves 34-01 Maxwell’s Equations and Hertz’s Discoveries 34-02 Plane Electromagnetic Waves 34-03 Speed of Electromagnetic Waves 34-04 Energy Carried by Electromagnetic Waves: Poynting Vector 34-05 Momentum and Radiation Pressure 34-06 Radiation from an Infinite Current Sheet 34-07 The Production of Electromagnetic Waves by an Antenna 34-08 Properties of Electromagnetic Waves 34-09 The Spectrum of Electromagnetic Waves 34-10 The Doppler Effect for Electromagnetic Waves 34-11 Radio and Television 34-99 Associated problems in Chapter 34 35 The Nature of Light and Geometric Optics 35-01 The Nature of Light 35-02 Wave-Particle Duality 35-03 The Speed of Light 35-04 Reflection 35-05 Transmission and Refraction 35-06 The Law of Refraction 35-07 Dispersion and Prisms 35-08 Huygens’ Principle 35-09 Total Internal Reflection -8- 35-10 Fermat’s Principle 35-11 Mixing Pigments 35-12 Luminous Intensity 35-99 Associated problems in Chapter 35 36 Geometric Optics 36-01 Two Types of Image 36-02 Images Formed by Flat Mirrors 36-03 Images Formed by Concave Mirrors 36-04 Images Formed by Convex Mirrors 36-05 Spherical Mirrors: Ray Tracing 36-06 Images Formed by Refracting Surfaces 36-07 Atmospheric Refraction 36-08 Images Formed by Thin Lenses 36-09 Combinations of Lenses and Mirrors 36-10 Thin Lenses: Ray Tracing 36-11 Lensmaker’s Equation 36-12 The Camera 36-13 The Eye and Corrective Lenses 36-14 The Simple Magnifier 36-15 The Compound Microscope 36-16 The Telescope 36-17 Lens and Mirror Aberrations 36-99 Associated problems in Chapter 36 37 Interference of Light Waves 37-01 Conditions for Interference 37-02 Double Slit Interference: Young’s Experiment 37-03 Coherence 37-04 Intensity Distribution of the DoubleSlit Interference Pattern 37-05 Phasor Addition of Waves 37-06 Change of Phase Due to Reflection 37-07 Interference in Thin Films 37-08 The Michelson Interferometer 37-09 Using Interference to Read CDs and DVDs 37-99 Associated problems in Chapter 37 38 Diffraction and Polarization 38-01 Diffraction 38-02 Huygens’ Principle and Diffraction 38-03 Huygens’ Principle and the Law of Refraction 38-04 Single-Slit Diffraction 38-05 Intensity in Single-Slit Diffraction 38-06 Using Phasors to Add Harmonic Waves 38-07 Fraunhofer and Fresnel Diffraction 38-08 Resolution of Single-Slit and Circular Apertures 38-09 Resolution of Telescopes and Micro- Homework Service Book — Physics scopes: the λ Limit 38-10 Resolution of the Human Eye and Useful Magnification 38-11 Diffraction by a Double Slit 38-12 The Diffraction Grating 38-13 Gratings: Dispersion and Resolving Power 38-14 X-Rays 38-15 Diffraction of X-Rays by Crystals 38-16 Polarization of Light Waves 38-17 Polarization by Reflection 38-18 The Spectrometer and Sprctroscopy 38-99 Associated problems in Chapter 38 39 Relativity 39-01 Galilean Coordinate Transformations 39-02 Lorenz Coordinate Transformations 39-03 Postulates: Speed of Light 39-04 The Michelson-Morley Experiment 39-05 Consequences of Special Relativity 39-06 The Lorentz Transformation for Displacements 39-07 The Lorentz Transformation for Time 39-08 The Lorentz Transformation for Velocities 39-09 Relativistic Momentum and Relativistic Form of Newton’s Laws 39-10 Relativistic Energy 39-11 Mass as a Measure of Energy 39-12 Photon Momentum 39-13 Conservation of Relativistic Momentum, Mass, and Energy 39-14 Doppler Shift for Light 39-15 Pair Production and Annihilation 39-16 Matter and Antimatter 39-17 General Relativity and Accelerating Reference Frames 39-99 Associated problems in Chapter 39 40 The Quantum Theory of Light 40-01 The Photon, the Quantum of Light 40-02 Hertz’s Experiments: Light as an Electromagnetic Wave 40-03 Blackbody Radiation and Planck’s Hypothesis 40-04 Light Quantization and the Photoelectric Effect 40-05 The Compton Effect 40-06 Particle-Wave Complementarity, Duality: Double Slits 40-07 Effect of Gravity on Light -9- 40-08 The Wave Function 40-09 Electron Microscopes 40-99 Associated problems in Chapter 40 41 The Particle Nature of Matter 41-01 The Atomic Nature of Matter 41-02 The Composition of Atoms 41-03 Molecules 41-04 The Bohr Atom 41-05 Quantum Model of the Hydrogen Atom 41-06 Franck-Herz Experiment 41-99 Associated problems in Chapter 41 42 Matter Waves 42-01 de Broglie Waves 42-02 The Time Independent Schrodinger Equation 42-03 The Davisson-Germer Experiment 42-04 Fourier Integrals 42-05 The Heisenberg Uncertainty Principle 42-06 Wave Groups and Dispersion 42-07 Wave-Particle Duality 42-08 String Waves and Matter Waves 42-99 Associated problems in Chapter 42 43 Quantum Mechanics in One Dimension 43-01 The Hydrogen Atom 43-02 The Born Interpretation 43-03 The Time-Dependent Schrodinger Equation 43-04 Wavefunction for a Free Particle 43-05 Wavefunctions in the Presence of Forces 43-06 Particle in a Box 43-07 Energies of a Trapped Electron 43-08 Wave Functions of a Trapped Electron 43-09 The Finite Square Well 43-10 More Electron Traps 43-11 Two- and Three-Dimensional Electron Traps 43-12 The Quantum Oscillator 43-13 Expectation Values 43-14 Observables and Operators 43-99 Associated problems in Chapter 43 44 Tunneling Phenomena 44-01 The Square Barrier 44-02 Barrier Penetration: Some Applications 44-03 Decay Rates 44-04 The Scanning Tunneling Microscope 44-99 Associated problems in Chapter 44 Homework Service Book — Physics 45 Quantum Mechanics in Three Dimensions 45-01 Three-Dimensional Schrodinger Equation 45-02 Particle in a Three-Dimensional Box 45-03 Central Forces and Angular Momentum 45-04 Space Quantization 45-05 Quantization of Angular Momentum and Energy 45-06 Atomic Hydrogen and Hydrogen-like Ions 45-99 Associated problems in Chapter 45 46 Atomic Structure 46-01 Some Properties of Atoms 46-02 Atomic Spectra 46-03 Orbital Magnetism and the Normal Zeeman Effect 46-04 Electron Spin 46-05 The Spin-Orbit Interaction and Other Magnetic Effects 46-06 Angular Momenta and Magnetic Dipole Moments 46-07 The Stern-Gerlach Experiment 46-08 Magnetic Resonance 46-09 Electron Clouds 46-10 Exchange Symmetry and the Exclusion Principle 46-11 Multiple Electrons in Rectangular Traps 46-12 Electron Interactions and Screening Effects 46-13 The Periodic Table 46-14 Isotopes 46-15 X-Ray Spectra and Moseley’s Law 46-16 Atomic Transitions 46-17 Lasers and Holography 46-18 How Lasers Work 46-99 Associated problems in Chapter 46 47 Statistical Physics 47-01 The Maxwell-Boltzmann Distribution 47-02 Quantum Statistics, Indistinguishability, and the Pauli Exclusion Principle 47-03 Applications of Bose-Einstein Statistics 47-04 An Application of Fermi-Dirac Statistics: The Free-Electron Gas Theory of Metals 47-99 Associated problems in Chapter 47 -10- 48 Molecular Structure 48-01 Bonding Mechanisms 48-02 Weak (van der Waals) Bonds 48-03 Polyatomic Molecules 48-04 Diatomic Molecules: Molecular Rotation and Vibration 48-05 Molecular Spectra 48-06 Electron Sharing and the Covalent Bond 48-07 Bonding in Complex Molecules 48-99 Associated problems in Chapter 48 49 The Solid State 49-01 Bonding in Solids 49-02 Electrical Properties of Solids 49-03 Energy Levels in a Crystalline Solid 49-04 Insulators 49-05 Metals 49-06 Classical Free-Electron Model 49-07 Quantum Theory of Metals 49-08 Band Theory of Solids 49-09 Semiconductor Devices 49-10 Doped Semiconductors 49-11 The p-n Junction 49-12 The Junction Rectifier 49-13 The Light-Emitting Diode (LED) 49-14 Transistors and Integrated Circuits 49-99 Associated problems in Chapter 49 50 Superconductivity 50-01 Magnetism in Matter 50-02 A Brief History of Superconductivity 50-03 Some Properties of Type I Superconductors 50-04 Type II Superconductors 50-05 Other Properties of Superconductors 50-06 Electronic Specific Heat 50-07 BCS Theory 50-08 Energy Gap Measurements 50-09 Josephson Tunneling 50-10 High-Temperature Superconductivity 50-11 Applications of Superconductivity 50-99 Associated problems in Chapter 50 51 Nuclear Structure 51-01 Discovering the Nucleus 51-02 Some Nuclear Properties 51-03 Binding Energy and Nuclear Forces 51-04 Nuclear Models 51-05 Radioactivity 51-06 Decay Processes 51-07 Alpha Decay Homework Service Book — Physics 51-08 Beta Decay 51-09 Gamma Decay 51-10 Half-Life and Rate of Decay 51-11 Decay Series 51-12 Radioactive Dating 51-13 Measuring Radiation Dosage 51-14 Natural Radioactivity 51-99 Associated problems in Chapter 51 52 Nuclear Physics Applications 52-01 Nuclear Reactions 52-02 Reaction Cross Section 52-03 Interactions Involving Neutrons 52-04 Nuclear Fission 52-05 A Model for Nuclear Fission 52-06 Nuclear Reactors 52-07 A Natural Nuclear Reactor 52-08 Nuclear Fusion 52-09 Thermonuclear Fusion in the Sun and Other Stars 52-10 Controlled Thermonuclear Fusion 52-11 Recent Fusion Energy Developments 52-12 Interaction of Particles with Matter 52-13 Radiation Damage in Matter 52-14 Radiation Detectors 52-15 Radiation Therapy 52-16 Tracers 52-17 Tomography Imaging: CAT Scans and Emission Tomography 52-18 NMR and MRI 52-99 Associated problems in Chapter 52 53 Particle Physics 53-01 Elementary Particles 53-02 The Fundamental Forces in Nature 53-03 Particle Accelerators and Detectors 53-04 Particle Exchange 53-05 Particles and Antiparticles 53-06 Mesons and the Beginning of Particle Physics 53-07 Classification of Particles 53-08 Conservation Laws 53-09 Particle Stability and Resonances 53-10 Antiproton in a Bubble Chamber 53-11 Leptons 53-12 Hadrons 53-13 Strange Particles and Strangeness 53-14 Elementary Particle Production; Measurement of Properties 53-15 The Eightfold Way 53-16 Quarks -11- 53-17 Electroweak Theory and the Standard Model 53-18 Quasars 53-19 Grand Unified Theory 53-99 Associated problems in Chapter 53 54 Astrophysics and Cosmology 54-01 Stars and Galaxies 54-02 The Birth and Death of Stars 54-03 General Relativity: Gravity and the Curvature of Space 54-04 The Expanding Universe 54-05 The Cosmic Connection 54-06 Cosmic Background Radiation 54-07 Dark Matter 54-08 The Big Bang 54-09 Early History of the Universe 54-10 The Future of the Universe 54-11 Problems and Perspectives 54-99 Associated problems in Chapter 54 55 Probability Distributions 55-01 Uncertainites 55-02 Parent and Sample Distributions 55-03 Mean and Standard Deviation of Distributions 55-04 Binomial Distribution 55-05 Poisson Distribution 55-06 Gaussian or Normal Error Distribution 55-07 Lorentzian Distribution 55-99 Associated problems in Chapter 55 56 Error Analysis (see 01:11) 56-01 Instrumental and Statistical Uncertainties 56-02 Propagation of Errors 56-03 Specific Error Formulas 56-04 Application of Error Equations 56-99 Associated problems in Chapter 56 57 Estimates of Mean and Errors 57-01 Method of Least Squares 57-02 Statistical Fluctuations 57-03 χ2 Test of a Distribution 57-99 Associated problems in Chapter 57 58 Monte Carlo Techniques 58-01 Introduction 58-02 Random Numbers 58-03 Random Numbers from Probability Distributions 58-04 Specific Distributions 58-05 Efficiency 58-99 Associated problems in Chapter 58 Homework Service Book — Physics 59 Least-Squares Fit to a Straight Line 59-01 Dependent and Independent Variables 59-02 Method of Least Squares 59-03 Minimizing χ2 59-04 Error Estimation 59-05 Some Limitations of the Least-Squares Method 59-06 Alternate Fitting Methods 59-99 Associated problems in Chapter 59 60 Least-Squares Fit to a Polynomial 60-01 Determinate Solution 60-02 Matrix Solution 60-03 Independent Parameters 60-04 Nonlinear Functions 60-99 Associated problems in Chapter 60 61 Least-Squares Fit to an Arbitrary Function 61-01 Nonlinear Fitting 61-02 Searching Parameter Space 61-03 Grid-Search Mechod 61-04 Gradient-Search Method 61-05 Expansion Methods 61-06 The Marquardt Method 61-07 Comments on the Fits 61-99 Associated problems in Chapter 61 62 Fitting Composite Curves 62-01 Lorentzian Peak on Quadratic Background 62-02 Area Determination 62-03 Composite Plots 62-99 Associated problems in Chapter 62 63 Direct Application of the MaximumLikelihood Method 63-01 Maximum-Likelihood Method 63-02 Computer Example 63-99 Associated problems in Chapter 63 64 Testing the Fit 64-01 χ2 Test of Goodness of Fit 64-02 Linear-Correlation Coefficient 64-03 F Test 64-04 Confidence Intervals 64-05 Monte Carlo Tests 64-99 Associated problems in Chapter 64 -12- Chapter 23, section 1, Static Electricity: Electric Charge 13 tumbling in a clothes dryer? Conceptual Q16 01 23:01, highSchool, multiple choice, < 1 min, fixed. 1. gravitational force 2. air pressure There is an old saying that the lightning never strikes the same place twice. Is this true? 1. Yes 2. No 3. electrical force 4. The dryer heat caused some of the fabrics to melt together. 5. The clothes are electrically neutral. Conceptual Q16 11 23:01, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 22 E05 23:01, highSchool, multiple choice, < 1 min, fixed. Static cling makes your clothes stick together. What causes this to happen? When combing your hair, you scuff electrons from your hair onto the comb. Is your hair then positively or negatively charged? What about the comb? 1. friction created by tumbling clothes 1. positively charged; negatively charged 2. the nature of the material 2. Both are positively charged. 3. external forces to the clothes 2. Both are negatively charged. 4. forces of nature 4. negatively charged; positively charged Hewitt CP9 11 E01 23:01, highSchool, multiple choice, < 1 min, fixed. How does the mass of an object change when it acquires a positive charge? 1. decreases 2. increases 3. doesn’t change 4. More information is needed. Hewitt CP9 22 E02 23:01, highSchool, multiple choice, < 1 min, fixed. Why do clothes often cling together after 5. Neither is charged. Hewitt CP9 22 E06 23:01, highSchool, multiple choice, < 1 min, fixed. At some automobile toll-collecting stations, a thin metal wire sticks up from the road and makes contact with cars before they reach the toll collector. What is the purpose of this wire? 1. To discharge the automobile 2. To count the vehicles 3. To warn the drivers 4. To transfer electrons to the automobile Chapter 23, section 1, Static Electricity: Electric Charge 14 is less than the net charge of the ions. 5. To transfer positive particles to the automobile Hewitt CP9 22 E07 23:01, highSchool, numeric, < 1 min, fixed. Why are the tires for trucks carrying gasoline and other flammable fluids manufactured to be electrically conducting? 1. To move the negative charges from the truck to the ground and avoid a fire 2. The net charge of the negative electrons is greater than the net charge of the ions. 3. The net charge of the negative electrons has the same magnitude as the net charge of the ions. 4. Sometimes the net charge of the negative electrons is greater than the net charge of the ions and sometimes it is less. 5. Unable to determine 2. To neutralize the charges on the trucks 3. To make the truck move faster Hewitt CP9 22 E18 23:01, highSchool, multiple choice, < 1 min, fixed. 4. To make the truck easier to drive 5. To move the positive charges from the truck to the ground and avoid fire The five thousand billion freely moving electrons in a penny repel one another. Why don’t they fly off the penny? Hewitt CP9 22 E11 23:01, highSchool, multiple choice, < 1 min, fixed. 1. They are attracted to the five thousand billion positively charged protons in the atomic nuclei of atoms in the penny. What happens to the mass of an object when it acquires a positive net charge by the transfer of electrons? 2. They don’t have enough speed. 3. They cause a jam when they try to fly away. 1. decreases 2. increases 3. Doesn’t change 4. Unable to determine Hewitt CP9 22 E13 23:01, highSchool, multiple choice, < 1 min, fixed. 4. The shell of the penny prevents the electrons from flying. 5. The electrons attract each other. Hewitt CP9 22 E27 23:01, highSchool, multiple choice, < 1 min, fixed. If you are caught outdoors in a thunderstorm, why should you not stand under a tree? In a crystal of salt there are electrons and positive ions. How does the net charge of the electrons compare with the net charge of the ions? 1. A tree is likely to accumulate an electric charge that can kill you if you touch the tree. 1. The net charge of the negative electrons 2. A tree attracts electrically polarized air Chapter 23, section 1, Static Electricity: Electric Charge molecules that can have a harmful effect on your body. 15 painted. What does the phenomenon of polarization have to do with this? 3. A tree is likely to be hit by lightning because you and the tree now form a polarized system. 1. The air is polarized and makes the paint flow uniformly. 4. A tree is likely to be hit by lightning because it provides a path of less resistance between the cloud overhead and the ground. 2. The paint particles in the mist are polarized and as such are attracted to the charged chassis. 5. The tree has more resistance than the air and thus is likely to be hit by lightning. 3. The car is polarized and easily attracts paint particles. Hewitt CP9 22 E30 23:01, highSchool, multiple choice, < 1 min, fixed. 4. The car is magnetic; with some polarization of the paint, it will be easier for the paint to be attracted to the car. What keeps an inflated balloon from falling down if you rub it against your hair and place it against a wall? Holt SF 17Rev 03 23:01, highSchool, numeric, > 1 min, wordingvariable. 1. Rubbing leaves a balloon electrically charged; the charged balloon polarizes the wall. A negatively charged balloon has 3.5 µC of charge. How many excess electrons are on this balloon? 2. Rubbing distorts the atoms inside the ballon and polarizes it. 3. When you rub the balloon against your hair, the balloon may have some oil attached to it, which can be sticky. 4. When you rub the balloon against your hair, it will remove some mass from the balloon and make it lighter. 5. Rubbing polarizes the air inside of the balloon. Holt SF 17Rev 40 23:01, highSchool, numeric, > 1 min, wordingvariable. Calculate the net charge on a substance consisting of a combination of 7.0 × 1013 protons and 4.0 × 1013 electrons. Holt SF 17Rev 42 23:01, highSchool, numeric, > 1 min, wordingvariable. Hewitt CP9 22 E32 23:01, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 One gram of copper has 9.48 × 1021 atoms, and each copper atom has 29 electrons. a) How many electrons are contained in 2.00 g of copper? When the chassis of a car is moved into a painting chamber, a mist of paint is sprayed around the chassis. When the car is given a sudden electric charge, the mist is attracted to it, and the car is quickly and uniformly Part 2 of 2 b) What is the total charge of these electrons? Chapter 23, section 2, Quantized Charge Hewitt CP9 22 E31 23:02, highSchool, multiple choice, < 1 min, fixed. How can a charged atom (an ion) attract a neutral atom? 1. The charged atom can hit the neutral atom and make it positively charged or negatively charged. 2. The charged atom can emit x rays to induce ionization of the neutral atom. 3. The charged atom can produce secondary electrons to interact with the neutral atom and make it positively charged or negatively charged. 4. An ion polarizes a nearby neutral atom, so that the part of the atom nearer to the ion acquires a charge opposite to the charge of the ion, and the part of the atom farther from the ion acquires a charge of the same sign as the ion. Holt SF 18Rev 35 23:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A certain moving electron has a kinetic energy of 1.00 × 10−19 J. a) Calculate the speed necessary for the electron to have this energy. Part 2 of 2 b) Calculate the speed of a proton, having a kinetic energy of 1.00 × 10−19 J. 16 Chapter 23, section 3, Insulators and Conductors 17 helps conduct electricity. Conceptual 24 Q01 23:03, highSchool, multiple choice, < 1 min, fixed. Why are metals generally good conductors of electricity? 1. Metals have free electrons in their outer shell. 2. Metals have strong bonding with other atoms. Conceptual 24 Q05 23:03, highSchool, multiple choice, < 1 min, fixed. How can a hole moving through a semiconductor be like an electric charge moving through the same material? 1. If an electron moves into the hole, the hole changes places with the electron. 2. A hole is a location of a proton. 3. Metals have more protons. Conceptual 24 Q02 23:03, highSchool, multiple choice, < 1 min, wording-variable. Conceptual 24 Q10 23:03, highSchool, multiple choice, < 1 min, fixed. How do we normally classify air? Take the point of view of an electron moving among other electrons and atoms in a material. Describe your motion in an insulator. 1. electrical conductor 1. free to move around but will occasionally bump into an atom 3. semiconductor 2. electrical insulator 4. superconductor 2. can move around but with difficulty 3. can move around freely with no limitations Hewitt CP9 22 E26 23:03, highSchool, multiple choice, < 1 min, fixed. 4. bonded to an atom and cannot stray from that location Why are metal-spiked shoes not a good idea for golfers on a stormy day? Conceptual 24 Q03 23:03, highSchool, multiple choice, < 1 min, fixed. 1. The metal spikes can accumulate a net charge. 2. The spikes attract electrical charges. How does salt water conduct electricity? 1. Salt dissolved in water gives out ions, which helps conduct electricity. 2. Salt insreases the density of water, which helps conduct electricity. 3. Salt decreases the density of water, which 3. There might be electrical sparks between the two spikes because they are conductors. 4. The metal spikes provide an effective electrical path from cloud to ground. Hewitt CP9 22 E29 23:03, highSchool, multiple choice, < 1 min, Chapter 23, section 3, Insulators and Conductors fixed. 18 23:03, highSchool, multiple choice, < 1 min, fixed. Why is a good conductor of electricity is also a good conductor of heat? 1. They all carry energies for both electricity and heat. 2. For both electricity and heat, the conduction is via atoms, which in a metal are loosely bound, easy flowing, and easy to start moving. 3. If there is a current through a conductor, there should also be heat produced by resistance. 4. Because both a good conductor for heat and a good conductor for electricity don’t have bound electrons in them. 5. For both electricity and heat, the conduction is via electrons, which in a metal are loosely bound, easy flowing, and easy to start moving. Hewitt CP9 22 E37 23:03, highSchool, multiple choice, < 1 min, fixed. Suppose that a metal file cabinet is charged. How will the charge concentration at the corners of the cabinet compare with the charge concentration on the flat parts of the cabinet? 1. Higher than the concentration at the flat parts. 2. Lower than the concentration at the flat parts. 3. Equal everywhere 4. More information is needed. A neutral ball is suspended by a string. A positively charged insulating rod is placed near the ball, which is observed to be attracted to the rod. This is because 1. the ball becomes positively charged by induction. 2. the ball becomes negatively charged by induction. 3. the number of electrons in the ball is greater than in the rod. 4. the string is not a perfect conductor. 5. there is a rearrangement of the electrons in the ball. Inside a Sphere 23:03, highSchool, multiple choice, < 1 min, fixed. Imagine a charge in the center of a conducting, hollow sphere. There is no net charge on the sphere, and the sphere is not connected to ground. q What will happen if the charge is moved a little away from the center? 1. The charge will return to the center. 2. The charge will remain stationary. 3. The charge will move away from the center. 5. None of these Induced Metal Ball 4. All of these can happen, depending on the size of the charge. Chapter 23, section 3, Insulators and Conductors 5. There is not enough information to tell. Inside Parallel Plates 23:03, highSchool, multiple choice, > 1 min, fixed. Imagine a charge in the middle between two parallel plate conductors. There is no net charge on the plates, and the plates are not connected to ground. q What will happen if the charge is moved a little away from the middle? 1. The charge will return to the middle. 2. The charge will remain stationary. 3. The charge will move away from the middle. 4. All of these can happen, depending on the size of the charge. 5. There is not enough information to tell. 19 Chapter 23, section 4, Induced Charge: the Electroscope Charging Two Metal Balls 23:04, highSchool, multiple choice, > 1 min, wording-variable. Two uncharged metal balls, X and Z, stand on insulating glass rods. A third ball, carrying a negative charge, is brought near the ball Z as shown in the figure. A conducting wire is then run between X and Z and then removed. Finally the third ball is removed. conducting wire − Z X When all this is finished 1. ball X is negative and ball Z is positive. 2. ball X is positive and ball Z is negative. 3. balls X and Z are both positive, but ball X carries more charge than ball Z. 4. balls X and Z are both negative. 5. balls X and Z are still uncharged. 6. ball X is neutral and ball Z is positive. 7. ball X is neutral and ball Z is negative. 8. ball X is positive and ball Z is neutral. 9. ball X is negative and ball Z is neutral. 10. balls X and Z are both positive, but ball Z carries more charge than ball X. Hewitt CP9 22 E08 23:04, highSchool, multiple choice, < 1 min, fixed. An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil pro- 20 tected from air disturbance in a jar. When the ball is touched by a charged body, the leaves that normally hang straight down, spread apart. Why? 1. The charge transfers to the leaves through the metal ball. Since the leaves have identical charges, they are pushed away from each other. 2. The charge transfers to the leaves through the glass. Since the leaves have different charges, they are pushed away from each other. 3. The charge transfers to the leaves through the metal ball. Since the leaves have different charges, they are pushed away from each other. 4. The charge transfers to the two leaves through the glass. Since the leaves have identical charges, they are pushed away from each other. 5. None of these Hewitt CP9 22 E09 23:04, highSchool, multiple choice, < 1 min, fixed. The leaves of a charged electroscope collapse in time. At higher altitudes they collapse more rapidly. Why is this true? 1. Cosmic rays have higher ionization capability at higher altitudes in air, allowing for easier discharge. 2. Cosmic rays ionize more air at lower altitudes. 3. Cosmic rays hit the leaves and knock the electrical charges off the leaves. 4. There is less air at higher altitudes. Chapter 23, section 4, Induced Charge: the Electroscope 21 5. Colder temperatures exist at higher altitudes. 23:04, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 22 E10 23:04, highSchool, multiple choice, < 1 min, fixed. When one material is rubbed against another, electrons jump readily from one to the other. Why don’t protons do that? Is it necessary for a charged body to actually touch the ball of the electroscope for the leaves to diverge? 1. Yes; charged particles transfer to the ball only with contact. 2. No; the charged particles will attract or push electrons out of the ball. 1. Electrons can attract each other while protons repel each other. 2. Electrons are much lighter than protons. 3. Electrons are much heavier than protons. 3. Yes; particles can’t move through the air. 4. Electrons are easily dislodged from the outer regions of atoms, but protons are held tightly within the nucleus. 4. No; the charged particles will move through the air. 5. Electrons travel at the speed of light while protons move very slowly. 5. None of these Hewitt CP9 22 E14 23:04, highSchool, multiple choice, < 1 min, fixed. Can an object be charged negatively with the help of a positively charged object? 1. Yes, by bringing the positively-charged object near the object to be charged, then discharging the far side 2. Yes, by bringing the positively-charged object near the object to be charged, then discharging the near side 3. Yes, by rubbing the two objects together 4. Yes, by letting the two objects touch each other 5. No; negative charges can only be obtained with other negatively charged objects. Hewitt CP9 22 E16 Chapter 23, section 5, Coulomb’s Law Charges on Spheres 01 23:05, highSchool, numeric, > 1 min, normal. 22 4. F = 5/2 F 5. F = 5/4 F Part 1 of 2 Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.108 N when separated by 0.5 m. Initial ++ ++ − − The spheres are suddenly connected by a thin conducting wire, which is then removed. Connected + + Now the spheres repel each other with a force of 0.036 N. Final + + What is the magnitude of the positive charge? Part 2 of 2 What is the negative charge? 6. F = 25 F 7. F = 50 F 8. F = 100 F 9. F = 25/2 F 10. F = 25/4 F Conceptual 16 01 23:05, highSchool, multiple choice, > 1 min, fixed. Based on electric charges and separations, which of the following atomic bonds is strongest? (You are interested only in the relative strengths, which depend only on the relative charges and distances.) 1. A +1 sodium atom separated by 2.0 distance units from a −1 chlorine atom in table salt 2. A +1 hydrogen atom separated by 1.0 distance units from a −2 oxygen atom in table salt Compare two coulomb forces 23:05, highSchool, multiple choice, < 1 min, fixed. 3. A +4 sodium atom separated by 1.5 distance units from a −2 oxygen atom in table salt Two charges q1 and q2 are separated by a distance d and exert a force F on each other. What is the new force F , if charge 1 is increased to q1 = 5 q , charge 2 is decreased to q2 = q2 /2, and the distance is decreased to d = d/2? Choose one Conceptual 16 02 23:05, highSchool, numeric, > 1 min, normal. 1. F = 5 F Part 1 of 3 Assume that in interstellar space the distance between two electrons is about 0.1 cm. The electric force between the two electrons is 2. F = 10 F 1. attractive. 3. F = 20 F 2. repulsive. Chapter 23, section 5, Coulomb’s Law Part 2 of 3 Calculate the electric force between these two electrons. Part 3 of 3 Calculate the gravitational force between these two electrons. Conceptual 16 03 23:05, highSchool, numeric, > 1 min, normal. Part 1 of 3 Assume that in interstellar space the distance between two protons is about 0.1 cm. The electric force between the two protons is 1. attractive 2. repulsive Part 2 of 3 Calculate the electric force between these two protons. 23 Assume that you have two objects, one with mass of 10 kg and the other with a mass of 15 kg, each with a charge of −0.03 C and separated by a distance of 2 meters, What is the electric force that these objects exert on one another? Part 2 of 2 What is the gravitational force between them? Conceptual 16 Q14 23:05, highSchool, multiple choice, < 1 min, fixed. Object A and object B are initially uncharged and are separated by a distance of 1 meter. Suppose 10,000 electrons are removed from object A and placed on object B, creating an attractive force between A and B. An additional 10,000 electrons are removed from A and placed on B and the objects are moved so that the distance between them increases to 2 meters. By what factor does the electric force between them change? Part 3 of 3 Calculate the gravitational force between these two protons. 1. Doubles Conceptual 16 04 23:05, highSchool, numeric, > 1 min, normal. 3. Quadruples 2. Triples 4. Halves Part 1 of 2 Assume that you have two objects, one with a mass of 10 kg and the other with a mass of 15 kg, each with a charge of −0.03 C and separated by a distance of 2 m. What is the electric force that these objects exert on one another? Conceptual Q16 02 23:05, highSchool, numeric, < 1 min, wordingvariable. Part 2 of 2 What is the gravitational force between them? If you triple the distance between two charged objects, by what factor is the electric force affected? Conceptual 16 4 23:05, highSchool, numeric, > 1 min, fixed. Conceptual Q16 03 23:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 5. No change Chapter 23, section 5, Coulomb’s Law If you double the charge on one of two charged objects, how does the force between them change? 24 7. − + + 8. − + + 9. − + + Conceptual Q16 04 23:05, highSchool, multiple choice, < 1 min, wording-variable. 10. − + + Three small spheres carry equal amounts of electric charge. They are equally spaced and lie along the same line. Conceptual Q16 13 23:05, highSchool, multiple choice, < 1 min, fixed. 1. Double 2. Quadruple 3. Triple 4. Halve 5. Does not change − + + What is the direction of the net electric force on each charge due to the other charge? 1. − + + Part 1 of 2 Object A and object B are initially uncharged and separated by a distance of 2 meters. Suppose 10,000 electrons are removed from object A and placed on object B, creating an electric force between A and B. The electric force is 1. repulsive. 2. − + + 2. attractive. 3. zero. 3. − + + 4. − + + 5. 6. − − + + Part 2 of 2 An additional 10,000 electrons are removed from A and placed on B. By what factor does the electric force change? + Conceptual Q16 20 23:05, highSchool, multiple choice, < 1 min, fixed. + A charge of +1 coulomb is place at the 0cm mark of a meter stick. A charge of −1 coulomb is placed at the 100-cm mark of the Chapter 23, section 5, Coulomb’s Law same meter stick. Is it possible to place a proton somewhere on the meter stick so that the net force on it due to the two charges is 0? 1. Yes; to the right of the 50-cm mark 2. Yes; to the left of the 50-cm mark 3. No 25 difficult to remove the inner electrons? 1. The inner electrons are stuck on the nucleus. 2. The outer electrons feel no force. 3. For the outer electrons, the attractive force of the nucleus is largely canceled by the repulsive force of the inner electrons. Conceptual Q16 21 23:05, highSchool, numeric, < 1 min, fixed. 4. No processes can affect the inner electrons. A charge of +1 coulomb is place at the 0cm mark of a meter stick. A charge of +4 coulombs is placed at the 100-cm mark of the same meter stick. Where should a proton be placed on the meter stick so that the net force on it due to the two charges is 0? 5. The outer electrons are always free electrons. Hewitt CP9 22 E01 23:05, highSchool, multiple choice, < 1 min, fixed. We do not feel the gravitational forces between ourselves and the objects around us because these forces are extremely small. Why don’t we usually feel electrical forces? Hewitt CP9 22 E19 23:05, highSchool, multiple choice, < 1 min, fixed. How does the magnitude of the electrical force between a pair of charged objects change when the objects are moved twice as far apart? 1. doubles 2. quadruples 3. Reduces to one quarter of original value 1. The force is small. 4. Reduces to one half of original value 2. We have the same number of positively charged particles and negatively charged particles in our bodies. 3. Electrical force cannot be felt. 4. Gravitational forces overwhelm the electric forces. Hewitt CP9 22 E15 23:05, highSchool, multiple choice, < 1 min, fixed. 5. Doesn’t change Hewitt CP9 22 E20 23:05, highSchool, multiple choice, < 1 min, fixed. How does the magnitude of the electrical force between change a pair of charged particles when they are brought to half their original distance of separation? 1. doubles Why is it relatively easy to strip the outer electrons from a heavy atom like uranium (which then becomes a uranium ion), but very 2. quadruples Chapter 23, section 5, Coulomb’s Law 26 3. Reduces to one quarter of original value 4. Reduces to one half of original value Hewitt CP9 22 E34 23:05, highSchool, multiple choice, < 1 min, fixed. 5. Doesn’t change Hewitt CP9 22 E22 23:05, highSchool, multiple choice, < 1 min, fixed. Two equal charges exert equal forces on each other. What if one charge has twice the magnitude of the other? 1. The bigger charge will exert a force twice as strong. 2. The bigger charge will exert a force four times as strong. 3. The smaller charge will exert a force twice as strong. Consider two charged plates with the same net charge on each. Imagine a proton at rest a certain distance from a negatively charged plate; after being released it collides with the plate. Then imagine an electron at rest the same distance from a positively charged plate. In which case will the moving particle have the greater speed when the collision occurs? 1. The proton and the electron will have the same speed on impact. 2. The proton will have the greater speed on impact. 3. The electron will have the greater speed on impact. 4. It cannot be determined. 4. The smaller charge will exert a force four times as strong. Hewitt CP9 22 P01 23:05, highSchool, numeric, > 1 min, normal. 5. The forces will be equal. Hewitt CP9 22 E33 23:05, highSchool, multiple choice, < 1 min, fixed. If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? 1. Equal in magnitude and direction 2. Different in both magnitude and direction 3. In the same direction but not equal in magnitude 4. Equal in magnitude, but opposite in direction 5. Comparison is not possible. Part 1 of 2 Two point charges are separated by 6 cm, with an attractive force between them of 20 N. Find the force between them when they are separated by 12 cm. The Coulomb constant is 8.99 × 109 N · m2 /C2 . Part 2 of 2 If the two charges have equal magnitude, what is the magnitude of each charge for the original force of 20 N? Hewitt CP9 22 P02 23:05, highSchool, numeric, > 1 min, normal. Part 1 of 2 Two pellets, each with a charge of 1 × 10−6 C, are located 0.03 m apart. The Coulomb constant is 8.99 × 10−9 N · m2 /C2 and the universal gravitational constant is 6.67259 × 10−11 m3 /kg · s2 . Chapter 23, section 5, Coulomb’s Law What is the electric force between the pellets? Part 2 of 2 What mass would experience this same force in the Earth’s gravitational field? Hewitt CP9 22 P04 23:05, highSchool, numeric, > 1 min, normal. Part 1 of 3 Atomic physicists usually ignore the effect of gravity within an atom. To see why, we may calculate and compare the magnitude of the ratio of the electrical force and gravitational Fe between an electron and a proton force Fg separated by a distance of 1 m. The Coulomb constant is 8.98755 × 9 10 N · m2 /C2 , the gravitational constant is 6.67259 × 10−11 m3 /kg · s2 , the mass of a proton is 1.67262 × 10−27 kg, the mass of an electron is 9.10939 × 10−31 kg, the charge on a proton is 1.602 × 10−19 C, and the charge on an electron is −1.602 × 10−19 C. What is the magnitude of the electrical force? Part 2 of 3 What is the magnitude of the gravitational force? Part 3 of 3 What is the ratio of the magnitude of the electrical force to the magnitude of the gravitational force? Hewitt CP9 22 R02 23:05, highSchool, multiple choice, < 1 min, fixed. Why does the gravitational force between the Earth and moon predominate over electric forces? 1. Because the masses of the Earth and moon are very large. 2. Because both the Earth and the moon are 27 electrically neutral. 3. Because the distance between the Earth and the moon is very large. 4. Because there is no electric charge on the moon. Hewitt CP9 22 R11 23:05, highSchool, multiple choice, < 1 min, fixed. How is Coulomb’s law similar to Newton’s law of gravitation? How is it different? 1. Both forces vary inversely as the square of the separation distance between the two objects; electrical forces may be either attractive or repulsive, whereas gravitational forces are only attractive. 2. Both forces are proportional to the product of the mass of the two objects; electrical forces may be either attractive or repulsive, whereas gravitational forces are only attractive. 3. Both forces are proportional to the same constant; electrical forces are only present on earth, whereas gravitational forces exist everywhere. 4. Both forces vary inversely as the square of the separation distance between the two objects; electrical forces are only present on earth, whereas gravitational forces can exist everywhere. 5. Both forces are proportional to the product of the masses of the two objects; electrical forces are only present on earth, whereas gravitational forces exist everywhere. 6. Both forces proportional to the same constant; electrical forces may be either attractive or repulsive, whereas gravitational forces are only attractive. Holt SF 17A 01 Chapter 23, section 5, Coulomb’s Law 23:05, highSchool, numeric, < 1 min, wordingvariable. A balloon rubbed against denim gains a charge of −8.0 µC. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . What is the electric force between the balloon and the denim when the two are separated by a distance of 5.0 cm? (Assume that the charges are located at a point.) Holt SF 17A 02 23:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Two identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of +12 × 10−9 C and the other is given a charge of −18 × 10−9 C. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . a) Find the electric force exerted on one sphere by the other. Part 2 of 2 The spheres are connected by a conducting wire. b) After equilibrium has occurred, find the electric force between the two spheres. Holt SF 17A 03 23:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A small cork with an excess charge of +6.0 µC is placed 0.12 m from another cork, which carries a charge of −4.3 µC. The Coulomb constant is 8.98755 × 9 10 N · m2 /C2 . a) What is the magnitude of the electric force between the corks? Part 2 of 4 b) Is this force attractive or repulsive? 1. attractive 28 2. repulsive 3. Unable to determine Part 3 of 4 c) How many excess electrons are on the negative cork? Part 4 of 4 d) How many electrons has the positive cork lost? Holt SF 17A 04 23:05, highSchool, numeric, > 1 min, wordingvariable. Two electrostatic point charges of +60.0 µC and +50.0 µC exert a repulsive force on each other of 175 N. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . What is the distance between the two charges? Holt SF 17B 01 23:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Three point charges, q1 = +6.0 µC, q2 = +1.5 µC, and q3 = −2.0 µC, lie along the x-axis at x = 0 cm, x = 3.0 cm, and x = 5.0 cm, respectively. The Coulomb constant is 8.99 × 109 N · m2 /C2 . a) What is the force exerted on q1 by the other two charges? (To the right is positive.) Part 2 of 3 b) What is the force exerted on q2 by the other two charges? (To the right is positive.) Part 3 of 3 c) What is the force exerted on q3 by the other two charges? (To the right is positive.) Holt SF 17B 02 23:05, highSchool, numeric, > 1 min, wording- Chapter 23, section 5, Coulomb’s Law variable. Part 1 of 6 Four charged particles are placed so that each particle is at the corner of a square. The sides of the square are 15 cm. The charge at the upper left corner is +3.0 µC, the charge at the upper right corner is −6.0 µC, the charge at the lower left corner is −2.4 µC, and the charge at the lower right corner is −9.0 µC. The Coulomb constant is 8.98755 × 9 10 N · m2 /C2 . a) What is the magnitude of the net electric force on the +3.0 µC charge? Part 2 of 6 b) What is the direction of this force (measured from the positive x-axis as an angle between −180◦ and 180◦ , with counterclockwise positive)? Part 3 of 6 c) What is the magnitude of the net electric force on the −6.0 µC charge? Part 4 of 6 d) What is the direction of this force (measured from the positive x-axis, with counterclockwise positive)? 29 Find the point (coordinate) between these two charges where a charge of +3.00 × 10−9 C should be placed so that the net electric force on it is zero. Holt SF 17C 02 23:05, highSchool, numeric, > 1 min, wordingvariable. A charge q1 of −5.00 × 10−9 C and a charge q2 of −2.00 × 10−9 C are separated by a distance of 40.0 cm. Find the equilibrium position for a third charge of +15.0 × 10−9 C by identifying its distance from q1 . Holt SF 17C 03 23:05, highSchool, numeric, > 1 min, fixed. An electron is released above the Earth’s surface. A second electron directly below it exerts just enough of an electric force on the first electron to cancel the gravitational force on it. The Coulomb constant is 8.98755 × 109 N · m2 /C2 and the acceleration of gravity is 9.81 m/s2 . Find the distance between the two electrons. Part 5 of 6 e) What is the magnitude of the net electric force on the −9.0 µC charge? 1. 5.07424 cm Part 6 of 6 f) What is the direction of this force (as an angle between −180◦ and 180◦ measured from the positive x-axis, with counterclockwise positive)? 3. 5.07424 km Holt SF 17C 01 23:05, highSchool, numeric, > 1 min, wordingvariable. A charge of +2.00 × 10−9 C is placed at the origin, and another charge of +4.00 × 10−9 C is placed at x = 1.5 m. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . 2. 5.07424 m 4. 50.7424 m 5. 0.507424 m Holt SF 17Rev 18 23:05, highSchool, numeric, > 1 min, fixed. At the point of fission, a nucleus of 235 U that has 92 protons is divided into two smaller spheres, each of which has 46 protons and a radius of 5.9 × 10−15 m. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . Chapter 23, section 5, Coulomb’s Law What is the magnitude of the repulsive force pushing these two spheres apart? 1. 4.75067 × 10 20 N /C 30 6. 94.359 N, attractive Holt SF 17Rev 21 23:05, highSchool, numeric, > 1 min, wordingvariable. 2. 3496.5 N 4. 4.12586 × 10−11 N · m 5. None of these 6. Unable to determine Holt SF 17Rev 19 23:05, highSchool, numeric, > 1 min, wordingvariable. What is the electric force between a glass ball that has +2.5 µC of charge and a rubber ball that has −5.0 µC of charge when they are separated by a distance of 5.0 cm? The Coulomb constant is 8.98755 × 109 N · m2 /C2 . Holt SF 17Rev 20 23:05, highSchool, numeric, > 1 min, wordingvariable. An alpha particle (charge = +2.0 e) is sent at high speed toward a gold nucleus (charge = +79 e). The Coulomb constant is 8.99 × 109 N · m2 /C2 . What is the electric force acting on the alpha particle when the alpha particle is 2.0 × 10−14 m from the gold nucleus? 1. 94.359 N, repulsive 2. 90.9069 N, repulsive 3. 90.9069 N, attractive 4. None of these 5. Unable to determine 3 nC + 1m N · m /C Part 1 of 2 Three positive point charges are arranged in a triangular pattern in a plane, as shown below. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . 1m 3. 4.02599 × 10 34 1m + 6 nC + 2 nC Find the magnitude of the net electric force on the 6 nC charge. Part 2 of 2 b) What is the direction of this force (measured from the positive x-axis as an angle between −180◦ and 180◦ , with counterclockwise positive)? Holt SF 17Rev 22 23:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Two positive point charges, each of which has a charge of 2.5 × 10−9 C, are located at y = +0.50 m and y = −0.50 m. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . a) Find the magnitude of the resultant electrical force on a charge of 3.0 × 10−9 C located at x = 0.70 m. Part 2 of 2 b) What is the direction of this force (measured from the positive x-axis as an angle be- Chapter 23, section 5, Coulomb’s Law tween −180◦ and 180◦ , with counterclockwise positive)? 31 tity of charge that would have to be placed on each to produce the required force. Holt SF 17Rev 23 23:05, highSchool, numeric, > 1 min, wordingvariable. 1. 6.71571 × 1013 C Three point charges lie in a straight line along the y -axis. A charge of q1 = −9.0 µC is at y = 6.0 m, and a charge of q2 = −8.0 µC is at y = −4.0 m. The net electric force on the third point charge is zero. Where along the y −axis is this charge located? 3. 4.71571 × 1013 C Holt SF 17Rev 24 23:05, highSchool, numeric, > 1 min, wordingvariable. A charge of +3.5 nC and a charge of +5.0 nC are separated by 40.0 cm. Find the equilibrium position for a −6.0 nC charge as a distance from the first charge. Holt SF 17Rev 45 23:05, highSchool, numeric, > 1 min, wordingvariable. 1.0 g of hydrogen contains 6.02 × 1023 atoms, each with one electron and one proton. Suppose that 1 g of hydrogen is separated into protons and electrons, that the protons are placed at Earth’s north pole, and that the electrons are placed at Earth’s south pole. Find the magnitude of the resulting compressional force on Earth. (The radius of Earth is approximately 6.38 × 106 m.) Holt SF 17Rev 47 23:05, highSchool, numeric, > 1 min, fixed. The moon (m = 7.36 × 1022 kg) is bound to Earth (m = 5.98 × 1024 kg) by gravity. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quan- 2. 5.71649 × 1013 C 4. 5.71649 × 1014 C 5. 5.71649 × 1012 C Holt SF 17Rev 48 23:05, highSchool, numeric, > 1 min, wordingvariable. Two small metallic spheres, each with a mass of 0.200 g, are suspended as pendulums by light strings from a common point. They are given the same electric charge, and the two come to equilibrium when each string is at an angle of 5.0◦ with the vertical. The Coulomb constant is 8.98755 × 109 N · m2 /C2 , and the acceleration of gravity is 9.81 m/s2 . If each string is 30.0 cm long, what is the magnitude of the charge on each sphere? Holt SF 17Rev 59 23:05, highSchool, numeric, > 1 min, wordingvariable. Three identical point charges hang from three strings, as shown. The Coulomb constant is 8.98755 × 109 N · m2 /C2 , and the acceleration of gravity is 9.81 m/s2 . Chapter 23, section 5, Coulomb’s Law 45◦ 45◦ 30.0 cm +q + 0.10 kg 30.0 cm +q +q + 0.10 kg Fg + 0.10 kg What is the value of q ? Holt SF 17Rev 63 23:05, highSchool, numeric, > 1 min, wordingvariable. A DNA molecule (deoxyribonucleic acid) is 2.17 µm long. The ends of the molecule become singly ionized so that there is −1.60 × 10−19 C on one end and +1.60 × 10−19 C on the other. The helical molecule acts as a spring and compresses 1.00 percent upon becoming charged. The value of Coulomb’s constant is 8.98755 × 109 N · m2 /C2 and the acceleration of gravity is 9.8 m/s2 . Find the effective spring constant of the molecule. Magnitude of Force 23:05, highSchool, numeric, > 1 min, normal. There are two identical small metal spheres with charges 33 µC and −26.4 µC. The distance between them is 5 cm. The spheres are placed in contact then set at their original distance. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . Calculate the magnitude of the force between the two spheres at the final position. 32 Chapter 23, section 7, The Electric Field AlF 3 23:07, highSchool, multiple choice, > 1 min, fixed. Part 1 of 6 A conceptual model of aluminum triflouride (AlF3 ) is approximately a square with charges at the corners. QA = 3 q Q B = −q 2. EC 3. EC 4. EC 5. EC a Q D = −q 7. EC Q C = −q The magnitude of the electric field EO at the center O is given by √ kq 2 2. a √ kq = 2 2. a √ kq =2 2 2 . a kq = 2. a 1 kq . =√ 2 a2 4kq = 2. a 1 kq . =√ 4 2 a2 kq =3 2 . a 8kq = 2. a 1 kq =√ . 3 2 a2 √ kq 2 2. a √ kq = 2 2. a √ kq =2 2 2 . a 3√ kq = −2 . 2 a2 3 kq . = 2 a2 9 kq . = 4 a2 √ kq = 3− 2 . a2 kq =3 2 . a √ kq =3 2 2 . a 1 kq =√ . 3 2 a2 1. EC = 4 6. EC O 33 8. EC 9. EC 1. EO = 4 10. EC 2. EO Part 3 of 6 Determine the absolute value of tan α, where α is the angle between the horizontal and the electric field at C due to the three charges at A, B , and D. √ 2 2−1 1. | tan α| = √ 2 2+1 √ 2. | tan α| = 2 2 − 1 √ 3. | tan α| = 2 2 + 1 √ 2 2+1 4. | tan α| = √ 2 2−1 1 5. | tan α| = √ 2 2−1 √ 6. | tan α| = 2 3. EO 4. EO 5. EO 6. EO 7. EO 8. EO 9. EO 10. EO Part 2 of 6 The magnitude of the electric field EC at C due to the 3 charges at A, B , and D is given by 1 7. | tan α| = √ 2 8. | tan α| = 2 √ 9. | tan α| = 1 √ 10. | tan α| = 3 1 2+1 Chapter 23, section 7, The Electric Field a Part 4 of 6 Consider charges in a square again, but this time with a different assignment of charges (shown in the figure below). QA = q QB = q O QD = q 2. EO 3. EO 4. EO 5. EO 6. EO 7. EO 8. EO 9. EO 10. EO Q C = −q kq =4 2 a √ kq =22 a √ kq =2 2 2 a kq =2 a 1 kq =√ 2 a2 1 kq =√ 5 2 a2 1 kq =√ 4 2 a2 kq =3 2 a √ kq =3 2 2 a 1 kq =√ 3 2 a2 Part 5 of 6 Find the electric field EC at C due to the 3 charges at A, B , and D for the setup in the previous Part. kq a2 √ kq 2. EC = 2 2 a kq 3. EC = 2 2 a 1. EC = 4 5. EC = kq a2 √ 2+ 1 2 kq a2 5 kq 2 a2 7 kq =√ 4 2 a2 kq =3 2 a √ kq =3 2 2 a 1 kq =√ 3 2 a2 6. EC = 7. EC 8. EC Find EO at O . 1. EO 4. EC = 34 9. EC 10. EC Part 6 of 6 Again, determine tan α, where α as the angle between the horizontal and the electric field at C due to the three charges at A, B , and D. √ 2 2−1 1. tan α = √ 2 2+1 √ 2. tan α = 2 2 − 1 √ 3. tan α = 2 2 + 1 √ 2 2+1 4. tan α = √ 2 2−1 1 5. tan α = √ 2 2−1 √ 6. tan α = 2 1 7. tan α = √ 2 8. tan α = 2 √ 1 2+1 9. tan α = 1 √ 10. tan α = 3 Conceptual 17 01 23:07, highSchool, numeric, > 1 min, normal. Part 1 of 4 The electric field at a point in space is defined as the force per unit charge at that Chapter 23, section 7, The Electric Field point in space. We can write the electric field E of a charge q at a distance d from that charge, experienced by a charge Q, as F q E= =k 2 Q d The electric field has a direction such that it points toward negative charges and points away from positive charges. Suppose your rub a balloon in your hair and it acquires a static charge of 3 × 10−9 C. What is the strength of the electric field created by the balloon at a location 1 m due north of the balloon? Part 2 of 4 What is the direction of that electric field? 1. south 35 6. upward Conceptual Q16 08 23:07, highSchool, multiple choice, > 1 min, wording-variable. Two small spheres carry equal amounts of electric charge. There are equally spaced points (a , b , and c) which lie along the same line. − − a c b What is the direction of the net electric field at each point due to these charges? 1. a − b − c a − b − c a − b − c a − b − c a − b − c a − b − c a − b − c a − b − c 2. north 3. east 2. 4. west 5. downward 3. 6. upward Part 3 of 4 You hair acquired an equal amount of positive charge when you rubbed the balloon on your head. What is the strength of the electric field created by your head, at the location of your feet, 1.5 meters below? 4. Part 4 of 4 What is the direction of that electric field? 6. 1. south 5. 7. 2. north 3. east 4. west 5. downward 8. Chapter 23, section 7, The Electric Field 9. 10. a − a − b − b − c c Part 1 of 2 Two charged particles of equal magnitude (+Q and −Q) are fixed at opposite corners of a square that lies in a plane (see figure below). A test charge −q is placed at a third corner. +Q −q −Q What is the direction of the force on the test charge due to the two other charges? 2. 3. 4. 5. 6. 7. 8. Part 2 of 2 Let the side of the square be a. What is the magnitude of the electric field at the location of −q due to the two charges: +Q and −Q. 1. 0 Force and Field 23:07, highSchool, multiple choice, > 1 min, wording-variable. 1. 36 kQ a2 √ kQ 3. 2 2 a √ kQ 4. 3 2 a kQ 5. 2 2 a kqQ 6. 2 2 a kQ 7. a √ kQ 8. 2 a √ kQ 9. 3 a kQ 10. 2 a 2. Hewitt CP9 22 E28 23:07, highSchool, multiple choice, < 1 min, fixed. If a large enough electric field is applied, even an insulator will conduct an electric current, as is evident in lightning discharges through the air. Explain how this happens, taking into account the opposite charges in an atom and how ionization occurs. 1. The insulator itself can produce an electric field under the influence of strong external electric field. 2. A neutral atom in an electric field is electrically distorted; if the field is strong enough, ionization occurs with charges being torn from each other. The ions then provide a conducting path for an electric current. Chapter 23, section 7, The Electric Field 3. If the field is strong enough, all the electrons in an insulator will become free, causing an electric current. 4. If the field is strong enough, air around the insulator would be ionized. The ionized particles can hit the insulator to change it into a conductor. 5. If the field is strong enough, the protons in a neutral atom will become neutrons. Hewitt CP9 22 P03 23:07, highSchool, numeric, > 1 min, normal. Part 1 of 2 Usually the force of gravity on electrons is neglected. To see why, we can compare the force of the Earth’s gravity on an electron with the force exerted on the electron by an electric field of magnitude of 10000 V/m (a relatively small field). The acceleration of gravity is 9.8 m/s2 , the mass of an electron is 9.10939 × 10−31 kg, and the charge on an electron is −1.602 × 10−19 C. What is the force exerted on the electron by an electric field of magnitude of 10000 V/m? Part 2 of 2 What is the force of the Earth’s gravity on the electron? Hewitt CP9 22 P05 23:07, highSchool, numeric, > 1 min, normal. A droplet of ink in an industrial ink-jet printer carries a charge of 1 × 10−10 C and is deflected onto paper by a force of 0.0003 N. Find the strength of the electric field to produce this force. Hewitt CP9 22 P08 23:07, highSchool, numeric, > 1 min, normal. Part 1 of 2 In 1909 Robert Millikan was the first to find the charge of an electron in his now-famous oil drop experiment. In the experiment tiny oil drops are sprayed into a uniform electric 37 field between a horizontal pair of oppositely charged plates. The drops are observed with a magnifying eyepiece, and the electric field is adjusted so that the upward force q E on some negatively charged oil drops is just sufficient to balance the downward force m g of gravity. Millikan accurately measured the charges on many oil drops and found the values to be whole-number multiples of 1.6 × 10−19 C — the charge of the electron. For this he won the Nobel Prize. The acceleration of gravity is 9.8 m/s2 . If a drop of mass 6.53061 × 10−15 kg remains stationary in an electric field of 100000 N/C, what is the charge on this drop? Part 2 of 2 How many extra electrons are on this particular oil drop (given the presently known charge of the electron)? Holt SF 17D 01 23:07, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A charge of 5.00 µC is at the origin and a second charge of −3.00 µC is on the positive x-axis 0.800 m from the origin. The Coulomb constant is 8.99 × 109 N · m2 /C2 . Find the magnitude of the electric field at a point P on the y -axis 0.500 m from the origin. Part 2 of 2 Determine the direction of this electric field (as an angle between −180◦ and 180◦ measured from the positive x-axis, with counterclockwise positive). Holt SF 17D 02 23:07, highSchool, numeric, > 1 min, fixed. A proton and an electron in a hydrogen atom are separated on the average by about 5.3 × 10−11 m. The Coulomb constant is 8.99 × 109 N · m2 /C2 . What is the magnitude and direction of Chapter 23, section 7, The Electric Field the electric field set up by the proton at the position of the electron? 1. 5.12068 × 1011 N/C away from the proton 2. 5.12068 × 1011 N/C toward the proton 3. 8.19309 × 10−8 N/C away from the proton 4. 8.19309 × 10−8 N/C toward the proton 5. 27.1396 N/C away from the proton 6. 27.1396 N/C toward the proton Holt SF 17Rev 38 23:07, highSchool, numeric, > 1 min, wordingvariable. Find the magnitude electric field at a point midway between two charges +30.0 × 10−9 C and +60.0 × 10−9 C separated by a distance of 30.0 cm. The Coulomb constant is 8.99 × 9 10 N · m2 /C2 . Holt SF 17Rev 39 23:07, highSchool, numeric, > 1 min, normal. Part 1 of 2 A 2 µC point charge is on the x-axis at x = 3 m , and a 5.7 µC point charge is on the x-axis at x = 1 m . The Coulomb constant is 8.98755 × 9 10 N m2 /C2 . Determine the magnitude of the net electric field at the point on the y -axis where y = 2 m . Part 2 of 2 Determine the direction of this electric field (as an angle between −180◦ and 180◦ measured from the positive x-axis, with counterclockwise positive.) Holt SF 17Rev 43 23:07, highSchool, numeric, > 1 min, normal. Part 1 of 2 38 READ AND DELETE: Comments by Yeung (21217). Solution code forgot to take absolute value. The second part of the problem asks for the magnitude of the force on a test charge but the some of the answers were negative. Consider three charges arranged as shown. The Coulomb constant is 8.99 × 109 N · m2 /C2 . 6 µC 1.5 µC + + 3 cm −2 µC - 2 cm What is the electric field strength at a point 1 cm to the left of the middle charge? Part 2 of 2 What is the magnitude of the force on a 2 µC charge placed at this point? Holt SF 17Rev 44 23:07, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 Consider three charges arranged in a triangle as shown. The Coulomb constant is 8.99 × 109 N · m2 /C2 . y 0.3 m 5.0 nC + + x 6.0 nC 0.1 m −3.0 nC What is the net electric force on the charge at the origin? Chapter 23, section 7, The Electric Field Part 2 of 4 What is the direction of this force (as an angle between −180◦ and +180◦ measured from the positive x-axis, with counterclockwise positive)? of 30.0◦ , 150.0◦ , and 270.0◦ , as shown. The Coulomb constant is 8.99 × 109 N · m2 /C2 . q Part 3 of 4 What is the magnitude of the net electric field at the position of the charge at the origin? Holt SF 17Rev 50 23:07, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Three positive charges are arranged as shown. The Couloumb constant is 8.99 × 9 10 N · m2 /C2 . 0.20 m 6.0 nC + 3.0 nC + + 5.0 nC 150.0◦ + + Part 4 of 4 What is the direction of the net electric field (as an angle between −180◦ and +180◦ measured from the positive x-axis, with counterclockwise positive). 39 q 30.0◦ 270.0◦ + q What is the resultant electric field at the center? 1. 0.0561875 N/C at 90◦ 2. 0 N/C 3. 0.0561875 N/C at 270◦ 4. 22.475 N/C at 90◦ 5. 22.475 N/C at 270◦ 6. 0.112375 N/C at 90◦ 7. 0.112375 N/C at 270◦ 8. None of these 0.60 m Find the magnitude of the electric field at the fourth corner of the rectangle. Holt SF 17Rev 61 23:07, highSchool, multiple choice, > 1 min, normal. Part 2 of 2 What is the direction of this electric field (as an angle between −180 and 180 measured from the positive x-axis, with counterclockwise positive)? In a laboratory experiment, five equal negative point charges are placed symmetrically around the circumference of a circle of radius r, with one at 0◦ . Calculate the electric field at the center of the circle. (Assume right and upward are positive.) Holt SF 17Rev 56 23:07, highSchool, numeric, > 1 min, wordingvariable. Three identical charges (q = +5.0 µC) are along a circle with a radius of 2.0 m at angles 1. kC q at 0◦ r2 2. 0 N/C Chapter 23, section 7, The Electric Field 3. kC 4. kC 5. kC q at 180◦ r2 5q at 180◦ r2 (5q )2 at 0◦ r2 6. Unable to determine 7. None of these Three Conducting Spheres 23:07, highSchool, numeric, < 1 min, normal. Consider three identical conducting spheres of radius 1 cm arranged in an equilateral triangle. 10 cm 4C −1 C 7C If the spheres are all connected by a thin wire, what is the final charge on the lower left-hand sphere? Three Point Charges 14 23:07, highSchool, numeric, > 1 min, normal. Three equal charges of 4 µC are in the x-y plane. One is placed at the origin, another is placed at (0.0, 30 cm), and the last is placed at (15 cm, 0.0). The Coulomb constant is 9 × 109 N m2 /C2 . Calculate the magnitude of the force on the charge at the origin. 40 Chapter 23, section 8, Electric Field Due to a Point Charge Hewitt CP9 22 E24 23:08, highSchool, multiple choice, < 1 min, normal. Suppose that the strength of the electric field about an isolated point charge has a certain value at a distance of 1 m. How will the electric field strength compare at a distance of 2 m from the point charge? 1. At twice the distance the field strength 1 will be of the original value. 4 2. At twice the distance the field strength 1 will be of the original value. 2 3. At twice the distance the field strength 1 will be of the original value. 3 4. At twice the distance the field strength will be the same. 5. At twice the distance the field strength will be twice the original value. Point Charge 02 23:08, highSchool, numeric, > 1 min, normal. The value of the E-field at a distance of 70 m from a point charge is 35 N/C. Its direction is radially in toward the charge. The Coulomb constant is 8.98755 × 109 N · m2 /C2 . Find the magnitude and sign of the point charge at the origin. 41 Chapter 23, section 12, Electric Field Due to a Continuous Charge Distribution Concept 34 E37 23:12, highSchool, multiple choice, < 1 min, fixed. Consider a fusion torch. If a star-hot flame is positioned between a pair of large electrically charged plates (one positive and the other negative) and materials dumped into the flame are dissociated into bare nuclei and electrons, in which direction will the nuclei move? In which direction will the electrons move? 1. both toward the positive plate 2. toward the positive plate; toward the negative plate 3. toward the negative plate; toward the positive plate 4. both toward the negative plate Holt SF 17Rev 53 23:12, highSchool, numeric, > 1 min, wordingvariable. Air becomes a conductor when the electric field strength exceeds 3.00 × 106 N/C. Determine the maximum amount of charge that can be carried by a metal sphere 2.0 m in radius. The value of the Coulomb constant is 8.99 × 109 N · m2 /C2 . 42 Chapter 23, section 13, Electric Field Lines Field Dir by Insp 5 23:13, highSchool, multiple choice, < 1 min, fixed. 43 field Enet is 1. aligned with the negative x-axis. 2. aligned with the negative y -axis. Given rectangular insulators with uniformly charged distributions of equal magnitude as shown in the figure below, find the net electric field at the origin. ++ ++ ++ ++ ++ ++ y 3. aligned with the positive y -axis. 4. aligned with the positive x-axis. 5. non-zero and is not aligned with either the x- or y -axis. x −−−−−− In the figure above, at the origin, the net field Enet is 6. zero and the direction is undefined. Part 2 of 4 y ++++ x 1. aligned with the negative y -axis. 2. aligned with the negative x-axis. 3. aligned with the positive y -axis. ++++ In the figure above, at the origin, the net field Enet is 4. aligned with the positive x-axis. 1. zero and the direction is undefined. 5. non-zero and is not aligned with either the x- or y -axis. 6. zero and the direction is undefined. Field Directions by Inspectio 23:13, highSchool, multiple choice, < 1 min, fixed. Part 1 of 4 Given symmetrically placed rectangular insulators with uniformly charged distributions of equal magnitude as shown in the figures below, find the net electric field at the origin in the figures below. y ++ ++ −− −− x In the figure above, at the origin, the net 2. aligned with the negative x-axis. 3. aligned with the negative y -axis. 4. aligned with the positive y -axis. 5. aligned with the positive x-axis. 6. non-zero and is not aligned with either the x- or y -axis. Part 3 of 4 Chapter 23, section 13, Electric Field Lines 44 6. zero and the direction is undefined. y ++++ Hewitt CP9 22 E35 23:13, highSchool, multiple choice, < 1 min, fixed. x −−−− In the figure above, at the origin, the net field Enet is 1. non-zero and is not aligned with either the x- or y -axis. 2. aligned with the negative x-axis. 3. aligned with the negative y -axis. 4. aligned with the positive y -axis. 5. aligned with the positive x-axis. 6. zero and the direction is undefined. Part 4 of 4 y +++++ + − + − + − + −x + − +++++ In the figure above, at the origin, the net field Enet is 1. aligned with the positive x-axis. 2. aligned with the negative x-axis. 3. aligned with the negative y -axis. 4. aligned with the positive y -axis. 5. non-zero and is not aligned with either the x- or y -axis. A gravitational field vector points toward the Earth; an electric field vector points toward an electron. Why do electric field vectors point away from protons? 1. Protons have much larger mass. 2. Protons are positively charged. 3. Protons have more net charge than electrons. 4. Unlike electrons, protons will produce the electric field of their own. 5. None of these Chapter 23, section 15, A Point Charge in a Electric Field Holt SF 17D 03 23:15, highSchool, numeric, > 1 min, normal. Part 1 of 2 An electric field of 20000 N/C is directed along the positive x-axis. The charge on an electron is −1.6 × 10−19 C. What is the electric force on an electron in this field? 1. 20000 N, along the negative x-axis 2. 20000 N, along the positive x-axis 3. 3.2 × 10−15 N, along the positive x-axis 4. 3.2 × 10 −15 5. 5.12 × 10 10−9 N · m2 /C2 . Find the magnitude of the electric force acting on the electron. Part 2 of 2 What is the magnitude of the electric field strength? Holt SF 17Rev 49 23:15, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 What is the magnitude of the electric field that will balance the weight of an electron? The acceleration of gravity is 9.81 m/s2 . N, along the negative x-axis 1. 5.58496 × 10−11 N/C downward N, along the negative x-axis 2. 5.58496 × 10−11 N/C upward N, along the positive x-axis 3. 1.02576 × 10−7 N/C downward −34 6. 5.12 × 10 45 −34 Part 2 of 2 What is the electric force on a proton in this field? 1. 20000 N, along the negative x-axis 4. 1.02576 × 10−7 N/C upward 5. 5.13158 × 10−8 N/C downward 6. 5.13158 × 10−8 N/C upward 7. None of these 2. 20000 N, along the positive x-axis 3. 3.2 × 10−15 N, along the positive x-axis 4. 3.2 × 10−15 N, along the negative x-axis 5. 5.12 × 10−34 N, along the negative x-axis 6. 5.12 × 10 −34 N, along the positive x-axis Holt SF 17Rev 41 23:15, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An electron moving through an electric field experiences an acceleration of 6300 × 103 m/s2 . The value of the Coulomb constant is 8.99 × 8. Unable to determine Part 2 of 2 What is the magnitude of the electric field that will balance the weight of a proton? 1. 1.02576 × 10−7 N/C upward 2. 1.02576 × 10−7 N/C downward 3. 5.58496 × 10−11 N/C downward 4. 5.58496 × 10−11 N/C upward 5. 5.13158 × 10−8 N/C downward 6. 5.13158 × 10−8 N/C upward Chapter 23, section 15, A Point Charge in a Electric Field 46 7. None of these 8. Unable to determine cm Thunderstorms can have an electric field of up to 3.40 × 105 N/C. What is the magnitude of the electric force on an electron in such a field? .4 10 Holt SF 17Rev 55 23:15, highSchool, numeric, > 1 min, wordingvariable. 9.81 m/s2 11000 N/C 38◦ 2g a) Is the ball’s charge positive or negative? 1. positive 1. 340000 N/C 2. negative 2. 5.44 × 10−14 N 3. Unable to determine 3. 1.088 × 10−13 N 4. 680000 N 5. 1.36 × 10−14 N Holt SF 17Rev 57 23:15, highSchool, numeric, > 1 min, wordingvariable. An object with a net charge of 24 µC is placed in a uniform electric field of 610 N/C, directed vertically. The acceleration of gravity is 9.81 m/s2 . What is the mass of this object if it floats in this electric field? Holt SF 17Rev 60 23:15, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A very small 2 g plastic ball (carrying a charge) is suspended by a 10.4 cm string in a uniform electric field of 11000 N/C, as shown. The acceleration of gravity is 9.81 m/s2 . Part 2 of 2 b) If the ball is in equilibrium when the string makes a 38 ◦ angle with the vertical as indicated, what is the net charge on the ball? Chapter 23, section 17, Motion of Charged Particles in a Uniform Electric Field Holt SF 17Rev 51 23:17, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An electron and a proton are each placed at rest in an external uniform electric field of 520 N/C. The mass of an electron is 9.109 × 10−31 kg and its charge is −1.6 × 10−19 C . a) Calculate the speed of the electron after 48 ns. Part 2 of 2 b) Calculate the speed of the proton after 48 ns. The mass of a proton is 1.673 × 10−27 kg and the charge on a proton is 1.6 × 10−19 C . Holt SF 17Rev 58 23:17, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A proton accelerates from rest in a uniform electric field of 640 N/C. At some time later, its speed is 1.20 × 106 m/s. The mass of a proton is 1.673 × 10−27 kg and the charge of an electron 1.6 × 10−19 C . a) What is the magnitude of the acceleration of the proton? Part 2 of 4 b) How long does it take the proton to reach this speed? Part 3 of 4 c) How far has it moved in this time interval? Part 4 of 4 d) What is its kinetic energy at the later time? Holt SF 17Rev 62 23:17, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 47 If the electric field strength is increased to about 3.0 × 106 N/C, air “breaks down” and loses its insulating quality. Under these conditions, sparking results. The mass of an electron is 9.109 × 10−31 kg and its charge is −1.6 × 10−19 C. a) How large an acceleration does an electron experience when the electron is placed in such an electric field? Part 2 of 3 b) If the electron starts from rest when it is placed in an electric field under these conditions, in what distance does it acquire a speed equal to 9.0 percent of the speed of light? Part 3 of 3 c) How large an acceleration does a proton experience when the proton is placed in such an electric field? The mass of an proton is 1.673 × 10−27 kg and the charge on an proton is 1.6 × 10−19 C. Holt SF 17Rev 64 23:17, highSchool, numeric, > 1 min, wordingvariable. An electron and a proton both start from rest and from the same point in a uniform electric field of 370.0 N/C. How far apart are they 1.00 µs after they are released? Ignore the attraction between the electron and the proton. (Imagine the experiment performed with the proton only, and then repeat with the electron only.) Holt SF 17Rev 65 23:17, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An electron is accelerated by a constant electric field of 300.0 N/C. a) Find the magnitude of the acceleration of the electron. Part 2 of 2 b) Find the electron’s speed after 1.00 × 10−8 s, assuming it starts from rest. Chapter 23, section 17, Motion of Charged Particles in a Uniform Electric Field Holt SF 17Rev 66 23:17, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A constant electric field directed along the positive x-axis has a strength of 2.0 × 103 N/C. a) Find the electric force exerted on a proton by the field. Part 2 of 3 b) Find the acceleration of the proton. Part 3 of 3 c) Find the time required for the proton to reach a speed of 1.00 × 106 m/s, assuming it starts from rest. Holt SF 17Rev 68 23:17, highSchool, numeric, > 1 min, wordingvariable. Each of the protons in a particle beam has a kinetic energy of 3.25 × 10−15 J. What electric field strength will stop these protons in a distance of 1.25 m? 48 Chapter 24, section 2, Gauss’s Law Pt Charge and Charged Ring 24:02, highSchool, numeric, < 1 min, normal. A point charge 6 µC is located at the center of a uniform ring having linear charge density 17 µC/m and radius 3 m. R λ q a ¡ ¡ Determine the total electric flux through a spherical surface centered at the point charge and having radius R, where R < a, as shown. 49 Chapter 25, section 1, Electric Potential Energy Holt SF 18A 01 25:01, highSchool, numeric, > 1 min, normal. Two alpha particles (helium nuclei), each consisting of two protons and two neutrons, have an electrical potential energy of 6.32 × 10−19 J . Given: ke = 8.98755 × 109 N m2 /C2 , qp = 1.6021 × 10−19 C , and g = 9.8 m/s2 . What is the distance between these particles at this time? Holt SF 18A 02 25:01, highSchool, numeric, > 1 min, wordingvariable. Two charges are located along the x-axis. One has a charge of 6.4 µC, and the second has a charge of −3.2 µC. The Coulomb constant is ke = 8.98755 × 109 N m2 /C2 . The acceleration of gravity is 9.81 m/s2 . If the electrical potential energy associated with the pair of charges is −4.1 × 10−2 J, what is the distance between the charges? Holt SF 18A 03 25:01, highSchool, numeric, > 1 min, normal. Initially, both metal spheres are neutral. In a charging process, 1 × 1013 electrons are removed from one metal sphere and placed on a second sphere. Then the electrical potential energy associated with the two spheres is found to be −0.072 J . The Coulomb constant is 8.98755 × 109 N · m2 /C2 and the charge on an electron is 1.6 × 10−19 C . What is the distance between the two spheres? Holt SF 18A 04 25:01, highSchool, numeric, > 1 min, wordingvariable. A charge moves a distance of 2.0 cm in the direction of a uniform electric field having a magnitude of 215 N/C. The electrical 50 potential energy of the charge decreases by 13.7710 × 10−19 J as it moves. Find the magnitude of the charge on the moving particle. (Hint: The electrical potential energy depends on the distance moved in the direction of the field.) Chapter 25, section 2, Potential Difference and Electric Potential Hewitt CP9 22 P06 25:02, highSchool, numeric, > 1 min, normal. The potential difference between a storm cloud and the ground is 1 × 108 V. If a bolt carrying 2 C falls from a cloud to Earth, what is the change of potential energy of the charge? Hewitt CP9 22 P09 25:02, highSchool, numeric, < 1 min, normal. Part 1 of 2 An electric field does 12 J of work on a 0.0001 C charge. What is the voltage change? Part 2 of 2 The same electric field does 24 J of work on a 0.0002 C charge. What is the voltage change? Hewitt CP9 25 E33 25:02, highSchool, multiple choice, < 1 min, fixed. The metal wing of an airplane acts like a “wire” flying through the Earth’s magnetic field. A voltage is induced between the wing tips and a current flows along the wing but only for a short time. Why does the current stop even though the airplane keeps flying through the Earth’s field? 1. We artificially exert a current to neutralize the current induced by the Earth’s magnetic field. 2. The Earth’s magnetic field in the high altitude is parallel to the wing of the airplane. 3. The airplane keeps flying in a constant velocity through the Earth’s field. 4. A voltage difference is induced across the wings of a moving airplane, which will produce only a momentary current. 51 5. None of these Kinetic Energy 02 25:02, highSchool, numeric, > 1 min, normal. Part 1 of 2 An object with a charge 1 C and a mass 0.2 kg accelerates from rest to a speed of 10 m/s. Calculate the kinetic energy gained. Part 2 of 2 Through how large a potential difference did the object fall? Potential Diff 25:02, highSchool, numeric, > 1 min, normal. The work needed to carry a 1 C charge from point A to point B is 10 J. Calculate the potential difference between point A and B. Potential Energy and Potential 25:02, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 Assume: An electric field set up by an unknown charge distribution. U0 is the amount of work needed to bring a point charge of charge q0 in from infinity to a point P . If the charge q0 is returned to infinity, how much work W would it take to bring a new charge q = 4 q0 from infinity to point P ? 1. W = 8 U0 2. W = 4 U0 3. W = 2 U0 4. W = U0 5. W = U0 2 Chapter 25, section 2, Potential Difference and Electric Potential U0 4 U0 7. W = 8 6. W = 8. W = 0 9. More information is needed. 10. The correct answer is not given. Part 2 of 3 What is the electric potential V at point P ? 1. V = 4 U0 q0 2. V = U0 q0 3. V = U 0 q0 4 4. V = U0 4 U0 q0 U0 6. V = q0 U0 7. V = 4 q0 5. V = 8. V = 0 9. More information is needed. 10. The correct answer is not given. Part 3 of 3 If point P in Part 1 is at a distance a along the x-axis, how much work W would it take to bring the charge q0 to a point P at a distance 4 a along the x-axis? 1. W = 8 U0 2. W = 4 U0 3. W = 2 U0 4. W = U0 U0 2 U0 6. W = 4 U0 7. W = 8 5. W = 8. W = 0 9. More information is needed. 10. The correct answer is not given. 52 Chapter 25, section 3, Equipotential Surfaces Equipotential Surfaces 01 25:03, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 +Q −Q + + + + + + + 53 − − − − − − − The dotted line or surface in the figure above 1. is an equipotential line or surface. The dotted line or surface in the figure above 1. is not an equipotential line or surface. 2. is not an equipotential line or surface. 3. cannot be determined from the information given. 2. is an equipotential line or surface. Part 2 of 6 3. cannot be determined from the information given. Part 2 of 2 +Q −Q + + + + + + + − − − − − − − The dotted line or surface in the figure above The dotted line or surface in the figure above 1. is an equipotential line or surface. 2. is not an equipotential line or surface. 3. cannot be determined from the information given. Equipotential Surfaces 25:03, highSchool, multiple choice, < 1 min, fixed. Part 1 of 6 1. is not an equipotential line or surface. 2. is an equipotential line or surface. 3. cannot be determined from the information given. Part 3 of 6 +Q The dotted line or surface in the figure above 1. is not an equipotential line or surface. Chapter 25, section 3, Equipotential Surfaces 54 2. is an equipotential line or surface. 1. is an equipotential line or surface. 3. cannot be determined from the information given. 3. cannot be determined from the information given. Part 4 of 6 +Q The dotted line or surface in the figure above 1. is an equipotential line or surface. 2. is not an equipotential line or surface. 3. cannot be determined from the information given. Part 5 of 6 +Q −Q The dotted line or surface in the figure above 1. is not an equipotential line or surface. 2. is an equipotential line or surface. 3. cannot be determined from the information given. Part 6 of 6 +Q 2. is not an equipotential line or surface. −Q The dotted line or surface in the figure above Chapter 25, section 4, Calculating the Potential from the Field Holt SF 18Rev 12 25:04, highSchool, numeric, > 1 min, normal. The magnitude of a uniform electric field between the two plates is about 1.7 × 106 N/C. If the distance between these plates is 1.5 cm, find the potential difference between the plates. Holt SF 18Rev 13 25:04, highSchool, numeric, > 1 min, wordingvariable. A force of 4.30 × 10−2 N is needed to move a charge of 56.0 µC a distance of 20.0 cm in the direction of a uniform electric field. What is the potential difference that will provide this force? 55 Chapter 25, section 5, Potential & Energy: Point Charges 56 b) Determine the charge. Energy gained from A to B 25:05, highSchool, numeric, < 1 min, normal. A proton is released from rest in a uniform electric field of magnitude 80000 V/m directed along the positive x axis. The proton undergoes a displacement of 0.5 m in the direction of the electric field as shown in the figure. 80000 V/m + − + − + − + − + − + − + vA = 0 v0 − ++ − + − 0. 5 m + − B− +A + − + − Apply the principle of energy conservation to find the amount of the kinetic energy gained after it has moved 0.5 m. Holt SF 18Rev 36 25:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A proton is accelerated from rest through a potential difference of 25700 V. a) What is the kinetic energy of this proton after this acceleration? Part 2 of 2 b) What is the speed of the proton after this acceleration? Holt SF 18Rev 37 25:05, highSchool, numeric, > 1 min, wordingvariable. A proton is accelerated from rest through a potential difference of 120 V. Calculate the final speed of this proton. Holt SF 18B 01 25:05, highSchool, numeric, > 1 min, normal. Holt SF 18Rev 42 25:05, highSchool, numeric, > 1 min, wordingvariable. The Coulomb constant is 8.98755 × 109 N m2 /C2 and the acceleration of gravity is 9.81 m/s2 . Find the potential difference between a point infinitely far away and a point 1 cm from a proton. An ion is displaced through a potential difference of 60.0 V and experiences an increase of electrical potential energy of 192.262 × 10−17 J. Calculate the charge on the ion. Holt SF 18Rev 29 25:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 At some distance from a point charge, the electric potential is 600.0 V and the magnitude of the electric field is 200.0 N/C. The value of the Coulomb constant is 8.98755 × 109 N · m2 /C2 and the acceleration of gravity is 9.81 m/s2 . a) Determine the distance from the charge. Part 2 of 2 Holt SF 18Rev 44 25:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A proton is accelerated through a potential difference of 4.5 × 106 V. a) How much kinetic energy has the proton acquired? Part 2 of 2 b) If the proton started at rest, how fast is it moving? Holt SF 18Rev 45 Chapter 25, section 5, Potential & Energy: Point Charges 25:05, highSchool, numeric, > 1 min, wordingvariable. A positron (a particle with a charge of +e and a mass equal to that of an electron) that is accelerated from rest between two points at a fixed potential difference acquires a speed of 9.0 × 107 m/s. What speed is achieved by a proton accelerated from rest between the same two points? (Disregard relativistic effects.) Holt SF 18Rev 46 25:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The speed of light is 3.00 × 108 m/s. a) Through what potential difference would an electron starting from rest need to accelerate to achieve a speed of 60.0% of light? (Disregard relativistic effects.) Part 2 of 2 b) Through what potential difference would a positron (a particle with a charge of +e and a mass equal to that of an electron) starting from rest need to accelerate to achieve a speed of 60.0% of light? (Disregard relativistic effects.) Holt SF 18Rev 47 25:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An electron moves from one plate of a capacitor to another, through a potential difference of 2200 V. a) Find the speed with which the electron strikes the positive plate. Part 2 of 2 b) If a proton moves from the positive plate to the negative plate, find the speed with which the proton strikes the negative plate. 57 Chapter 25, section 6, Potential & Energy: Systems of Point Charges 58 Add a Charge to Four 02 25:06, highSchool, numeric, > 1 min, normal. side a is 0.4 m, the magnitude of the electric force on the charge q when it is placed at the center is Part 1 of 3 Four charges are placed at the corners of a square of side a, with Q1 = Q2 = −q , Q3 = Q4 = +q , where q is positive. Initially there is no charge at the center of the square. Q 2 = −q Q 3 = +q Part 3 of 3 The magnitude of the total electrostatic energy of the final 5 charge system is given by (Hint: It may be useful to consider the symmetry property of the charge distribution which leads to cancellations among several terms). Qi = 0 a Q f = +q Q 1 = −q Q 4 = +q Find the work required to bring the charge q from infinity and place it at the center of the square. 2. U 3. U 4. U 5. U 1. W = 0 2. W = 3. W = 4. W = 5. W = 6. W = 7. W = 8. W = 9. W = 10. W = √ k q2 2 2. a √ k q2 =2 . a k q2 =2 2 . a √ k q2 = 2 2. a √ k q2 =2 2 2 . a 2 kq =4 . a k q2 =2 . a k q2 =4 2 . a √ k q2 =4 2 . a k q2 =8 2 . a 1. U = 4 4 k q2 a2 2 k q2 a2 −2 k q 2 a2 −4 k q 2 a2 4 k q2 a 2 k q2 a −2 k q 2 a −4 k q 2 a 8 k q2 a2 Part 2 of 3 If the charge of q is 5 µC and the length of 6. U 7. U 8. U 9. U 10. U Add a Charge to Four 3 25:06, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Four charges are placed at the corners of a square of side a, with q1 = q2 = −q , q3 = q4 = +q , where q is positive. Initially there is no charge at the center of the square. Chapter 25, section 6, Potential & Energy: Systems of Point Charges q 2 = −q q 3 = +q 4. U 5. U q 1 = −q q 4 = +q Find the work required to bring the charge q from infinity and place it at the center of the square. 1. W = 0 2. W = 3. W = 4. W = 5. W = 6. W = 7. W = 8. W = 9. W = 10. W = 4 k q2 a2 2 k q2 a2 −2 k q 2 a2 −4 k q 2 a2 4 k q2 a 2 k q2 a −2 k q 2 a −4 k q 2 a 8 k q2 a2 Part 2 of 2 The magnitude of the total electrostatic energy of the final 5 charge system is given by (Hint: It may be useful to consider the symmetry property of the charge distribution which leads to cancellations among several terms.) √ k q2 1. U = 4 2 2 . a √ k q2 2 . a k q2 =2 2 . a √ k q2 = 2 2. a √ k q2 =2 2 2 . a 2 kq . =4 a k q2 . =2 a k q2 =4 2 . a √ k q2 . =4 2 a k q2 =8 2 . a 2. U = 3. U q 59 6. U 7. U 8. U 9. U 10. U Add a Charge to Four JMS 25:06, highSchool, multiple choice, < 1 min, fixed. Four charges are placed at the corners of a square of side a, with q1 = q2 = −q , q3 = q4 = +q , where q is positive. Initially there is no charge at the center of the square. q 2 = −q q3 = +q q q 1 = −q q4 = +q Find the work required to bring the charge q from infinity and place it at the center of the square. 1. W = 0 2. W = 4 k q2 a2 Chapter 25, section 6, Potential & Energy: Systems of Point Charges 3. W = 4. W = 5. W = 6. W = 7. W = 8. W = 9. W = 10. W = 2 k q2 a2 −2 k q 2 a2 −4 k q 2 a2 4 k q2 a 2 k q2 a −2 k q 2 a −4 k q 2 a 8 k q2 a2 6. U = 10. None of these. Holt SF 18B 02 25:06, highSchool, numeric, > 1 min, normal. 2 +Q 2 +Q What is the electric potential energy of the following system of charges. 2. U = 3. U = −k Q 2 k Q2 3 −k Q 2 5. U = 3 4. U = 2 −k Q 2 8. U = 2 k Q2 9. U = 2 A system of charges are shown in the figure. −Q k Q2 k Q2 7. U = k Q2 Energy of a System of Charges 25:06, highSchool, multiple choice, < 1 min, fixed. 1. U = 0 60 Two point charges of magnitude 5 nC and −3 nC are separated by 35 cm . The Coulomb constant is 8.98755 × 109 N m2 /C2 and the acceleration of gravity is 9.81 m/s2 . What is the potential difference between a point infinitely far away and a point midway between the charges? Holt SF 18B 03 25:06, highSchool, numeric, > 1 min, normal. Four particles with charges of 5 µC, 3 µC, 3 µC and −5 µC are placed at the corners of a “2 m × 2 m” square. The acceleration of gravity is 9.81 m/s2 and the Coulomb constant is 8.98755 × 109 N m2 /C2 . Determine the potential difference between the center of the square and infinity. Holt SF 18Rev 04 25:06, highSchool, numeric, > 1 min, wordingvariable. A point charge of 9.00 × 10−9 C is located at the origin of a coordinate system. A positive charge of 3.00 × 10−9 C is brought in from infinity to a point such that the electrical potential energy associated with the two charges is 8.09 × 10−7 J. The Coulomb constant is 8.98755 × 109 N m2 /C2 and the acceleration of gravity is 9.81 m/s2 . How far apart are the charges at this Chapter 25, section 6, Potential & Energy: Systems of Point Charges 61 time? 8.0 µC P cm 4.0 Consider charges placed at the corners of a rectangle: Let: ke = 8.98755 × 109 N m2 /C2 and g = 9. 8 m /s 2 . The three charges shown in the figure are located at the vertices of an isosceles triangle. The Coulomb constant is 8.98755 × 109 N · m2 /C2 and the acceleration of gravity is 9.8 m/s2 . 4.0 × 10−9 C + 4.0 cm Holt SF 18Rev 14 25:06, highSchool, numeric, > 1 min, wordingvariable. + 0.20 m 0.35 m − − −8.0 µC −12 µC 5.0 × 10−9 C − − 5.0 × 10−9 C 2.0 cm Calculate the electric potential at the midpoint of the base if the magnitude of the positive charge is 4.0 × 10−9 C and the magnitude of the negative charges are 5.0 × 10−9 C. Find the electric potential at point P due to the grouping of charges at the other corners of the rectangle. Holt SF 18Rev 40 25:06, highSchool, numeric, > 1 min, wordingvariable. Holt SF 18Rev 31 25:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A charge of −3.00 × 10−9 C is at the origin of a coordinate system, and a charge of 8.00 × 10−9 C is on the x-axis at 2.00 m. There are two locations on the x-axis, where the electric potential is zero. a) Find the location of the point between the charges. Three charges are situated at three corners of a rectangle, as shown. The Coulomb constant is 8.98755 × 9 10 N · m2 /C2 and the acceleration of gravity is 9.8 m/s2 . Part 2 of 2 b) Find the location of the point to the left of the y − axis. 8.0 µC + 6.0 cm 3.0 cm + 2.0 µC + 4.0 µC How much electrical potential energy would be expended in moving the 8.0 µC charge to infinity? Holt SF 18Rev 39 25:06, highSchool, numeric, > 1 min, wordingvariable. Three Point Charges 04 25:06, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Three point charges −q , 2q and q are located at the corners of an equilateral triangle of side a. Chapter 25, section 6, Potential & Energy: Systems of Point Charges −2 q 4. U 5. U 6. U 7. U 8. U q2 = −k a q2 = 2k a q2 = −2 k a 2 q = 3k a q2 = −3 k a 2 q = 4k a Part 2 of 2 The total electric energy stored in the triangular system is L Aq 2. U = 0 1. WB = 2. WB = 3. WB = 4. WB = 5. WB = 2. U = 0 6. WB = q2 a q2 4. U = 2 k a q2 5. U = −2 k a 1 L Now leave q1 ,q3 , and q4 fixed and bring q2 from infinity to point B . The work WB required is given by q2 1. U = k a 3. U = −k q2 B q2 a Part 1 of 2 Four point charges are placed at the four corners of a square. Each side of the square has length L. Four point charges are q1 = q2 = q 3 = q 4 = q . q4 q3 P +q −q Remove −q to infinity. What is the work done (against the electric force due to 2q and q ) in bringing in charge −q from the infinity to the point bottom right vertex of the triangle. Work and potential in a square 25:06, highSchool, multiple choice, > 1 min, normal. a ˆ ı 60◦ 3. U q2 a q2 7. U = −3 k a q2 8. U = 4 k a 6. U = 3 k ˆ 1. U = k 62 7. WB = 8. WB = 9. WB = kq L2 k q2 L k q2 2L k q2 √ 2 L2 k q2 L2 k q2 2 L2 kq √ 2 L2 k q2 √ 2L kq 2 L2 Chapter 25, section 6, Potential & Energy: Systems of Point Charges 1 k q2 10. WB = (2 + √ ) 2L Part 2 of 2 Given q1 = q2 = 1 µC, L = 0.2 cm and k = 9 × 109 N · m2 /C2 , find the potential at B due to the charge q1 alone. 63 Chapter 25, section 7, Potential & Energy: Electric Dipoles Holt SF 18Rev 05 25:07, highSchool, numeric, > 1 min, wordingvariable. An electron that is initially 55 cm away from a proton is displaced to another point. The Coulomb constant is 8.98755 × 109 N m2 /C2 and the acceleration of gravity is 9.8 m/s2 . If the change in the electrical potential energy as a result of this movement is 2.1 × 10−28 J, what is the final distance between the electron and the proton? 64 Chapter 25, section 8, Potential & Energy: Continuous Charge Distributions Holt SF 18Rev 41 25:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A pair of oppositely charged parallel plates are separated by a distance of 5.0 cm with a potential difference of 550 V between the plates. A proton is released from rest at the positive plate at the same time that an electron is released from rest at the negative plate. Disregard any interaction between the proton and the electron. How long does it take for the paths of the proton and the electron to cross? Part 2 of 4 How fast will the electron be traveling when the particles’ paths cross? Part 3 of 4 How fast will the proton be traveling when the particles’ paths cross? Part 4 of 4 How much time will elapse before the proton reaches the opposite plate? 65 Chapter 25, section 9, Potential & Energy: Charged Conductor Conducting Spheres 07 25:09, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 2 Consider two “solid” conducting spheres with radii r1 = 4 R and r2 = 7 R ; i.e., 7R 7 r2 = =. r1 4R 4 The two spheres are separated by a large distance so that the field and the potential at the surface of sphere #1 only depends on the charge on #1 and the corresponding quantities on #2 only depend on the charge on #2. Place an equal amount of charge on both spheres, q1 = q2 = Q . r2 9. 1. 2. 3. 4. 5. 7. q1 #1 q2 8. #2 After the electrostatic equilibrium on each sphere has been established, what is the ratio V2 of the potentials at the “centers” of the V1 two solid conducting spheres? 1. 2. 3. 4. 5. 6. 7. 8. V2 V1 V2 V1 V2 V1 V2 V1 V2 V1 V2 V1 V2 V1 V2 V1 = = = = = = = = 4 7 7 4 7 2 7 8 16 49 49 16 49 8 49 32 V2 =1 V1 Part 2 of 2 E2 What is the ratio of the electric fields at E1 the “surfaces” of the two spheres? 6. r1 66 9. E2 E1 E2 E1 E2 E1 E2 E1 E2 E1 E2 E1 E2 E1 E2 E1 E2 E1 = = = = = = = = 16 49 49 16 49 8 49 32 4 7 7 4 7 2 7 8 =1 Chapter 25, section 10, Calculating the Field from the Potential Holt SF 18Rev 32 25:10, highSchool, numeric, > 1 min, wordingvariable. A 12 V battery is connected across two parallel metal plates separated by 0.30 cm. Find the magnitude of the electric field. 67 Chapter 25, section 14, The Van de Graaff Generator and Other Applications 68 strength at the surface of the dome. Hewitt CP9 22 E44 25:14, highSchool, multiple choice, < 1 min, fixed. Would you feel any electrical effects if you were inside the charged sphere of a van de Graaff generator? Why or why not? 1. Yes; the electric field is very strong inside the van de Graff generator. 2. Yes; the electric field exists both inside and outside of the generator. 3. No; the inside of the generator has zero charge and thus no electric field. 4. No; although there are charges inside the generator, the net charge is zero. 5. More information is needed. 6. None of these Hewitt CP9 22 P07 25:14, highSchool, numeric, > 1 min, normal. An energy of 0.1 J is stored in the metal ball on top of a Van de Graaff machine. A spark carrying 1 µC discharges the ball. What was the ball’s potential relative to ground? Holt SF 17Rev 52 25:14, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 The dome of a Van de Graaff generator receives a charge of 2.0 × 10−4 C. The radius of the dome is 1.0 m. The value of the Coulomb constant is 8.98755 × 109 N · m2 /C2 . Find the magnitude of the electric field strength inside the dome. Part 2 of 3 Find the magnitude of the electric field Part 3 of 3 Find the magnitude of the electric field strength at a distance of 4.0 m from the center of the dome. Holt SF 17Rev 54 25:14, highSchool, numeric, > 1 min, normal. Part 1 of 2 Given : mp = 1.673 × 10−27 kg qp = 1.60218 × 10 −19 and C. A Van de Graaff generator is charged so that the electric field at its surface is 33000 N/C . What is the magnitude of the electric force on a proton released at the surface of the generator? Part 2 of 2 Find the proton’s acceleration at this instant. The mass of a proton is given to be 1.673 × 10−27 kg. Chapter 26, section 1, Definition of Capacitance Holt SF 18C 03 26:01, highSchool, numeric, > 1 min, normal. Part 1 of 2 A capacitor has a capacitance of 2 pF. a) What potential difference would be required to store 18 pC? Part 2 of 2 b) How much charge is stored when the potential difference is 2.5 V? Holt SF 18Rev 43 26:01, highSchool, numeric, > 1 min, wordingvariable. A potential difference of 100.0 V exists across the plates of a capacitor when the charge on each plate is 400.0 µC. What is the capacitance? 69 Chapter 26, section 2, Calculation of Capacitance 70 Holt SF 18C 04 26:02, highSchool, numeric, > 1 min, wordingvariable. Holt SF 18Rev 33 26:02, highSchool, numeric, > 1 min, wordingvariable. You are asked to design a parallel-plate capacitor having a capacitance of 1.00 F and a plate separation of 1.00 mm. Calculate the required surface area of each plate. Part 1 of 2 A parallel-plate capacitor has an area of 5.00 cm2 and the plates are separated by 1.00 mm. The capacitor stores a charge of 400.0 pC. The permittivity of a vacuum is 8.85419 × 10−12 C2 /N · m2 . a) What is the potential difference across the plates of the capacitor? Holt SF 18Rev 24 26:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The potential difference between a pair of oppositely charged parallel plates is 400 V. a) If the spacing between the plates is doubled without altering the charge on the plates, what is the new potential difference between the plates? Part 2 of 2 b) If the plate spacing is doubled while the potential difference between the plates is kept constant, what is the ratio of the final charge on one of the plates to the original charge? Holt SF 18Rev 26 26:02, highSchool, numeric, > 1 min, wordingvariable. A 12.0 V battery is connected to a 6.0 pF parallel-plate capacitor. What is the magnitude of the charge on each plate? Holt SF 18Rev 30 26:02, highSchool, numeric, > 1 min, normal. A circular parallel-plate capacitor with a spacing of 3 mm is charged to produce a uniform electric field with a strength of 3 × 106 N/C. The permittivity of vacuum is 8.85 × −12 2 10 C /N · m 2 . What plate radius is required if the stored charge is −1 µC? Part 2 of 2 b) What is the magnitude of the uniform electric field in the region that is located between the plates? Holt SF 18Rev 34 26:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A parallel-plate capacitor has a plate area of 175 cm2 and a plate separation of 0.0400 mm. The permittivity of a vacuum is 8.85419 × −12 2 10 C /N · m 2 . a) Determine the capacitance. Part 2 of 2 b) Determine the potential difference when the charge on the capacitor is 500.0 pC. Holt SF 18Rev 48 26:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Each plate on a 3750 pF capacitor carries a charge with a magnitude of 1.75 × 10−8 C. a) What is the potential difference across the plates when the capacitor has been fully charged? Part 2 of 2 b) If the plates are 6.50 × 10−4 m apart, what Chapter 26, section 2, Calculation of Capacitance is the magnitude of the electric field between the two plates? 71 Chapter 26, section 3, Combinations of Capacitors 72 26:03, highSchool, numeric, > 1 min, normal. 12 µF 41 µF 34 µF Part 1 of 3 Consider the group of capacitors shown in the figure. Consider the capacitor circuit 19 µF Capacitor Circuit 04 shortened 26:03, highSchool, numeric, > 1 min, normal. 2. 4 µ F 5 µF a b 8. 3 µ F 2. 2 µ F c d 12 V Find the equivalent capacitance between points a and d. Part 2 of 3 Determine the charge on the 5 µF capacitor on the left-hand side of the circuit. Part 3 of 3 Determine the charge on the 2.4 µF capacitor at the top center part of the circuit. Capacitor Circuit 04 shortest 26:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 Consider the group of capacitors shown in the figure. 2. 4 µ F 5 µF a b 8. 3 µ F 2. 2 µ F c d 12 V Find the equivalent capacitance between points a and d. Part 2 of 2 Determine the charge on the 2.4 µF capacitor at the top center part of the circuit. Capacitor Circuit 07 30 V What is the effective capacitance of the circuit? Capacitor Circuit 09 26:03, highSchool, multiple choice, > 1 min, fixed. Consider the group of capacitors shown in the figure. C a C b C c 2C d EB Find the equivalent capacitance Cad between points a and d. 1. Cad = 2. Cad = 3. Cad = 4. Cad = 5. Cad = 6. Cad = 1 C 2 2 C 5 3 C 5 2 C 3 3 C 4 1 C 3 7. Cad = 2 C 8. Cad = 3 C Chapter 26, section 3, Combinations of Capacitors capacitor between points a and c. 9. Cad = 4 C 10. Cad = 5 C Four Capacitors 01 26:03, highSchool, numeric, > 1 min, normal. Part 1 of 8 In the figure below consider the case where switch S1 is closed and switch S2 is open. c 30 F µF 0µ 1 a 20 µF 50 V S2 S1 Part 2 of 8 Find the charge on the 20 µF lower-left capacitor between points a and d. Part 3 of 8 Find the charge on the 30 µF upper-right capacitor between points c and b. Part 4 of 8 Find the charge on the 40 µF lower-right capacitor between points d and b. Part 5 of 8 Now consider the case where switch S2 is also closed. c 30 µF µF 10 50 V 20 µF S2 d 40 Part 7 of 8 Find the charge on the 30 µF upper-right capacitor between points c and b. Part 8 of 8 Find the charge on the 40 µF lower-right capacitor between points d and b. Four Capacitors 01 shortened 26:03, highSchool, numeric, > 1 min, normal. 4 d Part 6 of 8 Find the charge on the 20 µF lower-left capacitor between points a and d. b F 0µ Find the charge on the 10 µF upper-left capacitor between points a and c. a 73 Part 1 of 2 In the figure below consider the case where switch S1 is closed and switch S2 is open. c 30 µF µF 0 1 a 20 µF 50 V S2 4 Find the charge on the 10 µF upper-left capacitor between points a and c. Part 2 of 2 Now consider the case where switch S2 is also closed. c 30 µF µF 10 a 50 V S1 Find the charge on the 10 µF upper-left S1 d 20 µF S2 b F 0µ 4 b µF b F 0µ d S1 Find the charge on the 10 µF upper-left capacitor between points a and c. Chapter 26, section 3, Combinations of Capacitors Four Capacitors 02 v2 26:03, highSchool, numeric, > 1 min, wordingvariable. 3 µF a Part 1 of 3 The capacitors in the figure are initially uncharged and are connected as in the diagram. Then switch S1 closed and switch S2 is left open. c 57 F µF 0µ 7 1 a 57 µF 113 V S2 b µF 70 1 S1 d After a long wait, what is the magnitude of the potential difference Vcd ≡ Vc − Vd ? Part 2 of 3 The potential difference Vcd is 1. positive. 2. negative. Part 3 of 3 The switch S2 is closed. c 57 F µF 0µ 7 1 a 113 V 57 µF S2 d b µF 70 1 S1 After closing the switch S2 , what is the potential difference Vad ? Voltage in capacitor network 26:03, highSchool, numeric, > 1 min, normal. A capacitor network is shown in the following figure. 74 4 µF 10 µF b 10 V What is the voltage across the 4 µF upper right-hand capacitor? Chapter 26, section 4, Energy Stored in a Charged Capacitor +Q A E The total energy stored in the capacitor is given by 2. U = 3. U = 4. U = 5. U = 6. U = 7. U = 8. U = 29 µF −Q A 1. U = 35 µF d Part 1 of 2 A capacitor network is shown below. 33 µF Part 1 of 2 Consider an air-filled parallel plate capacitor with plate area A and gap width d. The plate charge is Q. Circuit Energy e1 26:04, highSchool, numeric, > 1 min, wordingvariable. 31 µF Charge with battery connected 01 26:04, highSchool, multiple choice, > 1 min, normal. 75 Q2 . 2 0Ad Q2 . 0Ad Q2 d . 2 0A QA . 0d Q . 2 0Ad Qd . 0A Q . 0Ad Q2 A . 0d Part 2 of 2 With the battery connected, fill the gap by a slab with the dielectric constant κ. Given: E = 30 V, κ = 2, d = 0.1 mm, and A = 10 cm2 , 0 = 8.85 × 10−12 C 2 /N · m2 , find the electric charge on the plate. 30 V What is the effective capacitance of the circuit? Part 2 of 2 For the circuit above what is the total energy stored by the 29 µF capacitor on the righthand side of the circuit? (Hint: Notice that the equivalent capacitance of the 31 µF and 33 µF capacitors is equal the the equivalent capacitance of the 35 µF and 29 µF capacitors.) Energy in Par Plate Capacitor 26:04, highSchool, multiple choice, < 1 min, fixed. Consider a parallel plate capacitor with plate area A and a distance d between plates. The capacitor has a charge Q on the top plate and charge −Q on the bottom plate. How much electrostatic energy is stored in this capacitor? 1. U = 2. U = 3. U = 4. U = 5. U = Qd A A Qd Qd 0A Q2 d 2 0A A0 Qd Chapter 26, section 4, Energy Stored in a Charged Capacitor 6. U = 7. U = 8. U = 9. U = 10. U = Q 2 d2 2 0 A2 A2 0 Q 2 d2 A2 2 0 Q 2 d2 Q 2 d2 a2 A2 Q 2 d2 Hewitt CP9 22 E43 26:04, highSchool, multiple choice, < 1 min, fixed. In order to store more energy in a parallelplate capacitor whose plates differ by a fixed voltage, what change would you make in the plates? 1. Move the plates farther apart. 2. Decrease the area of the plates by half. 3. Insert a non-conducting material between the plates. 4. Replace the plates with ones made of more conductive material. 5. Replace the plates with ones made of less conductive material. 6. None of these Holt SF 18C 01 26:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A 4.00 µF capacitor is connected to a 12.0 V battery. a) What is the charge on each plate of the capacitor? Part 2 of 2 b) If this same capacitor is connected to a 1.50 V battery, how much electrical potential 76 energy is stored? Holt SF 18C 02 26:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A parallel-plate capacitor has a charge of 6.0 µC when charged by a potential difference of 1.25 V . a) Find its capacitance. Part 2 of 2 b) How much electrical potential energy is stored when this capacitor is connected to a 1.50 V battery? Holt SF 18Rev 27 26:04, highSchool, numeric, > 1 min, normal. Part 1 of 2 A parallel-plate capacitor has a capacitance of 0.2 µF and is to be operated at 6500 V. a) Calculate the charge stored. Part 2 of 2 b) What is the electrical potential energy stored in the capacitor at the operating potential difference? Holt SF 18Rev 28 26:04, highSchool, numeric, > 1 min, normal. Two devices with capacitances of 25 µF and 5 µF are each charged with separate 120 V power supplies. Calculate the total energy stored in the two capacitors. Holt SF 18Rev 38 26:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A pair of oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600.0 V exists between the plates. a) What is the magnitude of the electric field strength in the region that is located Chapter 26, section 4, Energy Stored in a Charged Capacitor between the plates? Part 2 of 3 b) What is the magnitude of the force on an electron that is in the region between the plates at a point that is exactly 2.9 mm from the positive plate? Part 3 of 3 The electron is moved to the negative plate from an initial position 2.9 mm from the positive plate. c) What is the change in electrical potential energy due to the movement of this electron? Holt SF 18Rev 49 26:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 5 A parallel-plate capacitor is made of two circular plates, each with a diameter of 2.50 × 10−3 m. The plates of this capacitor are separated by a space of 1.40 × 10−4 m. The permittivity of a vacuum is 8.85419 × 10−12 C2 /N · m2 . a) Assuming that the capacitor is operating in a vacuum, find the capacitance for this arrangement. Part 2 of 5 b) How much charge will be stored on each plate of this capacitor when it is connected across a potential difference of 0.120 V? Part 3 of 5 c) What is the electrical potential energy stored in this capacitor when it is fully charged by the potential difference of 0.120 V? Part 4 of 5 d) What is the potential difference between a point midway between the plates and a point that is 1.10 × 10−4 m from one of the plates? Part 5 of 5 e) If the potential difference of 0.120 V is removed from the circuit and if the circuit is 77 allowed to discharge until the charge on the plates has decreased to 70.7 percent of its fully charged value, what will the potential difference across the capacitor be? Chapter 26, section 5, Capacitors with Dielectrics Capacitor Comparison e1 26:05, highSchool, multiple choice, < 1 min, fixed. Consider the setup shown, where a capacitor with a capacitance C is connected to a battery with emf V and negligible internal resistance. Before the insertion of the dielectric slab with dielectric constant κ, the energy density within the gap is u. Now, keeping the battery connected, insert the dielectric, which fills the gap completely. ducting sphere with charge Q. Hint: Use the capacitance formula for a spherical capacitor which consists of two spherical shells. Take the inner sphere to have a radius a and the outer shell to have an infinite radius. 1. U = 2. U = 3. U = 4. U = d V C Determine the energy density u within the gap in the presence of the dielectric. 1. u = u κ2 2. u = u κ 3. u = u κ 4. u = u u κ2 u 6. u = √ κ √ 7. u = u κ 5. U = 6. U = 7. U = 8. U = 1. U = 2. U = 3. U = 4. U = uκ 2 u 10. u = 2κ 6. U = Capacitor Energy v2 26:05, highSchool, numeric, < 1 min, fixed. 7. U = 9. u = Part 1 of 4 Determine the total energy stored in a con- Q2 π 8 0a Q2 4π 0a Q2 16 π 0 a Q 8π 0a Q2 8 π 0 a2 Q2 a 4π 0 Q2 a Q2 8π 0a Part 2 of 4 Find the energy stored in a capacitor of charge Q filled with a dielectric with dielectric constant κ. 5. u = 8. u = 2 u κ 78 5. U = 8. U = Q 2κC Q2 κC Q2 2 (κ − 1) C Q2 2C Q 4κC Q2 3κC Q2 3 (κ − 1) C Q2 3C Chapter 26, section 5, Capacitors with Dielectrics Q2 9. U = 2κC Part 3 of 4 Work = Uf − Ui , where “i” is the initial state where there is a slab in the gap and “f” is the final state where there is no slab in the gap. Find the work done in pulling a dielectric slab of dielectric constant κ from the gap of a parallel plate capacitor of plate charge Q and capacitance C . 1. Wif = 2. Wif = 3. Wif = 4. Wif = 5. Wif = 6. Wif = 7. Wif = 8. Wif = 9. Wif = Q2 2κC Q2 1 κ− 2C κ 2 Q 2C Q2 (1 − κ) 2C Q2 1 −1 2C κ Q2 1 κ+ 2C κ Q2 1 1− 2C κ 2 Q (1 − κ) 2κC Q2 5κC Part 4 of 4 Consider a capacitor which is connected to a battery with an emf V . Denote the energy stored in the capacitor in the absence of a dielectric, with dielectric constant κ, to be U and in the presence of the dielectric to be U . U Find the ratio as the potential across U the plates is held at a constant value by the battery. U 1 1. = U κ U 2. =1 U 3. 4. 5. 6. 7. 8. U U U U U U U U U U U U = 79 1 2 =κ 1 2κ √ =2 = = 1 3 = 2κ Charge with battery connected 26:05, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Consider an air-filled parallel plate capacitor with plate area A and gap width d. The plate charge is Q. d +Q −Q A A E The total energy stored in the capacitor is given by 1. U = 2. U = 3. U = 4. U = 5. U = Q2 . 2 0Ad Q2 . 0Ad Q2 d . 2 0A QA . 0d Q . 2 0Ad Chapter 26, section 5, Capacitors with Dielectrics Part 2 of 2 With the battery connected, fill the gap by a slab with the dielectric constant κ. Compare the new plate charge Q with Q, the plate charge in part 1. Choose one: 1. Q = κ Q 2. Q = (κ + 1) Q 3. Q = κ+1 Q 2 4. Q = (κ − 1) Q 5. Q = 6. Q = 7. Q = 8. Q = 9. Q = 10. Q = κ−1 Q 2 Q κ Q κ+1 2Q κ+1 Q κ−1 2Q κ−1 dielectric 2.6 constant left 2 cm Qd . 0A Q 7. U = . 0Ad Q2 A 8. U = . 0d 6. U = 80 dielectric constant 6.7 right 0.75 mm Calculate the capacitance C of the device. Part 2 of 2 Vlef t of electric potential What is the ratio Vright across the dielectric in the left-half region to that across the dielectric in the right-half region? Series Dielectric Energy 26:05, highSchool, multiple choice, > 1 min, fixed. A capacitor is constructed from two metal plates. The left-hand portion of a capacitor is filled with air and right-hand portion is filled with a material of dielectric constant κ. Given: The gap width of the left-hand portion of the capacitor is the same as the gap width of the right-hand portion. Neglect edge effects. The size of the dielectric between the plates is of equal size as the metal plates, as shown in the figure below. dielectric constant κ Series Dielectric 26:05, highSchool, numeric, > 1 min, normal. Part 1 of 2 A capacitor is constructed from two square metal plates. The gap between the plates is filled with two dielectrics of equal size as shown in the figure below. Neglect edge effects. E Ur of energy stored in U right portion and the left portion. Determine the ratio 1. Ur 1 = U κ Chapter 26, section 5, Capacitors with Dielectrics 2. 3. 4. 5. 6. 7. 8. 9. 10. Ur U Ur U Ur U Ur U Ur U Ur U Ur U Ur U Ur U = 1 κ2 = κ2 =κ = 1 κ+1 = 2κ = 1 2κ = 2κ + 1 = 1 2κ + 1 =κ+1 81 Chapter 27, section 1, Electric Current Car electrons 27:01, highSchool, numeric, > 1 min, normal. 82 tery can supply without being recharged is given in terms of Ampere-hours. A typical 12-V battery has a rating of 60 A · h . Suppose you forget to turn off the headlights in your parked automobile. If each of the two headlights draws 3 A , find out the time before your battery is “dead”. How long does it take electrons to get from the car battery to the starting motor? Assume the current is 115 A and the electrons travel through copper wire with cross sectional area 31.2 mm2 and length 85.5 cm. The mass density of copper is 8960 kg/m3 and the molar mass is 63.5 g/mol. Holt SF 19A 01 27:01, highSchool, numeric, < 1 min, wordingvariable. Concept 23 E08 27:01, highSchool, multiple choice, < 1 min, fixed. If the current in a wire of a CD player is 5.00 mA, how long would it take for 2.00 C of charge to pass a point in this wire? Does more current flow out of a battery than into it? Does more current flow into a light bulb than out of it? Holt SF 19A 02 27:01, highSchool, numeric, < 1 min, normal. 1. More for both 2. less; more 3. more; less 4. Less for both 5. The same for both Conceptual 18 Q10 27:01, highSchool, multiple choice, < 1 min, fixed. A copper wire carries 1 amp of electric current. What kind of charge does the electron flow create in the wire? 1. Positive 2. Negative 3. No charge. Hewitt CP9 23 P04 27:01, highSchool, numeric, > 1 min, normal. The total charge that an automobile bat- In a particular television tube, a beam of electrons has a current of 6 × 10−5 A . The magnitude of the charge on an electron is 1.602 × 10−19 C . How long does it take for 3.75 × 1014 to strike the screen? Holt SF 19A 03 27:01, highSchool, numeric, < 1 min, wordingvariable. If a metal wire carries a current of 80.0 mA, how long does it take for 3.00×1020 electrons to pass a given cross-sectional area anywhere along the wire? The magnitude of the charge on an electron is 1.6 × 10−19 C. Holt SF 19A 04 27:01, highSchool, numeric, < 1 min, wordingvariable. The compressor on an air conditioner draws 40.0 A when it starts up. If the start-up time is 0.50 s, how much charge passes a cross-sectional area of the circuit in this time? Holt SF 19A 05 27:01, highSchool, numeric, > 1 min, wordingvariable. Chapter 27, section 1, Electric Current Part 1 of 3 A total charge of 9.0 mC passes through a cross-sectional area of a nichrome wire in 3.5 s. a) What is the current in the wire? Part 2 of 3 b) How many electrons pass through the cross-sectional area in 10.0 s? Part 3 of 3 c) If the number of charges that pass through the cross-sectional area during the given time interval doubles, what is the resulting current? Holt SF 19Rev 17 27:01, highSchool, numeric, < 1 min, wordingvariable. How long does it take a total charge of 10.0 C to pass through a cross-sectional area of a copper wire that carries a current of 5.0 A? Holt SF 19Rev 18 27:01, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A hair dryer draws a current of 9.1 A. a) How long does it take for 1.9 × 103 C of charge to pass through the hair dryer? Part 2 of 2 b) How many electrons does this amount of charge represent? Holt SF 19Rev 19 27:01, highSchool, numeric, < 1 min, wordingvariable. How long does it take for 5.0 C of charge to pass through a cross-sectional area of a copper wire if I = 5.0 A? Holt SF 19Rev 44 27:01, highSchool, numeric, < 1 min, wordingvariable. 83 Part 1 of 2 A net charge of 45 mC passes through the cross-sectional area of a wire in 15 s. a) What is the current in the wire? Part 2 of 2 b) How many electrons pass the crosssectional area in 1.0 min? Holt SF 19Rev 46 27:01, highSchool, numeric, < 1 min, wordingvariable. The current in a lightning bolt is 2.0 × 105 A. How much charge passes through a crosssectional area of the lightning bolt in 0.50 s? Holt SF 19Rev 54 27:01, highSchool, numeric, > 1 min, wordingvariable. The mass of a gold atom is 3.27 × 10−25 kg. If 1.25 kg of gold is deposited on the negative electrode of an electrolytic cell in a period of 2.78 h, what is the current in the cell in this period? Assume that each gold ion carries one elementary unit of positive charge. Holt SF 19Rev 58 27:01, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 The current in a conductor varies over time as shown in the figure below. Chapter 27, section 1, Electric Current Current(A) 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0 1 01 2 3 4 234 Time(s) 5 6 56 7 7 a) How much charge passes through a cross section of the conductor in the time interval t = 0 s to t = 5 s? Part 2 of 2 b) What constant current would transport the same total charge during the 5 s interval as does the actual current? 84 Chapter 27, section 2, Current Density and Drift Speed Hewitt CP9 23 03 27:02, highSchool, multiple choice, < 1 min, fixed. What is drift velocity? 1. the highest speed of an electron in a metal 2. the lowest speed of an electron in a metal 3. the speed of an electric field 4. the average speed of atoms in a liquid 5. the average speed of electrons in a conductor in an electric field 85 Chapter 27, section 3, Resistance and Resistivity Copper conductor 27:03, highSchool, multiple choice, < 1 min, fixed. Which of the following copper conductor conditions has the least resistance? 1. thick, short, and cool 2. thick, short, and hot 3. thick, long, and cool 4. thick, long, and hot 5. thin, short, and cool 6. thin, short, and hot 7. thin, long, and cool 8. thin, long, and hot Resistance and Resistivity JMS 27:03, highSchool, multiple choice, > 1 min, fixed. A resistor is made from a hollow cylinder of length l, inner radius a, and outer radius b. The region a < r < b is filled with material of resistivity ρ. Current runs along the axis of the cylinder. The resistance R of this component is ρ π b2 ρ 2. R = π a2 π b2 ρ 3. R = 1. R = 4. R = 5. R = 6. R = π b2 − a 2 ρ ρ − a2 ) π (b 2 ρ b2 π a4 ρa π b2 ρ a2 8. R = π b4 2ρ 9. R = π b2 2πρ 10. R = 2 (b − a 2 ) 7. R = 86 Chapter 27, section 4, Ohm’s Law Hewitt CP9 23 01 27:04, highSchool, multiple choice, < 1 min, fixed. How will a current change if the voltage in a circuit is held constant while the resistance doubles? 1. The current will remain the same. 2. The current will double. 3. The current will triple. 4. The current will drop to half of its original value. 87 device in a 120 V circuit has a current rating of 20 A. What is the resistance of the device? Hewitt CP9 23 09 27:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 What is the effect on the current in a wire if both the voltage across it and its resistance are doubled? 1. The current is doubled. 2. The current is 4 times bigger. 3. The current does not change. 5. It’s impossible to predict. 4. The current is halved. Hewitt CP9 23 02 27:04, highSchool, multiple choice, < 1 min, fixed. How will a current change if the resistance of a circuit remains constant while the voltage across the circuit decreases to half its original value? 1. The current will remain the same. 5. The current is reduced to a quarter of its original value. 6. It cannot be determined. Part 2 of 2 What is the effect on the current in a wire if both the voltage across it and its resistance are halved? 2. The current will double. 1. The current is doubled. 3. The current will triple. 2. The current is 4 times bigger. 4. The current will drop to half of its original value. 3. The current does not change. 4. The current is halved. 5. It’s impossible to predict. Hewitt CP9 23 02a 27:04, highSchool, numeric, < 1 min, normal. 5. The current is reduced to a quarter of its original value. 6. It cannot be determined. Rearrange the equation Voltage Current = Resistance to express resistance in terms of current and voltage. Then solve the following: A certain Hewitt CP9 23 10 27:04, highSchool, multiple choice, < 1 min, normal. How does the current in a light bulb con- Chapter 27, section 4, Ohm’s Law nected to a 220 V source compare to the current when this light bulb is connected to a 110 V source? 88 What is the current in this device? Holt SF 19B 03 27:04, highSchool, numeric, > 1 min, normal. 1. The 220 V current is larger. 2. The 110 V current is larger. 3. The currents are equal. 4. It cannot be determined. Hewitt CP9 23 P02 27:04, highSchool, numeric, < 1 min, fixed. A certain device in a 120 V circuit has a current rating of 20 A . Find the resistance of the device. Hewitt CP9 23 R11 27:04, highSchool, multiple choice, < 1 min, fixed. How will the current change if the voltage in a circuit is held constant while the resistance halves? 1. The current remains unchanged. 2. The current halves. 3. The current doubles. 4. The current quadruples. 5. It’s impossible to predict. Holt SF 19B 01 27:04, highSchool, numeric, < 1 min, normal. A 1.5 V battery is connected to a small light bulb with a resistance of 3.5 Ω. What is the current in the bulb? Holt SF 19B 02 27:04, highSchool, numeric, < 1 min, normal. A stereo with a resistance of 65 Ω is connected across a potential difference of 120 V. Part 1 of 2 A hot plate connected across a potential difference of 120 V has a resistance of 48 Ω. a) What is the current in the hot plate? Part 2 of 2 A microwave oven connected across a potential difference of 120 V has a resistance of 20 Ω. b) What is the current in the microwave oven? Holt SF 19B 04 27:04, highSchool, numeric, < 1 min, normal. The current in a microwave oven is 6.25 A. If the resistance of the oven’s circuitry is 17.6 Ω, what is the potential difference across the oven? Holt SF 19B 05 27:04, highSchool, numeric, < 1 min, normal. A typical color television draws 2.5 A of current when connected across a potential difference of 115 V. What is the effective resistance of the television set? Holt SF 19B 06 27:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The current in a certain resistor is 0.50 A when it is connected to a potential difference of 110 V. a) What is the current in this same resistor if the operating potential difference is 90.0 V? Part 2 of 2 b) What is the current in the resistor when the operating potential difference if 130 V? Chapter 27, section 4, Ohm’s Law 89 Holt SF 19Rev 28 27:04, highSchool, numeric, < 1 min, wordingvariable. Part 3 of 3 A 20 Ω resistor is connected to a 9 V battery in the circuit below. A nichrome wire with a resistance of 15 Ω is connected across the terminals of a 3.0 V flashlight battery. How much current is in the wire? 20 Ω Holt SF 19Rev 29 27:04, highSchool, numeric, < 1 min, normal. How much current is drawn by a television with a resistance of 35 Ω that is connected across a potential difference of 120 V? 9V S I c) When the switch is closed, calculate the current I . Holt SF 19Rev 30 27:04, highSchool, numeric, > 1 min, normal. Holt SF 19Rev 45 27:04, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 3 A 5 Ω resistor is connected to a 9 V battery in the circuit below. A potential difference of 12 V produces a current of 0.40 A in a piece of copper wire. What is the resistance of the wire? 5Ω Holt SF 19Rev 59 27:04, highSchool, numeric, < 1 min, wordingvariable. 9V S I a) When the switch is closed, calculate the current I . Part 2 of 3 A 2 Ω resistor is connected to a 9 V battery in the circuit below. 2Ω 9V S I b) When the switch is closed, calculate the current I . Birds resting on high-voltage power lines are a common sight. A certain copper power line carries a current of 50.0 A, and its resistance per unit length is 1.12 × 10−5 Ω/m. If a bird is standing on this line with its feet 4.0 cm apart, what is the potential difference across the bird’s feet? Chapter 27, section 5, Microscopic View of Ohm’s Law Concept 23 E17 27:05, highSchool, multiple choice, < 1 min, fixed. Why are thick wires rather than thin wires usually used to carry large current? 90 How do the length, diameter and temperature of a copper wire affect its resistance? 1. A longer wire will have more resistance, a larger diameter wire will have less resistance, and higher temperatures mean higher resistance. 1. Thick wires have less resistance. 2. Thick wires have a larger heat capacity. 3. Thick wires are difficult to break. 4. Thick wires are easier to make. Concept 23 E19 27:05, highSchool, numeric, < 1 min, normal. Part 1 of 2 A 1-mile long copper wire has a resistance of 10 Ω. What will be its new resistance when it is shortened by cutting it in half? Part 2 of 2 What will be its new resistance when it is shortened a second time by doubling it over and using it as “one” wire? Conceptual 18 Q09 27:05, highSchool, multiple choice, < 1 min, fixed. Consider the thickness of a wire. What is true? 1. A thicker wire has less resistance than thinner wire. 2. A thicker wire has more resistance than thinner wire. 3. Both wires have the same resistance since they are made of the same material. 1. A longer wire will have less resistance, a larger diameter wire will have more resistance, and higher temperatures mean less resistance. 2. A longer wire will have more resistance, a larger diameter wire will have less resistance, and higher temperatures mean less resistance. 3. A longer wire will have more resistance, a larger diameter wire will have more resistance, and higher temperatures mean higher resistance. 4. A longer wire will have less resistance, a larger diameter wire will have more resistance, and higher temperatures mean higher resistance. Conceptual 18 Q17 27:05, highSchool, multiple choice, < 1 min, fixed. Even though copper conducts electricity very well, it does have some resistance. How would the resistance of a 1-meter-long thick copper wire compare to the resistance of a 1-meter-long thin copper wire? 1. 1-meter-long thick copper wire will have higher resistance. 2. 1-meter-long thin copper wire will have higher resistance. 3. The will have the same resistance. Conceptual 18 Q11 27:05, highSchool, multiple choice, < 1 min, fixed. Conceptual 18 Q19 27:05, highSchool, multiple choice, < 1 min, Chapter 27, section 5, Microscopic View of Ohm’s Law fixed. Which of the following is correct? 1. 50-watt lightbulb has more resistance. 2. 100-watt lightbulb has more resistance. Figuring Physics 17 27:05, highSchool, multiple choice, < 1 min, fixed. Roll a piece of modeling clay into a cylinder and use an ohmmeter to measure its resistance. R ? ¡ Now roll it out until it is twice as long, and measure the resistance again. Compared with the initial resistance, the new resistance is 1. unchanged. 2. twice as much. 3. four times as much. 4. eight times as much. 5. actually less. Hewitt CP9 23 08 27:05, highSchool, numeric, > 1 min, normal. Part 1 of 2 A 1 mile long copper wire that has a resistance of 10 ohm is cut in half. What is the resistance of one of the halves? Part 2 of 2 What will be the new resistance if the two halves are doubled over and used as one wire? 91 Chapter 27, section 6, Resistance and Temperature 92 age and current. Concept 23 E12 27:06, highSchool, multiple choice, < 1 min, fixed. An electron moving in a wire collides again and again with atoms and travels an average distance between collisions that is called the mean free path. For a given conductor, what can you do to lengthen the mean free path? 1. Cool the conductor 2. Heat the conductor 3. Apply a large voltage across the conductor 3. The resistance remains constant with both voltage and current. 4. Cannot be determined from the information. Part 2 of 2 From your personal experience, can you predict whether the temperature of the filament of the lightbulb increases or decreases with the voltage? 1. The higher the temperature the higher the resistance 2. The lower the temperature the higher the resistance 4. Place the conductor in a vacuum 3. Voltage has no effect on resistance. Conceptual 18 07 27:06, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Giselle and Anna decided to impress their physical science professor with a simple experiment investigating the resistance of a 100 W lighbulb. They used a VARIAC (which provides a variable voltage to a circuit) in a series circuit with one 100-W lightbulb. They measured the current and voltage, which are listed in the following table. Voltage (Volts) Currents (amps) 120 0.81 100 0.72 80 0.62 60 0.51 40 0.40 20 0.23 Does the resistance of the lighbulb increase or decrease for each voltage and current setting? 1. The resistance increases with both voltage and current. 2. The resistance decreases with both volt- Hewitt CP9 15 E39 27:06, highSchool, multiple choice, < 1 min, fixed. One of the reasons the first light bulbs were expensive was that the electrical lead wires were made of platinum. What is wrong? 1. The metal leads and the glass have the same coefficient of expansion. 2. Platinum expands at about the same rate as glass when heated. 3. The metal leads and the glass have the same coefficient of resistance. 4. If the metal leads expand more than glass, the glass may crack. 5. If the metal expands less than glass upon being heated, air will leak in through the resulting gaps. Chapter 27, section 7, Semiconductors Conceptual 24 Q11 27:07, highSchool, multiple choice, < 1 min, wording-variable. If the temperature of a semiconductor is decreased what happens to its electrical resistance. 1. increases 2. decreases 3. No change Hewitt CP9 12 E01 27:07, highSchool, multiple choice, < 1 min, fixed. Silicon is the main ingredient of both glass and semiconductor materials. Why are the physical properties of glass different from those of semiconductors? 1. The silicon in glass does not have electrons, while the silicon in semiconductors does. 2. The silicon atoms in semiconductors form a crystal; in glass they are bonded with oxygen atoms to form the amorphous silicon dioxide. 3. The silicon atoms in semiconductors are bonded with oxygen atoms to form a crystal; in semiconductors the silicon is pure and thus forms the amorphous structure. 4. Silicon has no effect on the properties of glass and semiconductors. 93 Chapter 27, section 8, Superconductors Conceptual 24 Q12 27:08, highSchool, multiple choice, < 1 min, fixed. Based on Ohm’s law, how much current would you expect to run through a superconductor if the voltage across it were 100 volts? 1. infinite current 2. high current; superconductor breaks down. 3. no current 4. 100 A current 94 Chapter 27, section 9, Electrical Energy and Power Change potential 27:09, highSchool, numeric, > 1 min, fixed. Part 1 of 2 A potential difference V is applied to a wire of cross-section area of 1 unit, length 1 unit, and conductivity σ . You want to change the applied potential difference and draw out the wire so the power dissipated is increased by a factor of 30 and the current is increased by a factor of 4 . What should be the new values of the length? 95 Conceptual 18 Q21 27:09, highSchool, multiple choice, < 1 min, fixed. Two lightbulbs are wired in series and connected to a 12-volt battery. What happens to the current through the battery if a third bulb is wired in parallel with the other two bulbs? To the power? 1. Both increase. 2. Both decrease. 3. Decreases; increases Part 2 of 2 b) What is the new cross sectional area? Conceptual 18 05 27:09, highSchool, numeric, > 1 min, normal. Part 1 of 2 A typical 1.5 V alkaline D battery is rated at 3.5 amp-hours. What is the power that can be expended by the battery? 4. Increases; decreases Hewitt CP9 23 11 27:09, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 What unit is equivalent to “Joule per Coulomb?” 1. volt Part 2 of 2 What is the total energy stored by this battery? 2. Ampere 3. Coulomb Conceptual 18 Q20 27:09, highSchool, multiple choice, < 1 min, fixed. Two lightbulbs are wired in series and connected to a 12-volt battery. What happens to the current through the battery if a third bulb is added in series? To the power? 1. Both decrease. 4. kilogram 5. Ohm 6. Joule 7. Watt Part 2 of 3 What unit is equivalent to “Coulomb per second?” 2. Both increase. 1. volt 3. Increases; decreases 2. Ampere 4. Decreases; increases 3. Coulomb Chapter 27, section 9, Electrical Energy and Power 4. kilogram 5. Ohm 6. Joule 96 It is estimated that in the United States (population 250 million) there is one electric clock per person, with each clock using energy at a rate of 2.5 W. Using this estimate, how much energy is consumed by all of the electric clocks in the United States in a year? 7. Watt Part 3 of 3 What unit is equivalent to “Watt · second ?” 1. volt 2. Ampere Holt SF 19Rev 50 27:09, highSchool, numeric, < 1 min, wordingvariable. An X-ray tube used for cancer therapy operates at 4.0 MV with a beam current of 25 mA striking a metal target. Calculate the power of this beam. 3. Coulomb 4. kilogram Holt SF 19Rev 57 27:09, highSchool, numeric, < 1 min, wordingvariable. 5. Ohm 6. Joule 7. Watt Hewitt CP9 23 P03 27:09, highSchool, numeric, < 1 min, fixed. Part 1 of 2 Using Power = current×voltage, find the current drawn by a 1200 W hair dryer connected to 120 V . Part 2 of 2 Find the resistance of the hair-dryer. Holt SF 19C 03 27:09, highSchool, numeric, < 1 min, wordingvariable. A calculator is rated at 0.10 W when connected to 1.50 V battery. What is the resistance of this device? Holt SF 19Rev 38 27:09, highSchool, numeric, < 1 min, wordingvariable. The headlights on a car are rated at 80.0 W. If they are connected to a fully charged 90.0 A·h, 12.0 V battery, how long does it take the battery to completely discharge? Holt SF 19Rev 60 27:09, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 An electric car is designed to run on a bank of batteries with a total potential difference of 12 V and a total energy storage of 2.0×107 J. a) If the electric motor draws 8.0 kW, what is the current delivered to the motor? Part 2 of 2 b) If the electric motor draws 8.0 kW as the car moves at a steady speed of 20.0 m/s, how far will the car travel before it is “out of juice”? Lightbulb 75 watts 27:09, highSchool, multiple choice, < 1 min, fixed. You buy a 75 watt light bulb. Chapter 27, section 9, Electrical Energy and Power The label means that 1. no matter how you use the bulb, the power will be 75 watts. 2. the bulb was filled with 75 W at the factory. 3. the actual power dissipated will be much higher than 75 W since most of the power appears as heat. 4. the bulb is expected to burn out after you use up its 75 watts. 5. the power will be 75 watts if standard household voltage is applied to it. 97 Chapter 27, section 10, Power in Household Circuits Christmas Lights 03 27:10, highSchool, numeric, > 1 min, normal. Part 1 of 2 A string of 18 identical Christmas tree lights are connected in series to a 120 V source. The string dissipates 64 W. What is the equivalent resistance of the light string? Part 2 of 2 What is the resistance of a single light? Conceptual 18 08 27:10, highSchool, multiple choice, < 1 min, wording-variable. Most household circuits have fuses or circuit breakers that open a switch when the current in the circuit exceeds 15 A. What will happen when you plug in an air conditioner (1 kilowatt), a TV (250 watts), and four 100 watt lightbulbs? 1. The circuit breaker would not open 2. The circuit breaker would open 3. Cannot be determined from the information. Conceptual 18 10 27:10, highSchool, numeric, > 1 min, normal. An energy-efficient air conditioner draws 7 A in a standard 120-volt circuit. It costs $40 more than a standard air conditioner that draws 12 A. If electricity costs 8 cents per kilowatt-hour, how long would you have to run the efficient air conditioner to recoup the difference in price? Filament 27:10, highSchool, multiple choice, < 1 min, normal. A 1000 W bulb and a 500 W bulb are both 98 designed to operate at standard household voltage of 120 V. Determine which bulb has the lower filament resistance and then calculate the value of its resistance. Hewitt CP9 23 01a 27:10, highSchool, numeric, < 1 min, normal. Find the current through a 60 W bulb connected to a 120 V circuit. Hewitt CP9 23 P01 27:10, highSchool, multiple choice, < 1 min, fixed. The voltage marked on a light bulb is usually either 110 or 120 V . The power of a light bulb is 60 W . It is connected to a power supply with voltage 120 V . Find the current flowing through the light bulb. Hewitt CP9 23 P05 27:10, highSchool, numeric, > 1 min, fixed. How much does it cost to operate a 100 W lamp continuously for one week if the power utility rate is 0.15 dollars/kWh? Hewitt CP9 23 P06 27:10, highSchool, numeric, > 1 min, fixed. Part 1 of 2 An electric iron connected to a 110 V source draws 9 A of current. Find the heat the iron generates in a minute. Part 2 of 2 Find the charge flowing through the iron in one minute. Hewitt CP9 23 P07 27:10, highSchool, numeric, > 1 min, fixed. A certain light bulb with a resistance of 95 Ω (when the bulb is on) is labeled 150 W. Chapter 27, section 10, Power in Household Circuits 99 What voltage was this light bulb designed to use? when connected to 120 V. What is the resistance of this device? Hewitt CP9 23 R27 27:10, highSchool, multiple choice, < 1 min, fixed. Holt SF 19C 04 27:10, highSchool, numeric, < 1 min, wordingvariable. When you pay your household electric bill at the end of the month, which of the following are you paying for? Part 1 of 2 An electric heater is operated by applying a potential difference of 50.0 V across a nichrome wire of total resistance 8.00 Ω. a) Find the current in the wire. 1. voltage 2. current Part 2 of 2 b) Find the power rating of the heater. 3. power 4. energy Hewitt CP9 25 P05 27:10, highSchool, numeric, > 1 min, normal. Part 1 of 3 100 kW of power is delivered to the other side of a city by a pair of power lines with the voltage difference of 12000 V. a) How much current flows in the lines? Part 2 of 3 b) Each of the two lines has a resistance of 10 Ω. What is the voltage change along each line? Part 3 of 3 c) How much power is wasted as heat in both lines together? Holt SF 19C 01 27:10, highSchool, numeric, < 1 min, normal. A 1050 W electric toaster operates on a household circuit of 120 V. What is the resistance of the wire that makes up the heating element of the toaster? Holt SF 19C 02 27:10, highSchool, numeric, < 1 min, normal. A small electronic device is rated at 0.25 W Holt SF 19D 01 27:10, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Assume electrical energy costs $0.080 per kW·h, and that appliances have a potential difference across them of 115 V. a) Calculate the cost of running a 75.0 W stereo for 24 h. Part 2 of 3 b) Calculate the cost of running an electric oven that draws 20.0 A of current for 24 h. Part 3 of 3 c) Calculate the cost of running a television with a resistance of 60.0 Ω for 24 h. Holt SF 19D 02 27:10, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Several appliances are supplied with a potential difference of 115 V and are operated continuously for a 24 h period. a) How much energy is used if the appliance is a 75.0 W stereo? Part 2 of 3 b) How much of energy is used if the appli- Chapter 27, section 10, Power in Household Circuits ance is an electric oven that draws 20.0 A of current? Part 3 of 3 c) How much energy is used if the appliance is a television with a resistance of 60.0 Ω. Holt SF 19Rev 34 27:10, highSchool, numeric, < 1 min, wordingvariable. How much energy is dissipated by 50.0 W light bulb in 1.00 s? 100 Holt SF 19Rev 48 27:10, highSchool, numeric, < 1 min, wordingvariable. How much power is needed to operate a radio that draws 7.0 A of current when a potential difference of 115 V is applied across it? Holt SF 19Rev 49 27:10, highSchool, numeric, < 1 min, normal. Holt SF 19Rev 40 27:10, highSchool, numeric, < 1 min, normal. A color television has a power rating of 325 W. How much current does this set draw from a potential difference of 120 V? A computer is connected across a 110 V power supply. The computer dissipates 130 W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the computer. Holt SF 19Rev 51 27:10, highSchool, numeric, > 1 min, wordingvariable. Holt SF 19Rev 41 27:10, highSchool, numeric, < 1 min, normal. Part 1 of 3 A steam iron draws 6.0 A when connected to a potential difference of 120 V. a) What is the power rating of this iron? Part 1 of 2 The operating potential difference of a light bulb is 120 V. The power rating of the bulb is 75 W. a) Find the current in the bulb. Part 2 of 2 b) Find the bulb’s resistance. Holt SF 19Rev 42 27:10, highSchool, numeric, < 1 min, wordingvariable. How much would it cost to watch a football game for 3.0 h on a 325 W television if electrical energy costs $0.08 /kW · h? Holt SF 19Rev 43 27:10, highSchool, numeric, < 1 min, normal. Calculate the cost of operating a 75 W light bulb continuously for a 30-day month when electrical energy costs $0.15 /kW · h. Part 2 of 3 b) How much energy is produced in 20.0 min? Part 3 of 3 c) How much does it cost to run the iron for 20.0 min at $0.010/kW·h? Holt SF 19Rev 52 27:10, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 An 11.0 W energy-efficient fluorescent lamp is designed to produce the same illumination as a conventional 40.0 W lamp. a) How much energy does this lamp save during 100.0 h of use? Part 2 of 2 b) If electrical energy costs $0.080/kW·h, how much money is saved in 100.0 h? Chapter 27, section 10, Power in Household Circuits Holt SF 19Rev 53 27:10, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 Use the electric bill shown in the figure. In 33 days you used Read Date 01/21/00 12/19/99 Difference 471 kWh Meter # 0079051 60591 60120 471 Rate Calculation: Residential Service Rate, Multi-fuel Customer Charge: Energy: 471 kWh at $.03550/kWh Fuel: 471 kWh at $.01467/kWh Subtotal Electric Charges Sales Tax Total Cost for Electric Service For this 33 days period, your average daily cost for Electric service was $0.91 $6.00 16.72 6.91 $29.63 0.30 $29.93 a) How much energy was consumed in this billing cycle? Part 2 of 4 b) What is the average energy consumed per day in kilowatt-hours? Part 3 of 4 c) What is the average energy consumed per day in Joules? Part 4 of 4 d) If the cost of energy were increased to $0.15 /kWh, how much more would energy cost in this billing cycle? (Assume that the price of fuel remains constant.) Holt SF 19Rev 55 56 27:10, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 The power supplied to a typical black-andwhite television is 90.0 W when the set is con- 101 nected across a potential difference of 120 V. a) How much electrical energy does this set consume in 1.0 h? Part 2 of 2 A color television set draws about 2.5 A of current when connected to a potential difference of 120 V. b) How much time is required for it to consume the same energy that the black-andwhite model consumes in 1.0 h? Lightbulb100W 27:10, highSchool, numeric, > 1 min, normal. Part 1 of 3 A 100 W light bulb is plugged into a standard 120 V outlet. a) How much does it cost per month (31 days) to leave the light turned on? Assume electric energy cost of 6 cents/kW · h. Part 2 of 3 b) What is the resistance of the bulb? Part 3 of 3 c) What is the current in the bulb? Chapter 28, section 3, Resistance: Series Circuits 102 Concept 23 E44 28:03, highSchool, multiple choice, < 1 min, wording-variable. When a pair of identical resistors are connected in series, the A) current B) power C) voltage will be the same for each resistor. A B 1. Bulb A would again be brighter. 2. Bulb B would be brighter. 1. All of these 3. Either of the above would occur. 2. None of these Hewitt CP9 23 04 28:03, highSchool, multiple choice, < 1 min, normal. 3. A only 4. B only Part 1 of 2 In a circuit of two lamps in series, if the current through one lamp is 1 A, what is the current through the other lamp? 5. C only 6. A and B only 7. A and C only 8. B and C only Figuring Physics 21 28:03, highSchool, multiple choice, < 1 min, fixed. When the series circuit shown below E E B Part 2 of 2 If 6 V is applied to the above circuit and the voltage across the first lamp is 2 V, what is the voltage across the second lamp? Hewitt CP9 23 05 28:03, highSchool, multiple choice, < 1 min, normal. If 6 V are impressed across a circuit of two lamps in series and the voltage across the first lamp is 2 V, what is the voltage across the second lamp? Note: The lamps are not the same. 1. 4 V A is connected, Bulb A is brighter than Bulb B. If the positions of the bulbs were reversed, 2. 3 V 3. 12 V 4. 10 V 5. 9 V Chapter 28, section 3, Resistance: Series Circuits 6. 5 V Holt SF 20A 01 28:03, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A 12.0 V storage battery is connected to three resistors, 6.75 Ω, 15.3 Ω, and 21.6 Ω, respectively. The resistors are joined in series. Calculate the equivalent resistance. Part 2 of 2 What is the current in the circuit? Holt SF 20A 02 28:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A 4.0 Ω, an 8.0 Ω and a 12.0 Ω resistor are connected in series with a 24.0 V battery. Calculate the equivalent resistance. Part 2 of 3 What is the current in the circuit? 103 Part 3 of 4 Find the potential difference across the 5.0 Ω resistor. Part 4 of 4 Find the potential difference across the 7.0 Ω resistor. Holt SF 20A 04 28:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A series combination of two resistors, 7.25 Ω, and 4.03 Ω, is connected to a 9.00 V battery. Calculate the equivalent resistance of the circuit. Part 2 of 4 Calculate the current in the circuit. Part 3 of 4 What is the potential difference across the 7.25 Ω resistor? Part 3 of 3 What is the current in each resistor? Part 4 of 4 What is the potential difference across the 4.03 Ω resistor? Holt SF 20A 03 28:03, highSchool, numeric, < 1 min, wordingvariable. Holt SF 20A 05 28:03, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 4 Consider the circuit in the figure. 2Ω 4Ω 5Ω 7Ω 0.50 A E S Find the potential difference across the 2.0 Ω resistor. Part 2 of 4 Find the potential difference across the 4.0 Ω resistor. A 7.0 Ω resistor is connected in series with another resistor and a 4.5 V battery. The current in the circuit is 0.60 A. Calculate the value of the unknown resistance. Holt SF 20A 06 28:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Several light bulbs are connected in series across a 115 V source of emf. What is the equivalent resistance if the cur- Chapter 28, section 3, Resistance: Series Circuits 104 rent in the circuit is 1.70 A? variable. Part 2 of 2 If each light bulb has a resistance of 1.50 Ω, how many light bulbs are in the circuit? Part 1 of 3 18.0 Ω, 9.00 Ω, and 6.00 Ω resistors are connected in series with an emf source. The current in the 9.00 Ω resistor is measured to be 4.00 A. a) Calculate the equivalent resistance of the three resistors in the circuit. Holt SF 20Rev 16 28:03, highSchool, numeric, < 1 min, wordingvariable. A length of wire is cut into five equal pieces. If each piece has a resistance of 0.15 Ω, what was the resistance of the original length of wire? Holt SF 20Rev 27 28:03, highSchool, numeric, < 1 min, wordingvariable. Part 2 of 3 b) Find the potential difference across the emf source Part 3 of 3 c) Find the current in the other resistors. Holt SF 20Rev 37 28:03, highSchool, numeric, > 1 min, wordingvariable. An 8.0 Ω resistor and a 6.0 Ω resistor are connected in series with a battery. The potential difference across the 6.0 Ω resistor is measured as 12 V. Find the potential difference across the battery. Part 1 of 3 An 18 Ω resistor and a 6 Ω resistor are connected in series to an 18 V battery. Find the current in each resistor. Holt SF 20Rev 29 28:03, highSchool, numeric, < 1 min, wordingvariable. Part 2 of 3 Find the potential difference across the first resistor. A 9.0 Ω resistor and a 6.0 Ω resistor are connected in series to a battery, and the current through the 9.0 Ω resistor is 0.25 A. Find the potential difference across the battery. Part 3 of 3 Find the potential difference across the second resistor. Holt SF 20Rev 30 28:03, highSchool, numeric, < 1 min, wordingvariable. A 9.0 Ω resistor and a 6.0 Ω resistor are connected in series with an emf source. The potential difference across the 6.0 Ω resistor is measured with a voltmeter to be 12 V. Find the potential difference across the emf source. Holt SF 20Rev 31 28:03, highSchool, numeric, > 1 min, wording- Holt SF 20Rev 44 28:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 Two resistors A and B are connected in series to a 6 V battery. A voltmeter connected across resistor A measures a potential difference of 4 V. When the two resistors are connected in parallel across the 6 V battery, the current in B is found to be 2 A. Find the resistance of B. Part 2 of 2 Find the resistance of A. Chapter 28, section 3, Resistance: Series Circuits Short a Light Bulb 01 28:03, highSchool, multiple choice, > 1 min, fixed. Two identical light bulbs A and B are connected in series to a constant voltage source. Suppose a wire is connected across bulb B as shown. A E B After the wire is connected across B , 1. bulb A will go out and bulb B will go out. 2. bulb A will go out and bulb B will burn half as brightly as before. 3. bulb A will go out and bulb B will burn as brightly as before. 4. bulb A will burn twice as brightly as before and bulb B will go out. 5. bulb A will burn twice as brightly as before and bulb B will burn half as brightly as before. 6. bulb A will burn twice as brightly as before and bulb B will burn as brightly as before. 7. bulb A will burn as brightly as before and bulb B will go out. 8. bulb A will burn as brightly as before and bulb B will burn half as brightly as before. 9. bulb A will burn as brightly as before and bulb B will burn as brightly as before. 10. bulb A will burn four times as brightly as before and bulb B will go out. 105 Chapter 28, section 4, Resistance: Series/Parallel Combinations Four Resistors JMS 28:04, highSchool, multiple choice, > 1 min, normal. Four resistors are connected as shown in the figure. c 50 Ω Ω 10 b 30 Ω a 90 V 0Ω Part 2 of 4 Calculate the current in the 4.0 Ω resistor (second from the top). Part 3 of 4 Calculate the current in the 5.0 Ω resistor (third from the top). Part 4 of 4 Calculate the current in the 7.0 Ω resistor (fourth from the top). 7 S1 d Find the resistance between points a and b. Hewitt CP9 23 06 28:04, highSchool, numeric, < 1 min, normal. In a circuit of two lamps in parallel there is 6 V across one lamp. What is the voltage across the other lamp? Holt SF 20B 01 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A 9.0 V battery is connected to four resistors, as in the figure. 2Ω Holt SF 20B 02 28:04, highSchool, numeric, > 1 min, wordingvariable. A length of wire is cut into five equal pieces. The five pieces are then connected in parallel, with the resulting resistance being 24.0 Ω. What was the resistance of the original length of wire before it was cut up? Holt SF 20B 03 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A 4.0 Ω resistor, an 8.0 Ω resistor, and a 12.0 Ω resistor are connected in parallel across a 24.0 V battery. What is the equivalent resistance of the circuit? Part 2 of 4 What is the current in the 4.0 Ω resistor? Part 3 of 4 What is the current in the 8.0 Ω resistor? 4Ω 5Ω 7Ω I 106 9. 0 V S Calculate the current in the top 2.0 Ω resistor. Part 4 of 4 What is the current in the 12.0 Ω resistor? Holt SF 20B 04 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An 18.0 Ω, 9.00 Ω, and 6.00 Ω resistor are Chapter 28, section 4, Resistance: Series/Parallel Combinations connected in parallel to an emf source. A current of 4.00 A is in the 9.00 Ω resistor. Calculate the equivalent resistance of the circuit. 107 A 4 Ω resistor, an 8 Ω resistor, and a 12 Ω resistor are connected in parallel across a 24 V battery. a) Determine the equivalent resistance for the circuit. Part 2 of 4 What is the potential difference across the source? Part 2 of 2 b) Determine the current in the circuit. Part 3 of 4 Calculate the current in the 18.0 Ω resistor. Holt SF 20Rev 23 28:04, highSchool, numeric, < 1 min, normal. 18 Ω Part 4 of 4 Calculate the current in the 6.00 Ω resistor. 9Ω Holt SF 20C 01 28:04, highSchool, numeric, > 1 min, normal. Consider the circuit shown in the figure. 40 Ω 25 Ω 3Ω I 40 V 12 Ω 6Ω I 30 V S Find the equivalent resistance of the circuit shown in the figure. Holt SF 20Rev 24 28:04, highSchool, numeric, < 1 min, normal. Find its equivalent resistance. Holt SF 20C 02 28:04, highSchool, numeric, > 1 min, normal. Find the equivalent resistance of the circuit shown in the figure. 7Ω 7Ω Consider the circuit shown in the figure. 25 Ω 40 Ω 7Ω 7Ω 12 V 1.5 Ω 3Ω 15 Ω 25 V 18 Ω Find its equivalent resistance. Holt SF 20Rev 18 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Holt SF 20Rev 28 28:04, highSchool, numeric, < 1 min, wordingvariable. A 9.0 Ω resistor and a 6.00 Ω resistor are connected in parallel to a battery, and the current in the 9.0 Ω resistor is found to be 0.250 A. Find the potential difference across the battery. Chapter 28, section 4, Resistance: Series/Parallel Combinations 108 in the figure? Holt SF 20Rev 33 28:04, highSchool, numeric, > 1 min, wordingvariable. 6.0 Ω The equivalent resistance of the circuit in the figure is Req = 66.0 Ω . 17 Ω 89 Ω 6.0 Ω 89 Ω R 17 Ω E S 6.0 Ω Part 4 of 5 What is the equivalent resistance of the circuit in the figure? 6. 0 Ω 6.0 Ω 6.0 Ω Find the value of R. Holt SF 20Rev 34 28:04, highSchool, numeric, < 1 min, wordingvariable. Part 5 of 5 What is the equivalent resistance? 6.0 Ω 6. 0 Ω 6.0 Ω Two identical parallel-wired strings of 25 bulbs are connected to each other in series. If the equivalent resistance of the combination is 150.0 Ω when it is connected across a potential difference of 120.0 V, what is the resistance of each individual bulb? Holt SF 20Rev 39 28:04, highSchool, numeric, < 1 min, wordingvariable. Holt SF 20Rev 35 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 5 In the following circuit diagrams, each individual resistance is 6.0 Ω. What is the equivalent resistance of the circuit in the figure? 6. 0 Ω 6. 0 Ω Part 2 of 5 What is the equivalent resistance of the circuit in the figure? 6. 0 Ω 6. 0 Ω Part 3 of 5 What is the equivalent resistance of the circuit A resistor with an unknown resistance is connected in parallel to a 12 Ω resistor. When both resistors are connected in parallel to an emf source of 12 V, the current across the unknown resistor is measured with an ammeter to be 3 A. What is the resistance of the unknown resistor? Holt SF 20Rev 40 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Two resistors 18.0 Ω and 6.0 Ω are connected in parallel across an 18.0 V battery. a) Find the potential difference across each resistor. Part 2 of 3 b) Find the current in the first resistor. Chapter 28, section 4, Resistance: Series/Parallel Combinations Part 3 of 3 c) Find the current in the circuit. Holt SF 20Rev 41 28:04, highSchool, numeric, > 1 min, normal. In the circuit shown below, the current i in the resistor R doubles its original value when the switch S is closed. 10 Ω 90 Ω 109 Part 2 of 2 What can you do if you need a 5 Ω resistor? 1. 2 in series with 2 in parallel 2. 1 in series with 3 in parallel 3. 3 in series 4. 4 in series 5. 2 in series S 90 Ω 10 Ω R E i Find the value of R. 6. 2 in parallel 7. 3 in parallel 8. 4 in parallel 9. None of these Holt SF 20Rev 42 28:04, highSchool, multiple choice, > 1 min, normal. Holt SF 20Rev 47 28:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 You can obtain only four 20 Ω resistors from the stockroom. How can you achieve a resistance of 50 Ω under these circumstances? Part 1 of 2 The power supplied to the circuit shown in the figure is 4.00 W. 10.0 Ω 1. 2 in series with 2 in parallel 4.0 Ω 5. 0 Ω 3.0 Ω 2. 1 in series with 3 in parallel 3. 3 in series 4. 4 in series 5. 2 in series 6. 2 in parallel 7. 3 in parallel 8. 4 in parallel 9. None of these 3. 0 Ω E a) Find the equivalent resistance of the circuit. Part 2 of 2 b) Find the potential difference across the battery. Tetrahedron Resistors 02 28:04, highSchool, numeric, > 1 min, normal. Chapter 28, section 4, Resistance: Series/Parallel Combinations 7Ω Ω 21 7Ω A 21 2.5 Ω A tetrahedron (a four cornered, six edged, four sided body with congruent isosceles triangles as each side) has resistors on each of its edges and electric potential is across two of its corners, A and B , as shown in the figure. Let: Ii be the current through resistor Ri and Vi be the potential across resistor Ri . Hint: Simplify by using symmetry observations before applying straight-forward circuit analysis. 14 Ω Ω B What is the resistance between A and B using the given resistances? 110 Chapter 28, section 5, Potential Difference Between Two Points Battery with internal resistance 28:05, highSchool, numeric, > 1 min, normal. Part 1 of 2 The internal resistance r of a battery with emf E is connected to a load resistor with resistance R. 100 Ω I 10 V A 10 Ω B internal resistance Find the potential difference VBA = VA − VB . Part 2 of 2 What is the power P dissipated by the load resistor R? 1. P = E r+R 2 R 2. P = r E 2 E2 r E2 4. P = r+R 3. P = 5. P = E r+R 2 6. P = (r + R) E 2 7. P = R E 2 8. P = E R E2 r R E2 10. P = rR 9. P = 2 r r 111 Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules Five Bulbs 01 28:06, highSchool, multiple choice, > 1 min, fixed. Consider the following circuit containing identical bulbs A, B , C , D, and E respectively. Denote the potentials across bulbs as VA , VB , VC , VD , and VE . D E C B In the figure below consider the case where switch S1 is closed and switch S2 is open. c 30 Ω Ω 10 a 20 E Ω S2 50 V 2. VA = VB = VC = VD = VE 3. VA = VD = VE > VB > VC 4. VA = VD = VE > VB = VC 5. VB = VC > VA = VD = VE 6. VA = VB > VA = VD = VE 7. VA = VC > VB > VD = VE 8. VC > VB > VA > VD > VE 9. VE = VD > VA > VB = VC 10. VA = VB = VC > VD > VE Four Resistors 01 shortened 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 2 40 Ω S1 d Part 2 of 2 Now consider the case where switch S2 is also closed, so c 30 Ω Ω 10 20 Ω b S2 0Ω 4 50 V d Rank the potentials across the bulbs. 1. VA = VB = VC > VD = VE b Find the current in the path from a to c. a A 112 S1 Find the current in the path from a to c through the 10 Ω resistor. Four Resistors 02 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 Four resistors connected to a battery are shown in the figure below. The switch S1 is closed and switch S2 is left open. c 170 Ω 57 Ω a b S2 170 Ω 57 Ω 113 V d S1 What is the magnitude of the potential difference Vcd ? Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules Part 2 of 4 The potential difference Vcd is Four Resistors 04 28:06, highSchool, numeric, > 1 min, normal. 1. positive. Part 1 of 2 Four resistors are connected as shown in the figure. c 50 Ω 10 Ω a b Ω 70 Part 3 of 4 The switch S2 is closed. c 57 Ω 170 S2 Ω 113 V 170 30 Ω 2. negative. a 113 Ω b 57 Ω S1 d Find the resistance between points a and b. S1 d 90 V After closing the switch S2 , what is the potential difference Vad ? Part 2 of 2 What is the current through the 50 Ω resistor? Part 4 of 4 How much current passes through the switch S2 when it is closed? Four Resistors 06 28:06, highSchool, multiple choice, > 1 min, fixed. Four Resistors 03 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 2 All the bulbs in the figure below have the same resistance R. The switch S is initially closed. Part 1 of 2 Four resistors are connected as shown in the figure. c 90 V iB b 30 Ω a S Ω 50 Ω 10 iD 0Ω 7 d iA V S1 Find the resistance between points a and b. Part 2 of 2 What is the current in the 30 Ω resistor? iC i0 If bulb B is removed from the circuit, i.e., the switch S is opened, what happens to the current through 1) the battery, 2) bulb A, and 3) bulb D; i.e., the brightness of bulb A, and bulb D? Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules Hint: You may find it helpful to work out the currents through bulb A and bulb D, and the battery for both cases by using V = 1 volt and R = 1 Ω. 1. iA decreases, iD remains the same, ibattery decreases 2. iA increases, iD increases, ibattery increases 3. iA increases, iD increases, ibattery decreases 4. iA increases, iD remains the same, ibattery increases 5. iA remains the same, iD increases, ibattery increases 6. iA increases, iD increases, ibattery remains the same 7. iA increases, iD decreases, ibattery decreases 8. iA decreases, iD decreases, ibattery decreases 9. iA remains the same, iD remains the same, ibattery remains the same 10. iA decreases, iD decreases, ibattery remains the same 114 pens to the current through 1) the battery, 2) bulb A, and 3) bulb D; i.e., the brightness of bulb A, and bulb D? 1. iA increases, iD remains the same, ibattery increases 2. iA increases, iD increases, ibattery decreases 3. iA increases, iD increases, ibattery increases 4. iA decreases, iD remains the same, ibattery decreases 5. iA remains the same, iD increases, ibattery increases 6. iA increases, iD increases, ibattery remains the same 7. iA increases, iD decreases, ibattery decreases 8. iA decreases, iD decreases, ibattery decreases 10. iA remains the same, iD remains the same, ibattery remains the same Part 2 of 2 Four Resistors 07 28:06, highSchool, multiple choice, > 1 min, fixed. iD All the bulbs in the figure below above have the same resistance R. The switch S is initially closed. S iC iA V iB i0 If a wire is added to the circuit, what hap- Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 115 9. iA remains the same, iD remains the same, ibattery remains the same 10. iA decreases, iD decreases, ibattery remains the same iD S iB iA V iC i0 If bulb B is removed from the circuit, i.e., the switch S is opened, what happens to the current through 1) the battery, 2) bulb A, and 3) bulb D; i.e., the brightness of bulb A, and bulb D? You may find it helpful to work out the currents through bulb A and bulb D, and the battery for both cases by using V = 1 volt and R = 1 Ω. 1. iA decreases, iD remains the same, ibattery decreases 2. iA increases, iD increases, ibattery increases 3. iA increases, iD increases, ibattery decreases 4. iA increases, iD remains the same, ibattery increases 5. iA remains the same, iD increases, ibattery increases 6. iA increases, iD increases, ibattery remains the same 7. iA increases, iD decreases, ibattery decreases 8. iA decreases, iD decreases, ibattery decreases Four Resistors 08 28:06, highSchool, multiple choice, < 1 min, fixed. All the bulbs in the figure below have the same resistance R. The switch S is initially closed. iD S iB iA V iC i0 If bulb B is removed from the circuit, i.e., the switch S is opened, what happens to the currents through 1) the battery, 2) bulb A, and 3) bulb D; Notice that in the diagram the current through the battery, ibattery , is labeled as i0 . Hint: You may find it helpful to work out the currents through bulb A , bulb D , and the battery for both cases by using V = 1 volt and R = 1 Ω. 1. iA decreases, iD remains the same, ibattery decreases 2. iA increases, iD increases, ibattery increases 3. iA increases, iD increases, ibattery decreases 4. iA increases, iD remains the same, ibattery increases Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 5. iA remains the same, iD increases, ibattery increases 6. iA increases, iD increases, ibattery remains the same 7. iA increases, iD decreases, ibattery decreases 8. iA decreases, iD decreases, ibattery decreases 3. 4. 5. 6. 7. 8. i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 i0 116 5 2 9 = 2 = =5 =3 =1 10 3 2 = 5 1 = 2 = 9. iA remains the same, iD remains the same, ibattery remains the same 9. 10. iA decreases, iD decreases, ibattery remains the same 10. Four Resistors 10 28:06, highSchool, multiple choice, > 1 min, fixed. Hewitt CP9 23 07 28:06, highSchool, multiple choice, < 1 min, fixed. All the bulbs in the figure below above have the same resistance R. How does the sum of the currents flowing through the branches of a sample parallel circuit compare to the current that flows through the voltage source? 1. The sum of currents in the branches is bigger than the current of the voltage source. iD S iB 2. The sum of currents in the branches is equal to the current of the voltage source. iA V iC i0 i0 , where i0 is the current i0 through the battery when the switch is closed and i0 is the current through the battery when the switch is open. Determine i0 9 = i0 10 i 2 2. 0 = i0 3 1. 3. The sum of currents in the branches is smaller than the current of the voltage source. 4. It cannot be determined. Hewitt CP9 23 E40 28:06, highSchool, multiple choice, > 1 min, fixed. Part 1 of 4 In the circuit shown, the light bulbs are identical. Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 117 3. B is brighter. 4. A is brighter. A B C S V Which bulb is brightest? 1. A 2. B 3. C 4. A, B and C have the same brightnesses. 5. A and B are brighter than C . 6. It can’t be determined unless the voltage of the power supply is known. Part 2 of 4 Which lightbulb draws the most current? 1. C 2. B 3. A 4. A, B and C have the same current. 5. Both A and B turn off. 6. Can’t determine unless we know the voltage of the power supply. Part 4 of 4 What will happen if bulb C is unscrewed? 1. A short circuit occurs and the circuit catches fire. 2. A and B have same brightnesses. 3. B is brighter. 4. C is brighter. 5. A is brighter. 6. Can’t determine unless we know the voltage of the power supply. Holt SF 20D 01 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 6 Consider the circuit in the figure. 2. 0 Ω 8.0 Ω 10 Ω 5. 0 Ω 5. A and B have more current than C . 6. It can’t be determined unless the voltage of the power supply is known. Part 3 of 4 What will happen if bulb A is unscrewed? 1. A short circuit occurs and the circuit catches fire. 2. C is brighter. S 10 Ω 14.0 V 15 Ω a) Find the current in the 5.0 Ω resistor. Part 2 of 6 b) Find the potential difference across the 2.0 Ω resistor. Part 3 of 6 c) Find the potential difference across the 8.0 Ω resistor. Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules Part 4 of 6 d) Find the potential difference across either of the 10 Ω resistors. Part 5 of 6 e) Find the current in either one of the 10 Ω resistors. Part 6 of 6 f) Find the potential difference across the 15 Ω resistor. Holt SF 20Rev 25 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 3 Consider the circuit in the figure. 5. 5 Ω 8. 5 Ω 2. 5 Ω 12 V Find the current in the 2.5 Ω resistor. Part 2 of 3 Find the current in the 8.5 Ω resistor. Part 3 of 3 Find the current in the 5.5 Ω resistor. 6.0 Ω 3.0 Ω 6.0 Ω 4.0 Ω 2. 0 Ω 12.0 Ω 18.0 V 3.0 Ω Find the current in the 2.0 Ω resistor. Part 2 of 4 Find the potential difference across the 2.0 Ω resistor. Part 3 of 4 Find the potential difference across the 12.0 Ω resistor. Part 4 of 4 Find the current in the 12.0 Ω resistor. Holt SF 20Rev 36 28:06, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 4 Three small lamps are connected to a 9 V battery, as shown in the figure. Assume the battery is ideal (has no internal resistance and given in the figure) and the connecting wires have no resistance. Unlike most real bulbs, the resistances (given in the figure) of the bulbs do not vary. The switch S is closed. Holt SF 20Rev 26 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 Consider the circuit in the figure. 118 S 2Ω 4. 5 Ω 9V 3Ω a) What is the equivalent resistance of this circuit? Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 30.0 Ω Part 2 of 4 b) What is the total current of this circuit? Part 3 of 4 c) What is the current in the 3 Ω bulb? Part 5 of 5 e) Calculate the potential difference across the first resistor. Holt SF 20Rev 43 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 6 Four resistors are connected to a battery with a terminal voltage of 12.0 V, as shown in the figure. Part 3 of 6 c) Find the current in the 30.0 Ω resistor. Part 4 of 6 d) Find the power dissipated by the 50.0 Ω resistor. Part 5 of 6 e) Find the power dissipated by the 20.0 Ω resistor. Part 6 of 6 f) Find the power dissipated by the 90.0 Ω resistor. Holt SF 20Rev 46 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Consider the following circuit. 5. 0 Ω 3 .0 Ω 3.0 Ω 4. 0 Ω 2 .0 Ω 4.0 Ω Part 4 of 5 d) Calculate the current in the second resistor. Part 2 of 6 b) Find the current in the battery. 10.0 Ω Part 3 of 5 c) Calculate the current in the first resistor. 12.0 V a) Find the equivalent resistance of the circuit. 10.0 Ω Part 2 of 5 b) Calculate the current in the third resistor. 20.0 Ω 28 V Part 1 of 5 A 30.0 Ω resistor is connected in parallel to a 15.0 Ω resistor. These are joined in series to a 5.00 Ω resistor and a source with a potential difference of 30.0 V. a) Calculate the equivalent resistance. 50.0 Ω 90.0 Ω Part 4 of 4 d) What is the potential difference across the 4.5 Ω bulb? Holt SF 20Rev 38 28:06, highSchool, numeric, > 1 min, wordingvariable. 119 3.0 Ω a) Find the equivalent resistance. Part 2 of 2 Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules b) Find the current in the 5 Ω resistor. Resistance Circuit 05 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 3 In the circuit below R1 = R2 = R, R3 = 2 R, and R4 = 4 R. C R3 R1 A i1 R2 E I5 i2 R4 Seven Resistors 28:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Consider the circuit in the figure. 6.0 Ω 3.0 Ω 6.0 Ω 4.0 Ω 2. 0 Ω 12.0 Ω i4 D Find RAB when R = 1 Ω . Part 2 of 3 i3 Find the ratio . i4 i3 1. =2 i4 i3 2. =1 i4 i3 =3 3. i4 i3 =4 4. i4 i3 5. =8 i4 i3 1 6. = i4 2 i3 1 7. = i4 4 i3 1 8. = i4 8 i3 1 9. = i4 3 i3 10. =0 i4 Part 3 of 3 Let I = 5 A. Find i5 . B i3 120 18.0 V 3.0 Ω Find the current in the 2.0 Ω resistor. Part 2 of 3 Find the potential difference across the 2.0 Ω resistor. Part 3 of 3 Find the current in the 12.0 Ω resistor. Two Loop Circuit 01 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 2 Consider the circuit shown below. There are three resistors, r1 , r2 , and R; and two emf’s, E1 and E2 . The directions of the currents i1 , i2 , and i are shown in the figure. B E1 r1 A i1 R F C E2 i r2 E D i2 Apply Kirchhoff’s rules. What equation does the loop ABCDA yield? Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 1. E1 − E2 + i2 r2 − i1 r1 = 0 B E1 2. E1 − E2 − i2 r2 − i1 r1 = 0 C 5. E1 + E2 − i2 r2 − i1 r1 = 0 7. E1 + E2 + i2 r2 − i1 r1 = 0 i r2 D 2. E1 − E2 − i2 r2 − i1 r1 = 0 9. E1 − E2 − i1 r2 + i2 r1 = 0 3. E1 − E2 − i2 r2 + i1 r1 = 0 10. E1 − E − i1 r2 − i2 r1 = 0 Part 2 of 2 Hint: From symmetry, one expects i1 = i2 ) Let E1 = E2 = 10 V, r1 = r2 = 1 Ω, and R = 3 Ω. 10 V 1Ω B A i1 4. E1 − E2 + i2 r2 + i1 r1 = 0 5. E1 + E2 − i2 r2 − i1 r1 = 0 6. E1 + E2 + i2 r2 + i1 r1 = 0 7. E1 + E2 + i2 r2 − i1 r1 = 0 8. E1 + E2 − i2 r2 + i1 r1 = 0 E i 1Ω E2 E 1. E1 − E2 + i2 r2 − i1 r1 = 0 8. E1 + E2 − i2 r2 + i1 r1 = 0 C A i2 Apply Kirchhoff’s rules. What equation does the loop BADCB yield? 6. E1 + E2 + i2 r2 + i1 r1 = 0 10 V R F 4. E1 − E2 + i2 r2 + i1 r1 = 0 3Ω r1 i1 3. E1 − E2 − i2 r2 + i1 r1 = 0 F 121 D i2 Find the current i. Two Loop Circuit 02 28:06, highSchool, numeric, > 1 min, normal. Part 1 of 3 Consider the circuit shown below. There are three resistors, r1 , r2 , and R; and two emf’s, E1 and E2 . The directions of the currents i1 , i2 , and i are shown in the figure. 9. E1 − E2 − i1 r2 + i2 r1 = 0 10. E1 − E2 − i1 r2 − i2 r1 = 0 Part 2 of 3 What equation does the loop DCFED yield? 1. −E2 + i2 r2 + i R = 0 2. −E2 − i2 r2 − i R = 0 3. −E2 − i2 r2 + i R = 0 4. E2 − i2 r2 + i R = 0 5. E2 − i2 R + i r2 = 0 6. E2 + i2 R − i r2 = 0 Chapter 28, section 6, Complicated Circuits: Kirchoff’s Rules 7. −E2 − i2 R − i r2 = 0 9. E1 + i1 R1 + i3 R3 + E2 − i4 R4 − i2 R2 = 0 . 8. −E2 + i2 R + i r2 = 0 10. E1 − i1 R1 − i3 R3 + E2 + i4 R4 + i2 R2 = 0 . 9. E2 + i2 r2 − i1 R = 0 Part 2 of 3 Choose the correct relationships among the currents. 10. E2 − i2 r2 − i1 R = 0 Part 3 of 3 Let: E1 = E2 = 10 V, r1 = r2 = 1 Ω, and R = 3 Ω. Hint: From symmetry, one expects i1 = i2 . Find the current i. A1 : A2 : B1 : B2 : B3 : B4 : B5 : Two loops 28:06, highSchool, multiple choice, > 1 min, normal. R2 122 Part 1 of 3 E1 A B i 1 + i3 = i5 ; i 1 = i3 + i5 ; i1 > i2 and i3 i1 < i2 and i3 i1 > i2 and i3 i1 = i2 and i3 i1 < i2 and i3 R1 1. A1 and B1. i1 2. A1 and B2. 3. A1 and B3. 4. A1 and B4. 5. A1 and B5. i3 E2 For the loop ABCDEF A, the corresponding loop equation is given by 6. A2 and B1. 7. A2 and B2. 1. E1 + i1 R1 + i3 R3 + E2 + i4 R4 + i2 R2 = 0 . 8. A2 and B3. 2. E1 − i1 R1 − i3 R3 + E2 − i4 R4 − i2 R2 = 0 . 9. A2 and B4. 3. E1 + i1 R1 + i3 R3 −E2 + i4 R4 + i2 R2 = 0 . 10. A2 > i4 ; > i4 ; < i4 ; = i4 ; < i4 . and B5. i2 R5 F C i5 R4 E D R3 i4 4. E1 − i1 R1 − i3 R3 −E2 − i4 R4 − i2 R2 = 0 . 5. E1 + i1 R1 − i3 R3 −E2 − i4 R4 + i2 R2 = 0 . 6. E1 − i1 R1 + i3 R3 −E2 + i4 R4 − i2 R2 = 0 . 7. E1 + i1 R1 + i3 R3 −E2 − i4 R4 − i2 R2 = 0 . 8. E1 − i1 R1 − i3 R3 −E2 + i4 R4 + i2 R2 = 0 . Part 3 of 3 Given E1 = E 2 = E = 1 V , R1 = R 2 = R 3 = R 4 = R 5 = R = 2 Ω , find the value of i5 . Notice that the setup of the left loop is symmetric to the setup of the right loop. Chapter 28, section 7, RC Circuits 123 itor is steady. Bulbs in a Circuit 03 28:07, highSchool, multiple choice, < 1 min, fixed. 3. The bulb is on and is bright. 4. The current in the circuit is steady. Part 1 of 2 Unlike most real bulbs, the resistance of the bulb in the questions below does not change as the current through it changes. A capacitor, a bulb, and a switch are in the circuit as shown below. S R C The switch is initially open as shown in the above diagram, and the capacitor is charged. S R C 5. None of these is correct. Bulbs in a Circuit 04 28:07, highSchool, multiple choice, > 1 min, fixed. Unlike most real bulbs, the resistance of the bulb in this question does not change as the current through it changes. A capacitor, a bulb, and a switch are in the circuit as shown below. S R C The switch is initially open as shown in the above diagram, and the capacitor is charged. Which of the following correctly describes what happens to the bulb when the switch is closed? S R 1. The bulb is dim and remains dim. 2. At first the bulb is dim and it gets brighter and brighter until the brightness levels off. C Which of the following correctly describes what happens to the bulb when the switch is closed? 3. The bulb is bright and remains bright. 1. The bulb is dim and remains dim. 4. At first the bulb is bright and it gets dimmer and dimmer until it goes off. 2. At first the bulb is dim and it gets brighter and brighter until the brightness levels off. 5. None of these is correct. 3. The bulb is bright and remains bright. Part 2 of 2 Which correctly describes what happens after the switch has remained closed for a long time? 4. At first the bulb is bright and it gets dimmer and dimmer until it goes off. 5. None of these is correct. 1. The bulb is permanently off. 2. The potential difference across the capac- Charging RC Circuit 28:07, highSchool, multiple choice, > 1 min, Chapter 28, section 7, RC Circuits fixed. 124 R3 The switch S has been in position b for a long period of time. R3 C R2 E R1 C R2 R1 Sb a Sb E a When the switch is moved to position “a”, find the characteristic time constant. 1. τ = R1 C When the switch is moved to position “a”, find the characteristic time constant. 1. τ = R1 C 2. τ = R2 C 3. τ = 1 R1 C 1 4. τ = R2 C 5. τ = (R1 + R2 ) C 1 (R 1 + R 2 ) C R1 + R 2 7. τ = C 2 2 8. τ = (R 1 + R 2 ) C 6. τ = 9. τ = 10. τ = √ 2. τ = R2 C 3. τ = 1 R1 C 1 4. τ = R2 C 5. τ = (R1 + R2 ) C 1 (R 1 + R 2 ) C R1 + R 2 7. τ = C 2 2 8. τ = (R 1 + R 2 ) C 6. τ = 9. τ = 10. τ = √ R1 R2 C 1 R 1 R2 C R 1 R2 C Part 2 of 2 3.3 MΩ 1 R 1 R2 C Discharging RC Circuit 28:07, highSchool, multiple choice, > 1 min, normal. Part 1 of 2 The switch S has been in position b for a long period of time. 1.3 µF 2 MΩ 1.1 MΩ Sb 1.2 V a S has been left at position “a” for a long time. It is then switched from “a” to “b” at t = 0. Determine the energy dissipated through the resistor R2 alone from t = 0 to t = ∞. Series RC Circuit 07S 28:07, highSchool, multiple choice, > 1 min, Chapter 28, section 7, RC Circuits 125 normal. Part 1 of 2 Consider the RC circuit shown. The emf of the battery is V , the resistance R, and the capacitance C . The capacitor is uncharged. C R V Series rc circuit 28:07, highSchool, multiple choice, > 1 min, fixed. Consider the RC circuit shown. The emf of the battery is V , the resistance R, and the capacitance C . C R S Consider the following statements. A1: I = 0 V A2: I = R V −1/RC A3: I = e R B1: VC = 0 B2: VC = V B3: VC = V e−1/RC Immediately after the switch is closed, the current, I , and the potential across the capacitor, VC , are respectively given by 1. A2, B1 E i Consider the following statements. A1: I = 0 V A2: I = R V A3: I = e−1/(RC ) R B1: VC = 0 B2: VC = V B3: VC = V e−1/(RC ) After S has been closed for a very long time, the current through R and the potential across the capacitor are given respectively by: 2. A2, B2 1. A2, B1 3. A2, B3 2. A2, B2 4. A1, B1 3. A2, B3 5. A1, B2 4. A1, B1 6. A1, B3 5. A1, B2 7. A3, B1 6. A1, B3 8. A3, B2 7. A3, B1 9. A3, B3 8. A3, B2 Part 2 of 2 Find the time for the plate charge to reach one third of its maximum value if R = 1 Ω, C = 1 µf, V = 10 V. S 9. A3, B3 Chapter 28, section 9, Household Wiring and Electrical Safety Holt SF 20Rev 48 28:09, highSchool, numeric, > 1 min, normal. Your toaster oven and coffeemaker each dissipate 1200 W of power. You have a 120 V line in your kitchen. For what current must the circuit breaker be rated for you to operate both of these appliances at the same time? Holt SF 20Rev 49 28:09, highSchool, numeric, > 1 min, normal. Part 1 of 3 An electric heater is rated at 1300 W, a toaster is rated at 1100 W, and an electric grill is rated at 1500 W. The three appliances are connected in parallel across a 120 V emf source. Find the current in the heater. Part 2 of 3 Find the current in the toaster. Part 3 of 3 For what current must the circuit breaker be rated for you to operate all of these appliances at the same time? 126 Chapter 29, section 1, Magnetic Fields and Forces Conceptual 17 02 29:01, highSchool, numeric, > 1 min, normal. 127 6. downward 7. There is no force. Part 1 of 4 The strength of Earth’s magnetic field B at the equator is approximately equal to 5 × 10−5 T, where T stands for tesla, the unit of magnetic field. The force on a charge q moving in a direction perpendicular to a magnetic field is given by F = q v B , where v is the speed of the particle. The direction of the force is given by the right-hand rule. Suppose you rub a balloon in your hair and your head acquires a static charge of 3 × 10−9 C. If you are at the equator and driving west at a speed of 30 m/s, what is the strength of the magnetic force on your head due to Earth’s magnetic field? Part 2 of 4 What is the direction of that magnetic force? Part 4 of 4 If you are driving east, how fast would you have to drive in order for the magnetic force on your head to equal 200 N (probably enough to knock you over)? Conceptual 17 Q20 29:01, highSchool, multiple choice, < 1 min, fixed. A positively charged particle passes through a laboratory traveling in an easterly direction. There are both electric and magnetic field in the room and their effects on the charged particle cancel. If the electric field points upward, what must be the direction of the magnetic field? 1. east 1. east 2. west 2. west 3. north 3. south 4. south 4. north 5. upward 5. upward 6. downward 6. downward Part 3 of 4 If you are at the equator and driving north at a speed of 30 m/s, what is direction of the magnetic force on your head? 1. east 2. west Conceptual 24 Q04 29:01, highSchool, multiple choice, < 1 min, fixed. When you go in to have an MRI done, the technician always tells you to remove your watch, pens, and other metal objects from your pockets. Why is this request made? 3. north 4. south 5. upward 1. There is a strong magnetic field in the MRI machine. 2. There is a strong electric field in the MRI Chapter 29, section 1, Magnetic Fields and Forces machine. 3. There is a weak electric field in the MRI machine. 128 (for example, a baseball with some electrons removed) to the east, what is the direction of the magnetic force on the object? 1. downward Conceptual 24 Q06 29:01, highSchool, multiple choice, < 1 min, fixed. 2. toward the east 3. toward the west If all atoms have electrons that are in motion about an atom, why aren’t all materials magnetic? 1. The net magnetic field created by ordinary materials is zero. 2. Ordinary materials do not create magnetic fields. 3. Random motion of electrons does not create magnetic fields. Conceptual Q16 12 29:01, highSchool, multiple choice, < 1 min, fixed. 4. upward Conceptual Q16 16 29:01, highSchool, multiple choice, < 1 min, fixed. The magnetic field at the equator points north. If you throw a negatively charged object (for example, a baseball with some electrons removed) to the east, what is the direction of the magnetic force on the object? 1. upward 2. toward the east The Greeks had a legend that there was an island in the Mediterranean Sea made entirely of lodestone. They used this story as an argument that ships should not be built with iron nails. Because of this legend, why would they not use iron nails? 1. They had strong magnetic attraction. 2. They were not strong enough. 3. toward the west 4. downward Conceptual Q16 19 29:01, highSchool, numeric, < 1 min, normal. A small bar magnet pulls on a larger one with a force of 100 newtons. What is the magnitude of the force the larger one exerts on the smaller one? 3. They were expensive. 4. They were rarely found. Conceptual Q16 15 29:01, highSchool, multiple choice, < 1 min, fixed. The magnetic field at the equator points north. If you throw a positively charged object Field Direction 29:01, highSchool, multiple choice, < 1 min, fixed. The direction of the magnetic field in a certain region of space is determined by firing a test charge into the region with its velocity in various directions in different trials. The field direction is Chapter 29, section 1, Magnetic Fields and Forces 1. one of the direction of the velocity when the magnetic field is zero. 2. the direction of the velocity when the magnetic force is a maximum. 3. the direction of the magnetic force. 4. perpendicular to the velocity when the magnetic force is zero. 129 magnetic field. 3. Sometimes a magnetic field disappears when an electron is placed in it. 4. If the velocity of an electron is greater than a critical value, a magnetic field cannot exert any force on the electron. 5. Away from the Earth an electron does not feel any magnetic force. 5. None of these Hewitt CP9 24 E05 29:01, highSchool, multiple choice, < 1 min, fixed. Why is it inadvisable to make a horseshoe magnet from a flexible material? 1. A flexible material is not easily magnetized. 2. A flexible material is easily loses its magnetism. Hewitt CP9 24 E09 29:01, highSchool, multiple choice, < 1 min, fixed. Why will a magnet attract an ordinary nail or paper clip, but not a wooden pencil? 1. A nail or paper clip has magnetic domains which a wooden pencil does not have. 2. A nail or paper clip has a magnet inside which a wooden pencil does not have. 3. A flexible material cannot be easily made into a horseshoe shape. 3. A magnet can generate electromagnetic waves which can be absorbed by a nail but not by a pencil. 4. The poles of the magnet attract each other and will cause the magnet to bend. 4. A nail or paper clip has molecular circuits which a wooden pencil does not have. 5. None of these is correct. Hewitt CP9 24 E08 29:01, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 24 E10 29:01, highSchool, multiple choice, < 1 min, fixed. “An electron always experiences a force in an electric field, but not always in a magnetic field.” Defend this statement. A friend tells you that a refrigerator door, beneath its layer of white painted plastic, is made of aluminum. How could you check to see if this is true (without any scraping)? 1. An electron always has a charge in an electric field, but not always in a magnetic field. 1. Burn the refrigerator door and then analyze the remains with chemical reagents to find if aluminum is present. 2. An electric field always acts on charged particles. The magnetic force vanishes when the velocity of the electron is parallel to the 2. Apply a small magnet to the door. If it sticks, your friend might be right because aluminum is magnetic. If it doesn’t stick, Chapter 29, section 1, Magnetic Fields and Forces your friend might be wrong. 3. Apply a small magnet to the door. If it sticks, your friend is wrong because aluminum is not magnetic. If it doesn’t stick, your friend might be right, (but not necessarily). 4. It cannot be checked without scraping the painted plastic. Hewitt CP9 24 E21 29:01, highSchool, multiple choice, < 1 min, fixed. Why will a magnet placed in front of a television picture tube distort the picture? (Do NOT try this with a color set!) 130 strong magnet? If not, why not? If so, does it exert as much force on the magnet as the magnet exerts on it? 1. No force; the paper clip is not itself a magnet. 2. A smaller force; the magnetic field of the paper clip is much weaker than the magnetic field of the strong magnet. 3. Equal force; Newton’s third law applies here. 4. It depends on the material in the magnet. 5. None of these 1. The magnetic field will distort the TV signal. 2. The magnetic field will magnetize the materials in the TV screen. 3. Moving electrons in the TV set are deflected from their paths by magnetic field. 4. The iron parts in the TV set are magnetized and thus do not work properly. Hewitt CP9 24 E27 29:01, highSchool, multiple choice, < 1 min, fixed. Can an electron at rest in a magnetic field be set into motion by the magnetic field? What if it were at rest in an electric field? 1. yes; no 2. no; yes 5. None of these 3. yes for both Hewitt CP9 24 E22 29:01, highSchool, numeric, < 1 min, normal. Magnet A has twice the magnetic field strength of magnet B (at equal distance) and at a certain distance pulls on magnet B with a force of 50 N. With how much force, then, does magnet B pull on magnet A? Hewitt CP9 24 E24 29:01, highSchool, multiple choice, < 1 min, fixed. A strong magnet attracts a paper clip to itself with a certain force. Does the paper clip exert a force on the 4. no for both 5. It depends on the intensity of the fields, which is not provided in the problem. 6. None of these Hewitt CP9 24 E29 29:01, highSchool, multiple choice, < 1 min, fixed. A magnetic field can deflect a beam of electrons, but it cannot do work on the electrons to change their speed. Why? Chapter 29, section 1, Magnetic Fields and Forces 1. When a magnetic field does work on the electrons, the work is changed into light instead of increasing the energy of electrons. 131 2. a massive object at rest 3. a moving electric charge 2. A magnetic field can do work on the electrons to either increase or decrease the speed of the electrons; however, with timeaveraging their speeds remain constant. 3. Moving electrons change the magnetic field such that it cannot do work on the electrons. 4. The direction of a magnetic force is always perpendicular to the velocity of an electron, so it cannot do work on the electron. Hewitt CP9 24 E30 29:01, highSchool, multiple choice, < 1 min, fixed. Two charged particles are projected into a magnetic field that is perpendicular to their initial velocities. If the charges are deflected in opposite directions, what does this tell you about them? (Ignore the interaction between these two particles.) 1. They have opposite charges if their initial velocities are in the same direction. 2. Their velocities have opposite directions. 3. One particle is an electron and the other is a positive ion. 4. One particle comes from nature; the other is man-made. Hewitt CP9 24 R07 29:01, highSchool, multiple choice, < 1 min, fixed. What produces a magnetic field? 1. a nonuniform but time-constant electric field 4. a moving atom Holt SF 21A 01 29:01, highSchool, numeric, < 1 min, wordingvariable. A proton moves perpendicularly to a magnetic field that has a magnitude of 4.20 × 10−2 T. The charge on a proton is 1.60×10−19 . What is the speed of the particle if the magnitude of the magnetic force on it is 2.40 × 10−14 N? Holt SF 21A 02 29:01, highSchool, numeric, < 1 min, wordingvariable. A proton traveling to the right along the x-axis enters a region where there is a magnetic field of magnitude 2.5 T directed upward along the y -axis. The charge on a proton is 1.60×10−19 . If the proton experiences a force of 3.2 × 10−12 N, find its speed. Holt SF 21A 03 29:01, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 An electron in an electron beam experiences a downward force of 2.0 × 10−14 N while traveling in a magnetic field of 8.3 × 10−2 T west. The charge on a proton is 1.60×10−19 . a) What is the magnitude of the velocity? Part 2 of 2 b) What is its direction? 1. North 2. East Chapter 29, section 1, Magnetic Fields and Forces 3. South 1. North 4. West 2. South 5. None of these 132 3. West Holt SF 21A 04 29:01, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A uniform 1.5 T magnetic field points north. If an electron moves vertically downward (toward the ground) with a speed of 2.5 × 107 m/s through this field. The charge on a proton is 1.60×10−19 . a) What is the magnitude of the force acting on it? Part 2 of 2 b) What is the direction of the force? 1. North 2. South 3. West 4. East 5. None of these Holt SF 21A 05 29:01, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A proton moves straight upward (away from the ground) through a uniform magnetic field that points from east to west and has a magnitude of 2.5 T. The charge on a proton is 1.60×10−19 . a) If the proton moves with a speed 1.5 × 107 m/s through this field, what is the magnitude of the force acting on it? Part 2 of 2 b) What is its direction? 4. East 5. None of these Holt SF 21A 06 29:01, highSchool, numeric, < 1 min, normal. An alpha particle (the nucleus of a helium atom, carrying a charge of 3.2 × 10−19 C moves at 5.5 × 107 m/s at a right angle to a magnetic field. The charge on a proton is 3.2 × 10−19 C. If the particle experiences a force of 1.5 × 10−14 N due to the magnetic field, what is the magnitude of the magnetic field? Holt SF 21Rev 30 29:01, highSchool, numeric, < 1 min, wordingvariable. A duck flying due east passes over Atlanta, where the magnetic field of the Earth is 5.0 × 10−5 T directed north. The duck has a positive charge of 4.0 × 10−8 C. If the magnetic force acting on the duck is 3.00 × 10−11 N upward, what is the magnitude of the duck’s velocity? Holt SF 21Rev 31 29:01, highSchool, numeric, < 1 min, wordingvariable. A proton moves eastward in the plane of Earth’s magnetic equator so that its distance from the ground remains constant. The acceleration of gravity is 9.81 m/s2 and the charge on a proton is 1.60×10−19 . What is the speed of the proton if Earth’s magnetic field points north and has a magnitude of 5.0 × 10−5 T? Holt SF 21Rev 34 Chapter 29, section 1, Magnetic Fields and Forces 29:01, highSchool, numeric, > 1 min, wordingvariable. 133 3. Negative y direction 4. Positive y direction Part 1 of 2 A proton moves at 2.50 × 106 m/s horizontally at a right angle to a magnetic field. The acceleration of gravity is 9.81 m/s2 . What is the strength of the magnetic field required to exactly balance the weight of the proton and keep it moving horizontally? Part 2 of 2 What is its direction? 1. In a horizontal plane 2. In a vertical plane 3. None of these Holt SF 21Rev 38 29:01, highSchool, numeric, < 1 min, wordingvariable. A proton moves at a speed of 2.0 × 107 m/s at right angles to a magnetic field with a magnitude of 0.10 T. Find the magnitude of the acceleration of the proton. 5. Negative z direction 6. Positive z direction 7. None of these Holt SF 21Rev 40 29:01, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A proton travels with a speed of 3.0 × 106 m/s at an angle of 37◦ west of north. A magnetic field of 0.30 T points to the north. Find the magnitude of the magnetic force on the proton. (The magnetic force experienced by the proton in the magnetic field is proportional to the component of the proton’s velocity that is perpendicular to the magnetic field.) Part 2 of 3 What is its direction? 1. North Holt SF 21Rev 39 29:01, highSchool, numeric, < 1 min, wordingvariable. 2. South Part 1 of 2 A proton moves perpendicularly to a uniform magnetic field, B, with a speed of 1.0 × 107 m/s and experiences an acceleration of 2.0 × 1013 m/s2 in the positive x direction when its velocity is in the positive z direction. Find the magnitude of the field. 4. East Part 2 of 2 What is its direction? 1. Negative x direction 2. Positive x direction 3. West 5. out of the Earth 6. into the Earth 7. None of these Part 3 of 3 Find the magnitude of the proton’s acceleration as it moves through the magnetic field. Chapter 29, section 2, Magnetism from Electric Currents 134 Conceptual 17 Q01 29:02, highSchool, multiple choice, < 1 min, fixed. Conceptual 17 Q19 29:02, highSchool, multiple choice, > 1 min, fixed. The figure represents two long, straight, parallel wires extending in a direction perpendicular to the page. The current in the left wire runs into the page and the current in the right runs out of the page. Part 1 of 3 A long straight wire is aligned north-south and carries current in the northerly direction. What is the direction of the magnetic field created directly above the wire? a b c 1. east 2. west What is the direction of the magnetic field created by these wires at location a, b and c? (b is midway between the wires.) 1. up, up, down 2. up, down, up 3. down, down, up 4. down, zero, up 5. up, zero, down 6. down, up, down Conceptual 17 Q12 29:02, highSchool, multiple choice, < 1 min, fixed. A current is flowing clockwise around a loop placed on your desk. What would be the direction of the resulting magnetic field inside the loop? 1. downward 2. upward 3. clockwise 4. counterclockwise 5. no magnetic field was generated. 3. south 4. north 5. upward 6. downward Part 2 of 3 What is the direction of the magnetic field created immediately to the left of the wire? 1. east 2. west 3. south 4. north 5. upward 6. downward Part 3 of 3 If a proton is traveling north directly above the wire, what is the direction of the magnetic force on the proton due to the wire? 1. east 2. west 3. south Chapter 29, section 2, Magnetism from Electric Currents 4. north 5. upward 6. downward 135 Chapter 29, section 3, Magnetic Force on a Current-Carrying Conductor 136 Drummond HW2 01 29:03, highSchool, numeric, > 1 min, normal. A wire carrying a current 30 A has a length 0.12 m between the pole faces of a magnet at an angle 60 ◦ (see the figure). The magnetic field is approximately uniform at 0.9 T. We ignore the field beyond the pole pieces. I I I B a b F B θ What is the force on the wire? Drummond HW2 02 29:03, highSchool, numeric, > 1 min, normal. A rectangular loop of wire hangs vertically as shown in the figure. A magnetic field is directed horizontally, perpendicular to the wire, and points out of the page at all points as represented by the symbol . The magnetic field is very nearly uniform along the horizontal portion of the wire ab (length is 0.1 m) which is near the center of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward force (in addition to the gravitational force) of 3.48 × 10−2 N when the wire carries a current 0.245 A. What is the magnitude of the magnet field B at the center of the magnet? Drummond HW2 05 29:03, highSchool, numeric, > 1 min, normal. The two wires of length 2 m are 3 mm apart and carry a current of 8 A dc. Calculate the force between these wires. Holt SF 21B 01 29:03, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A 6.0 m wire carries a current of 7.0 A toward the +x direction. A magnetic force of 7.0 × 10−6 N acts on wire in the −y direction. a) Find the magnitude of the magnetic field producing the force. Part 2 of 2 b) What is its direction? 1. +x direction 2. −x direction 3. +y direction 4. −y direction 3. +z direction 4. −z direction Chapter 29, section 3, Magnetic Force on a Current-Carrying Conductor 5. None of these Holt SF 21B 02 29:03, highSchool, numeric, < 1 min, wordingvariable. A wire 1.0 m long experiences a magnetic force of 0.50 N due to a perpendicular uniform magnetic field. If the wire carries a current of 10.0 A, what is the magnitude of the magnetic field? Holt SF 21B 03 29:03, highSchool, numeric, < 1 min, wordingvariable. The magnetic force on a straight 0.15 m segment of wire carrying a current of 4.5 A is 1.0 N. What is the magnitude of the component of the magnetic field that is perpendicular to the wire? Holt SF 21B 04 29:03, highSchool, numeric, < 1 min, wordingvariable. The magnetic force acting on a wire that is perpendicular to a 1.5 T uniform magnetic field is 4.4 N. If the current in the wire is 5.0 A, what is the length of the wire that is inside the magnetic field? Holt SF 21Rev 32 29:03, highSchool, numeric, < 1 min, wordingvariable. A wire carries a 10.0 A current at an angle 90.0◦ from the direction of a magnetic field If the magnitude of the magnetic force on a 5.00 m length of the wire is 15.0 N, what is the strength of the magnetic Field? Holt SF 21Rev 33 29:03, highSchool, numeric, < 1 min, wordingvariable. 137 A thin 1.00 m long copper rod in a uniform magnetic field has a mass of 50.0 g. When the rod carries a current of 0.245 A, it floats in the magnetic field. The acceleration of gravity is 9.81 m/s2 . What is the field strength of the magnetic field? Holt SF 21Rev 41 29:03, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 In the figure, a 15 cm length of conducting wire that is free to move is held in place between two thin conducting wires. All of the wires are in a magnetic field. When a 5.0 A current is in the wire, as shown in the figure, the wire segment moves upward at a constant velocity. The acceleration of gravity is 9.81 m/s2 . 15 cm 5A 5A 5A a) Assuming the wire slides without friction on the two vertical conductors and has a mass of 0.15 kg, find the magnitude of the minimum magnetic field that is required to move the wire. Part 2 of 2 b) What is its direction? 1. Out of the page 2. Into the page 3. Toward the left edge of the page 4. Toward the right edge of the page 5. Toward the top edge of the page 6. Toward the bottom edge of the page Chapter 29, section 3, Magnetic Force on a Current-Carrying Conductor 7. None of these Holt SF 21Rev 42 29:03, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A 15 A current is directed along the positive x-axis and perpendicular to a uniform magnetic field. The conductor experiences a magnetic force per unit length of 0.12 N/m in the negative y direction. Calculate the magnitude of the magnetic field in the region through which the current passes. Part 2 of 2 What is its direction? 1. positive x direction 2. negative x direction 3. positive y direction 4. negative y direction 5. positive z direction 6. negative z direction 7. None of these Sliding 29:03, highSchool, numeric, > 1 min, normal. A metal wire of mass 50 kg slides without friction on two horizontal rails spaced a distance of 50 m apart. The track lies in a vertical uniform magnetic field of 50 T. A constant current 50 A from a generator flows down one rail, across the wire, down the other rail back to the generator. Find the velocity of the wire at t = 50 s, assuming it to be at rest at t = 0. 138 Chapter 29, section 5, Motion of a Charged Particle in a Magnetic Field Circular Motion mid2 29:05, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Consider the circular motion of a positively charged particle in the plane of this paper, due to a constant magnetic field B which points out of the paper. Neglect the effects due to gravity. B B What is the direction of the orbital motion of the particle? 1. counterclockwise 2. clockwise 3. Unable to determine Part 2 of 2 What is the radius of the orbit? 1. r = 2. r = 3. r = 4. r = 5. r = 6. r = 7. r = 8. r = qv mB qB mv mB qv mv qB qm vB vB qm m v2 qB qB m v2 139 q v2 mB v2 B 10. r = qm 9. r = Holt SF 21Rev 43 29:05, highSchool, numeric, < 1 min, wordingvariable. A proton moves in a circular path perpendicular to a constant magnetic field so that it takes 1.00 × 10−6 s to complete the revolution. Determine the strength of the constant magnetic field. The angular speed is given in radians per unit time. Holt SF 21Rev 44 29:05, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A single charged positive ion that has a mass of 6.68 × 10−27 kg moves clockwise with a speed of 1.00 × 104 m/s. The positively charged ion moves in a circular path that has a radius of 3.00 cm. Find the strength of the uniform magnetic field. Part 2 of 2 What is its direction? 1. toward the observer 2. away from the observer 3. to the observer’s left 4. to the observer’s right 5. None of these Holt SF 21Rev 45 29:05, highSchool, numeric, < 1 min, wordingvariable. Assume that Earth’s magnetic field is everywhere perpendicular to the path of a proton and that Earth’s magnetic field has an Chapter 29, section 5, Motion of a Charged Particle in a Magnetic Field intensity of 4.00 × 10−8 T. What speed would a proton need to achieve in order to circle Earth 1000.0 km above the magnetic equator? Holt SF 21Rev 46 29:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An electron moves in a circular path perpendicular to a magnetic field that has a magnitude of 1.00 × 10−3 T. The angular momentum of the electron as it moves around the center of the circle is 4.00 × 10−25 J·s. Find the radius of the circular path. Part 2 of 2 Find the speed of the electron. 140 Chapter 29, section 10, Cyclotrons and Synchrotrons Hewitt CP9 24 E31 29:10, highSchool, multiple choice, < 1 min, fixed. A beam of high-energy protons emerges from a cyclotron. Is there a magnetic field associated with these particles? Why or why not? 1. There is a magnetic field associated with these protons because they are positively charged and in motion. 2. There is no magnetic field associated with these protons because there is an electric field around them. 3. There is a magnetic field associated with these protons because they have very high energy. 4. There is no magnetic field associated with these protons because they have a positive charge. 141 Chapter 29, section 11, Mass Spectrometer Hewitt CP9 24 E36 29:11, highSchool, multiple choice, < 1 min, fixed. In a mass spectrometer, ions are directed into a magnetic field, where they curve around a magnetic field line and strike a detector. If a variety of singly ionized atoms travel at the same speed through the magnetic field, what kind of deflection would you expect? 1. All of them should be deflected by the same amount. 2. The ions with smaller masses will be bent more. 3. The ions with smaller masses will be bent less. 4. It cannot be predicted. 142 Chapter 30, section 2, Magnetic Field Due to a Straight Wire Current Induced by Wire 30:02, highSchool, multiple choice, > 1 min, wording-variable. wire Consider a long straight wire and a wire loop in the same plane. The long wire has a current flowing in the direction shown. The wire loop is moving in the direction shown. straight I v wire loop The current in the loop is flowing 1. clockwise. 2. counter-clockwise. 3. There is no current in the loop. Drummond HW2 03 30:02, highSchool, numeric, > 1 min, normal. A vertical electric wire in the wall of a building carries a DC current of 25 A upward. x I S E (out) N What is the magnitude of the magnet field at a point 0.1 m due north of this wire? 143 Chapter 30, section 3, Magnetic Force Between Two Parallel Conductors Hewitt CP9 24 E40 30:03, highSchool, multiple choice, < 1 min, fixed. Will a pair of parallel current-carrying wires exert forces on each other? 2. 3. 4. 1. No; the magnetic field generated by the currents of the wires does not affect the wires themselves. 5. 2. No; the two wires attract each other by the magnetic field generated by their currents and repel each other due to the like charges of the moving particles in the wires. The two forces are equal in magnitude. 7. 6. 8. 9. 3. Yes; the magnetic field generated by the current in one wire is perpendicular to the current in the other wire and vise versa. 4. Yes; the wires are electrically charged. 5. No; no net magnetic field is generated. Wires with different currents 30:03, highSchool, multiple choice, > 1 min, fixed. Consider two parallel wires where the magnitude of the left current is 2 I0 and that of the right current is I0 . Point A is midway between the wires, and B is an equal distance on the other side of the wires. A B The ratio of the magnitude of the magnetic field at point A to that at point B is 1. 5 BA = BB 2 10. BA BB BA BB BA BB BA BB BA BB BA BB BA BB BA BB BA BB =2 =4 =3 =9 4 3 2 = 3 1 = 2 1 = 3 = =0 144 Chapter 30, section 4, Ampere’s Law Crossed Wires 30:04, highSchool, multiple choice, > 1 min, fixed. A long straight wire 1 lies along the x-axis. A long straight wire 2 lies along the y -axis so as to pass very near, but not quite touch wire 1 at the origin. If both wires are free to move, what happens when currents are sent simultaneously in the +x direction through wire 1 and in the +y direction through wire 2? [Note: “clockwise around origin” refers to an observer looking down on an xy plane in which +x is to the right and +y upward]. 1. Neither wire moves. 2. 1 accelerates in the +y direction, 2 in the +x direction. 3. 1 accelerates in the −y direction, 2 in the +x direction. 4. 1 accelerates in the −y direction, 2 in the -x direction. 5. 1 accelerates in the +y direction, 2 in the -x direction. 6. 1 rotates counterclockwise, 2 clockwise around the origin. 7. 1 rotates clockwise, 2 counterclockwise around the origin. 8. Both wires rotate counterclockwise around the origin. 9. Both wires rotate clockwise around the origin. 10. Both wires accelerate along the direction of current flow. 145 Chapter 30, section 5, The Magnetic Field of Current Loops Conceptual 17 Q03 30:05, highSchool, multiple choice, < 1 min, fixed. An electric current runs through a coil of wire as shown. A permanent magnet is located to the right of the coil. The magnet is free to rotate. N i i S Pivot What will happen to the magnet if its original orientation is as shown in the figure? 1. rotate clockwise 2. rotate counterclockwise 3. remain still 4. Unable to determine Hewitt CP9 25 E02 30:05, highSchool, multiple choice, < 1 min, fixed. Why does an iron core increase the magnetic induction of a coil? 1. An iron core can increase the current in the coil. 2. The magnetic domains that become aligned in the iron core contribute to increase the overall magnetic field of the coil. 3. An iron core can generate an electromagnetic wave to change the magnetic field in a coil. 4. An iron core is a magnet and generates a magnetic field with or without a coil. 146 Chapter 30, section 9, Gauss’s Law in Magnetism Gauss Law Magnetism 30:09, highSchool, multiple choice, < 1 min, fixed. Gauss’ law for magnetism tells us 1. the net charge in any given volume. 2. that the line integral of a magnetic field around any closed loop vanishes. 3. the magnetic field of a current element. 4. that the magnetic monopoles do not exist. 5. that charges must be moving to produce magnetic fields. 147 Chapter 30, section 12, Magnetism in Matter 148 3. No difference Conceptual 17 Q08 30:12, highSchool, multiple choice, < 1 min, fixed. What is the underlying basis of the magnetic field in a magnetized piece of iron? Two Magnetic Moments 30:12, highSchool, multiple choice, < 1 min, fixed. Given: A loop with current I produces a magnetic moment µ , as shown below. 1. The motion of electrons constitues an electric current which produces a magnetic field. µ 2. The charge in the atom produces a magnetic field. 3. The magnetic monopole in the atom creates the magnetic field. Conceptual 24 Q08 30:12, highSchool, multiple choice, < 1 min, fixed. A normal piece of iron produces no external magnetic field. Suppose a piece of iron consisted of one very large domain instead of many small ferromagnetic domains. Would this piece of iron produce an external magnetic field? 1. No. It does not create magnetic field because the net magnetic field is zero. 2. No. It does not create magnetic field at all. 3. Yes. It creates magnetic field. Conceptual 24 Q13 30:12, highSchool, multiple choice, < 1 min, fixed. What is the difference of one material having larger Curie constant than another (when placed in an applied magnetic field)? Consider the following four configurations of two loops each, A, B , C , and D. The placement and current directions of the loops are shown below. The loops are characterized by their magnetic moments µ. µ µ A B µ Cµ µ µ µ µD For configurations A and B , assume that the two current loops have the same axis and move freely along the axis. For configurations C and D, assume that the two current loops are on in same plane and move freely only in that plane. In which case(s) are the current loops attracted to one-another? 1. A, C 2. A 1. Produces stronger extra magnetic field. 3. B 2. Produces weaker extra magnetic field. 4. C Chapter 30, section 12, Magnetism in Matter 5. D 6. A, D 7. B , C 8. B , D 9. None of these. 149 Chapter 30, section 13, Diamagnetism Conceptual 24 Q07 30:13, highSchool, multiple choice, < 1 min, fixed. Compare the way that the motion of electrons in a diamagnetic material creates an opposing magnetic field with the way electrons in a copper wire accomplish the same end. 1. They have the same motion. 2. Diamagnetic material creates a magnetic field making the motion of electrons faster. 3. Magnetic field created by the copper wire makes the motion of electrons faster. 150 Chapter 30, section 14, Paramagnetism 151 rection. Conceptual 24 Q09 30:14, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 2 A paramagnetic material will acquire a magnetization if it is placed in an applied magnetic field. What happens to the magnetization of a paramagnetic material if the temperature of the material is quadrupled? 1. decrease by a factor of 4 2. decrease by a factor of 2 3. decrease by a factor of 3 5. increase by a factor of 4 6. No change Part 2 of 2 What happens to the magnetization of a paramagnetic material if the temperature of the material and the applied magnetic field is simultaneously quadrupled? 1. decrease by a factor of 4 2. decrease by a factor of 2 3. decrease by a factor of 3 5. increase by a factor of 4 6. No change Paramagnet 30:14, highSchool, multiple choice, < 1 min, fixed. A magnetic field B0 is applied to a paramagnet at room temperature. In the interior, the field produced by the magnetic dipoles of this substance is 1. greater than B0 and in the opposite di- 2. less than B0 and in the opposite direction. 3. greater than B0 and in the same direction. 4. less than B0 and in the same direction. 5. the same as B0 . Chapter 31, section 1, Faraday’s Law of Induction Brightest Light Bulb 31:01, highSchool, multiple choice, > 1 min, wording-variable. A conducting loop (octagonal) around a magnetic field (circular) contains three lightbulbs (labeled A, B , and C ). The wires connecting the bulbs are ideal, with no resistance. The loop is ground at one point as shown in the figure below. The magnetic field is increasing rapidly. B B B B B A C Initial Case: The circuit consists of two identical light bulbs of equal resistance, R, connected in series, leading to a loop equation E − 2 i R = 0. i Figure 1: B B X Y B B i Primed Case: Now connect the points C and D with a wire CAD, (see the figure below). i3 Figure 2: D i1 Rank order the brightness of the three bulbs, from brightest to least bright. 1. None of these. 152 B A B X Y B i2 B 2. A > B > C 3. A > C > B 4. A > B = C 5. A = C > B 6. B > C > A Circuit Around a Solenoid 04 31:01, highSchool, multiple choice, > 1 min, fixed. A solenoid with circular cross section produces a steadily increasing magnetic flux through its cross section. There is an octagonally shaped circuit surrounding the solenoid as shown below. The increasing magnetic flux gives rise to a counterclockwise induced emf E . i3 C What happens after the points C and D are connected by a wire as in the second (primed) case? 1. Bulb Y goes out and bulb X gets brighter. 2. Bulb X goes out and bulb Y gets brighter. 3. Bulb Y goes out and bulb X remains at the same brightness. 4. Bulb X goes out and bulb Y remains at the same brightness. 5. Bulb Y goes out and bulb X gets dim- Chapter 31, section 1, Faraday’s Law of Induction 153 mer. 6. Bulb X goes out and bulb Y gets dimmer. Conceptual 17 Q17 31:01, highSchool, multiple choice, < 1 min, fixed. Assume you wrap a wire around Earth’s equator at an altitude of 200 kilometers and run an electric current through it in the westerly direction. What effect would this have on the Earth’s natural magnetic field at the Earth’s surface? 1. reinforcing the field 2. canceling the field 3. no effect 4. Unable to determine Faraday Equation 31:01, highSchool, multiple choice, < 1 min, fixed. Suppose you are looking into the end of a long cylindrical tube in which there is a uniform magnetic field pointing away from you. What is the direction of the induced electric field if the magnitude of the magnetic field is decreased with time? 1. clockwise 2. counterclockwise 3. toward you 4. away from you 5. radially outward from the axis of the tube 6. radially inward toward the axis of the tube Hewitt CP9 25 R01 31:01, highSchool, multiple choice, < 1 min, fixed. Exactly what was it that Michael Faraday and Joseph Henry discovered? 1. The force acting on an electron in a magnetic field is perpendicular to its velocity. 2. A wire of constant current can produce a magnetic field. 3. Voltaic cells 4. Electric current can be produced in a wire simply by moving a magnet in or out of a coiled part of the wire. Holt SF 22A 02 31:01, highSchool, numeric, > 1 min, wordingvariable. A coil with 205 turns of wire, a total resistance of 23 Ω, and a cross-sectional area of 0.25 m2 is positioned with its plane perpendicular to the field of a powerful electromagnet. What average current is induced in the coil during the 0.25 s that the magnetic field drops from 1.6 T to 0.0 T? Holt SF 22A 03 31:01, highSchool, numeric, > 1 min, wordingvariable. A circular wire loop with a radius of 0.33 m is located in an external magnetic field of strength +0.35 T that is perpendicular to the plane of the loop. The field strength changes to −0.25 T in 1.5 s. (The plus and minus signs for a magnetic field refer to opposite directions through the coil.) Find the magnitude of the average induced emf during this interval. Holt SF 22Rev 11 31:01, highSchool, numeric, > 1 min, wordingvariable. Chapter 31, section 1, Faraday’s Law of Induction A rectangular coil 0.055 m by 0.085 m is positioned so that its cross-sectional area is perpendicular to the direction of a magnetic field. The coil has 75 and a total resistance of 8.7 Ω and the field decreases at a rate of 3.0 T/s. What is the magnitude of the induced current in the coil? Holt SF 22Rev 42 31:01, highSchool, numeric, > 1 min, wordingvariable. A bolt of lightning, such as the one shown on the left in the figure below, behaves like a vertical wire conducting electric current. As a result, it produces a magnetic field whose strength varies with the distance from the lightning. A 105-turn circular coil is oriented perpendicular to the magnetic field, as shown in the figure. 0.833 m The coil has a radius of 0.833 m. The magnetic field at the coil drops from 4.72 ×10−3 T to 0.00 T in 10.5 µs. What is the average emf induced in the coil? 154 Chapter 31, section 2, Motional EMF 155 Conceptual 17 03 31:02, highSchool, numeric, > 1 min, normal. 2. The motor would rotate with an constant speed even if you stop turning it. Part 1 of 3 In the laboratory, you have arranged to have a magnetic field that points north with a strength of 0.5 T and an electric field that points downward with a strength 6 × 106 N/C. An electric charge with a magnitude 9 × 10−9 C passes through the laboratory. The force on the charge due to the electric field is given by F = q E . The force on the charge due to the magnetic field is given by F = q v B , where v is the speed of the particle. The direction of the magnetic force is given by the right-hand rule. Neglect the gravitational force. What direction would the charge have to travel in order for it to pass through the room undeflected? 3. There would be no current in the wires. 1. east 2. west 3. north 4. south 5. downward 6. upward Part 2 of 3 What is the strength of the electric force? Part 3 of 3 How fast would it have to travel so that it passes through the room undeflected? Conceptual 17 Q07 31:02, highSchool, multiple choice, < 1 min, fixed. If you took an electric motor and turned it by hand, what would happen then? 1. Current would flow in the wires. Chapter 31, section 3, Lenz’s Law Conceptual 17 Q15 31:03, highSchool, multiple choice, < 1 min, fixed. A bar magnet is dropped, north pole down, so that it falls through a circular piece of wire, as shown. S N What is the direction of the induced current in the loop before it passes through the wire (viewed from top)? After it passes through? 156 3. The magnet will slow down because the changing magnetic field will induce current in the loop, which will interact with the magnet and repel it. 4. None of these Light Bulb and Solenoid 01 31:03, highSchool, multiple choice, > 1 min, fixed. A light bulb and a solenoid are connected in series to a battery. An irod rod is thrust rapidly into the solenoid and later rapidly removed. The bulb 1. Brightens in, Brightens out 2. Dims in, Dims out 1. clockwise; counterclockwise 3. No change in or out 2. clockwise; clockwise 4. No change in, Dims out 2. counterclockwise; clockwise 5. No change in, Brightens out 2. counterclockwise; counterclockwise 6. Dims in, No change out 3. no induced current 7. Brightens in, No change out 4. Unable to determine 8. Brightens in, Dims out Hewitt CP9 25 E31 31:03, highSchool, multiple choice, < 1 min, fixed. If a bar magnet is thrown into a coil of high-resistance wire, what will happen? 1. The magnet will change its polarity because the electromagnetic waves produced by the magnet and the coil will interact with each other. 2. The magnet will slow down and get hotter because the kinetic energy of the magnet will transfer to heat. 9. Dims in, Brightens out 10. Remains brighter the entire time Solenoid and a Ring 31:03, highSchool, multiple choice, > 1 min, fixed. The switch S has been closed for a long time and a constant current is flowing through a solenoid, creating a magnetic field. Chapter 31, section 3, Lenz’s Law iron core S The force which the magnetic field exerts on a conducting ring positioned as shown is 1. upward. 2. downward. 3. to the right. 4. to the left. 5. There is neither a force nor a torque. 6. There is no force, only a torque. 157 Chapter 31, section 4, Induced EMF in a Moving Conductor Conceptual 17 Q05 31:04, highSchool, multiple choice, < 1 min, fixed. 158 4. No; the amount of magnetic field penetrating the loop does not change as it rotates. 5. Unable to determine Part 1 of 2 Suppose you are in a location where the magnetic field of Earth points north and is horizontal to the ground. A circular wire is rotated as shown in the figure (the axis of rotation is along the north-south direction). N W B B E Conceptual 17 Q13 31:04, highSchool, multiple choice, < 1 min, fixed. A rectangular piece of wire is moving to the right as shown. It passes through a region where there is a magnetic field pointing into the page, (magnetic field indicated by the shaded region). S wire v Will there be an induced current in the wire? 1. Yes; current direction doesn’t change. 2. Yes; current direction reverses every cycle. 3. Yes; the amount of magnetic field penetrating the loop changes as it rotates. When the loop of wire is in the position shown in the figure, is there an induced current in the loop? 1. Yes; the current runs clockwise. 2. Yes; the current runs counterclockwise 4. No; the amount of magnetic field penetrating the loop does not change as it rotates. 3. No 4. Unable to determine 5. Unable to determine Part 2 of 2 What if the axis of rotation were in the eastwest direction? 1. Yes; current direction doesn’t change. 2. Yes; current direction reverses every cycle. 3. Yes; the amount of magnetic field penetrating the loop changes as it rotates. Conceptual 17 Q16 31:04, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 A square loop of copper wire is moving to the right in a uniform, downward-pointing magnetic field, as shown. Chapter 31, section 4, Induced EMF in a Moving Conductor wire loop B v What is the direction of the force on an electron moving to the right in this magnetic field? 159 31:04, highSchool, numeric, > 1 min, wordingvariable. A single circular loop with a radius of 22 cm is placed in a uniform external magnetic field with a strength of 0.50 T so that the plane of the coil is perpendicular to the field. The coil is pulled steadily out of the field in 0.25 s. Find the average induced emf during this interval. Holt SF 22A 04 31:04, highSchool, numeric, > 1 min, wordingvariable. 1. right 2. left 3. upward 4. downward Part 2 of 2 Is there an induced current in this square current loop? 1. Yes; the direction is clockwise. 2. Yes; the direction is counterclockwise. 3. No 4. Unable to determine Hewitt CP9 26 R02 31:04, highSchool, multiple choice, < 1 min, fixed. What does a changing electric field induce? 1. charges 2. magnetic field 3. light 4. electrons 5. Nothing Holt SF 22A 01 A 505-turn circular-loop coil with a diameter of 15.5 cm is initially aligned so that its plane is perpendicular to the Earth’s magnetic field. In 2.77 ms the coil is rotated 90.0◦ so that its plane is parallel to the Earth’s magnetic field. An average emf of 0.166 V is induced in the coil. What is the value of the Earth’s magnetic field? Holt SF 22B 02 31:04, highSchool, numeric, < 1 min, wordingvariable. A circular coil with a radius of 0.22 m and 17 turns is rotated in a uniform magnetic field of 1.7 T. The coil rotates with a constant frequency of 2.0 Hz. Determine the maximum value of the emf induced in the coil. Holt SF 22B 03 31:04, highSchool, numeric, < 1 min, wordingvariable. A square coil with an area of 0.045 m2 consists of 120 of wire. The coil rotates about a vertical axis at 157 rad/s. The horizontal component of the Earth’s magnetic field at the location of the loop is 2.0 × 10−5 T. Calculate the maximum emf induced in the coil. Holt SF 22Rev 10 Chapter 31, section 4, Induced EMF in a Moving Conductor 31:04, highSchool, numeric, > 1 min, wordingvariable. A flexible loop of conducting wire has a radius of 0.12 m and is perpendicular to a uniform magnetic field with a strength of 0.15 T, as shown in the figure. 160 the poles of a horseshoe magnet with a magnetic field of 2.5 ×10−2 T. The area of the loop is 7.54 ×10−3 m2 and is moved perpendicular to the magnetic field lines. In what time interval will the student have to move the loop out of the magnetic field in order to induce an emf of 1.5 V? Holt SF 22Rev 38 31:04, highSchool, numeric, > 1 min, wordingvariable. The loop is grasped at opposite ends and stretched until it closes to an area of 3 ×10−3 m2 , as shown in the figure. It takes 0.20 s to close the loop. Find the magnitude of the average emf induced in the loop during this time. Holt SF 22Rev 12 31:04, highSchool, numeric, > 1 min, wordingvariable. A 52-turn coil with an area of 5.5 ×10−3 m2 is dropped from a position where B = 0.0 T to a new position where B = 0.55 T. The displacement occurs in 0.25 s and the area of the coil is perpendicular to the magnetic field lines. What is the resulting average emf induced in the coil? Holt SF 22Rev 37 31:04, highSchool, numeric, < 1 min, wordingvariable. A student attempts to make a simple generator by passing a single loop of wire between A student attempts to make a simple generator by wrapping a long piece of wire across a cylinder with a cross-sectional area of 1.886 ×10−3 m2 . She then passes the coil between the poles of a horseshoe magnet with a magnetic field of 2.5 ×10−2 T. The student finds that by removing the coil perpendicular to the magnetic field lines during 0.25 s, an emf of 149 mV can be induced. How many turns of wire are wrapped around the coil? Holt SF 22Rev 39 31:04, highSchool, numeric, > 1 min, wordingvariable. A coil of 325 and an area of 19.5 ×10−4 m2 is removed from a uniform magnetic field at an angle of 45◦ in 1.25 s. The induced emf is 15 mV. What is the magnetic field strength? Rectangular Loop 02 31:04, highSchool, multiple choice, > 1 min, wording-variable. A rectangular loop of wire is pulled through a magnetic field B (into the page). Shown below are four different stages of development of this procedure, labeled A, B , C , and D. The rectangular loop has a constant speed as it is pulled through the loop. Chapter 31, section 4, Induced EMF in a Moving Conductor B 4. FB = FC > FA = FD B 5. FB > FD = FA > FC v FA 6. FA > FD = FB > FC B B 7. FA > FC = FB > FD 8. FB > FC = FA > FD B B 9. FA > FC > FB > FD v FB B 10. FB > FC > FA > FD B B B v FC B B B B FD B B v Figure: The force vector is not to scale. The velocity vector is to scale; (i.e., constant speed). Select the correct rank ordering of the magnitudes of the force pulling the rectangular loop (at constant speed) in the four stages shown above. 1. FB = FD > FA = FC 2. FA = FD > FB = FC 3. FA = FC > FB = FD 161 Chapter 31, section 5, Induced Electric Fields Conceptual 17 Q04 31:05, highSchool, multiple choice, < 1 min, fixed. Suppose you have a Frisbee with a copper wire glued around its outer circumference. When you throw the Frisbee correctly, it maintains a constant orientation with the ground. When you throw it incorrectly, it wobbles. In which of case will a current be induced in the copper wire due to Earth’s magnetic field? 1. correct throw 2. incorrect throw 3. Either 4. Neither Hewitt CP9 24 E07 31:05, highSchool, multiple choice, < 1 min, fixed. What surrounds a stationary electric charge? What surrounds a moving electric charge? (Ignore the gravitational field.) 1. electric fields for both 2. magnetic fields for both 3. electric field; magnetic field 4. magnetic field; electric field 5. electric field; electric and magnetic fields 6. It cannot be predicted. Hewitt CP9 25 E40 31:05, highSchool, multiple choice, < 1 min, fixed. Would electromagnetic waves exist if changing magnetic fields could produce elec- 162 tric fields, but changing electric fields could not in turn produce magnetic fields? 1. Yes; only the magnetic field changes in electromagnetic waves. 2. Yes; as long as we have a magnet, there is a magnetic field to form the electromagnetic waves. 3. No; electric and magnetic fields coexist in electromagnetic waves by field induction. 4. Yes; electromagnetic waves consist of either electric or magnetic fields, but not necessary both. 5. Can’t be determined unless we know the propagation medium of the electromagnetic waves. 6. More information is needed. Chapter 31, section 6, Electric Field from a Changing Magnetic Flux Hewitt CP9 26 R01 31:06, highSchool, multiple choice, < 1 min, fixed. What does a changing magnetic field induce? 1. charges 2. electric field 3. light 4. electrons 5. Nothing Light Bulb and Solenoid 02 31:06, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Consider the set up shown in the figure where a solenoid has a steadily increasing magnetic flux which generates identical induced emf’s for the two cases illustrated. i (1) #2 #1 A B Case 1: Two identical light bulbs are in series. The corresponding electrical power consumed by bulb 1 and bulb 2 are P1 and P2 , respectively. C (2) D #2 #1 A B F Case 2: Bulb 2 is shorted by a wire which is connected between the two points C and F . The corresponding electrical power consumed by bulb 1 and bulb 2 are P1 and P2 , respectively. Hint: It may be helpful to first write down 163 the loop equation for ACDF A and ACBF A. P The ratio of 1 is given by P1 P 1. 1 = 4 . P1 P 2. 1 = 8 . P1 P 3. 1 = 3 . P1 P 4. 1 = 2 . P1 P 5. 1 = 1 . P1 P 6. 1 = 0 . P1 P 1 7. 1 = . P1 2 1 P 8. 1 = . P1 3 P 1 9. 1 = . P1 4 P 1 10. 1 = . P1 8 Part 2 of 2 Consider the set up shown in the figure where a solenoid has a steadily increasing magnetic flux which generates identical induced emf’s for the two cases illustrated. i (1) #2 #1 B A Case 1: Two identical light bulbs are in series. The corresponding electrical power consumed by bulb 1 and bulb 2 are P1 and P2 , respectively. Chapter 31, section 6, Electric Field from a Changing Magnetic Flux C (3) o #2 #1 A B i2 D i1 Case 2: Let the points C and D be on the symmetry line of the diagram. Connect points C and D by a wire, which equally divides the magnetic flux. The corresponding electrical power consumed by bulb 1 and bulb 2 are P1 and P2 , respectively. Hint: It may be helpful to first write down the loop equation for ACODA. P The ratio of 1 is given by P1 P 1. 1 = 1 . P1 P 2. 1 = 8 . P1 P 3. 1 = 3 . P1 P 4. 1 = 2 . P1 P 5. 1 = 4 . P1 P 6. 1 = 0 . P1 1 P 7. 1 = . P1 2 P 1 8. 1 = . P1 3 P 1 9. 1 = . P1 4 1 P 10. 1 = . P1 8 164 Chapter 31, section 7, Generators and Motors 165 Hewitt CP9 25 E11 31:07, highSchool, multiple choice, < 1 min, fixed. Holt SF 22B 01 31:07, highSchool, numeric, < 1 min, wordingvariable. What is the primary difference between an electric motor and an electric generator? 1. An electric motor produces electricity while an electric generator does mechanic work with the input of electricity. In a model generator, a 510-turn rectangular coil 0.082 m by 0.25 m rotates with an angular frequency of 12.8 rad/s in a uniform magnetic field of 0.65 T. What is the maximum emf induced in the coil? 2. An electric motor is often much more complicated in structure than electric generator. Holt SF 22B 04 31:07, highSchool, numeric, < 1 min, wordingvariable. 3. Structurally they are similar but the electric generator is more efficient than the electric motor. A maximum emf of 90.4 V is induced in a generator coil rotating with a frequency of 65 Hz. The coil has an area of 230 cm2 and rotates in a magnetic field of 1.2 T. How many turns are in the coil? 4. Structurally they are similar and some devices are designed to operate either as motors or generators. 5. Structurally they are similar but the electric motor is more efficient than the electric generator. Hewitt CP9 25 E13 31:07, highSchool, multiple choice, < 1 min, fixed. Does the voltage output increase when a generator is made to spin faster? 1. No; it will only increase the output current of the generator. 2. Yes; according to Faraday’s law of induction, the faster the change of magnetic field in a coil, the greater the induced voltage. 3. No; the voltage output increases only when the magnetic field gets stronger. 4. Yes; the faster a generator spins, the stronger the magnetic field it produces. 5. None of these Holt SF 22Rev 23 31:07, highSchool, numeric, < 1 min, wordingvariable. A generator can be made using the component of Earth’s magnetic field that is parallel to Earth’s surface. A 112-turn square wire coil with an area of 4.41 ×10−2 m2 is mounted on a shaft so that the cross-sectional area of the coil is perpendicular to the ground. The shaft then rotates with a frequency of 25.0 Hz. The horizontal component of the Earth’s magnetic field at the location of the loop is 5.00 ×10−5 T. Calculate the maximum emf induced in the coil by Earth’s magnetic field. Holt SF 22Rev 24 31:07, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 An ac generator consists of 45 turns of wire with an area of 0.12 m2 . The loop rotates in a magnetic field of 0.118 T at a constant frequency of 60.0 Hz. The generator is connected across a circuit load with a total resistance of Chapter 31, section 7, Generators and Motors 35 Ω. a) Find the maximum emf induced by the generator. Part 2 of 2 b) Find the maximum induced current. 166 Chapter 31, section 9, Maxwell’s Equations Maxwell Contribution 31:09, highSchool, multiple choice, < 1 min, fixed. Maxwell’s great contribution to electrodynamic theory was his idea that 1. work is required to move a magnetic pole through a current loop. 2. a time-varying electric flux acts as a current for the purposes of producing a magnetic field. 3. the speed of light could be determined from simple electrostatic and magnetostatic experiments (finding the values of µ0 and 0 ). 4. the magnetic force on moving charges is perpendicular to both v and B . 5. magnetism could be explained in terms of circulating currents in atoms. 6. the charge to mass ratio of the electron was a constant. 167 Chapter 32, section 7, Oscillations in an LC Circuit Simple lc circuit 32:07, highSchool, numeric, > 1 min, normal. A 40 µF capacitor is connected in series with a 10 mH inductance and a switch. The capacitor is first charged to a voltage of 120 V. The charging battery is then removed, and the switch is closed. Then the current undergoes oscillations. What is the maximum current in the circuit? 168 Chapter 33, section 1, AC Sources Holt SF 22C 02 33:01, highSchool, numeric, < 1 min, wordingvariable. The current in an AC circuit is measured with an ammeter, which gives a reading of 5.5 A. Calculate the maximum AC current. Holt SF 22Rev 25 33:01, highSchool, numeric, < 1 min, normal. The rms potential difference across highvoltage transmission lines in Great Britain is 220000 V. What is the maximum potential difference? Holt SF 22Rev 44 33:01, highSchool, numeric, > 1 min, normal. Part 1 of 2 The alternating potential difference of a generator is represented by the equation E = (245 V) sin(560 rad/s) t , where E is in volts and t is in seconds. Find the frequency of the potential difference of the source. Part 2 of 2 Find the maximum potential difference output of the source. 169 Chapter 33, section 3, Resistors in an AC Circuit 170 difference? Holt SF 22C 01 33:03, highSchool, numeric, > 1 min, normal. Part 1 of 3 An rms potential difference of 120 V is placed across a light bulb with a resistance of 25 Ω. What is the rms current in the light bulb? Part 2 of 3 What is the maximum value of current? Part 3 of 3 What is the maximum value for the potential difference? Holt SF 22C 03 33:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A toaster is plugged into a source of alternating potential difference with an rms value of 110 V. The heating element is designed to convey a current with a maximum value of 10.5 A. Find the rms current in the heating element. Part 2 of 2 Find the resistance of the heating element. Holt SF 22C 04 33:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 An audio amplifier provides an alternating rms potential difference of 15.0 V. A loudspeaker connected to the amplifier has a resistance of 10.4 Ω. What is the rms current in the speaker? Part 2 of 3 What is the maximum value of current? Part 3 of 3 What is the maximum value for the potential Holt SF 22C 05 33:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 An AC generator has a maximum potential difference output of 155 V. Find the rms potential difference output. Part 2 of 2 Find the rms current in the circuit when the generator is connected to a 53 Ω resistor. Holt SF 22Rev 26 33:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 The maximum potential difference across certain heavy-duty appliances is 340 V. The total resistance of an appliance is 120 Ω. Find the rms potential difference across the appliance. Part 2 of 2 Find the rms current in the appliance. Chapter 33, section 5, Capacitors in an AC Circuit Holt SF 22C 06 33:05, highSchool, numeric, < 1 min, normal. The largest potential difference that can be placed across a certain capacitor at any instant is 451 V. What is the largest rms potential difference that can be placed across the capacitor without damaging it? 171 Chapter 33, section 7, The RLC Series Circuit RC and LC Circuits 05 33:07, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Consider the following circuit. After leaving the switch at the position “a” for a long time, move the switch from “a” to “b”. There will be the usual LC circuit oscillations. B2. The charge on the left plate of C is zero. B3. The charge on the left plate of C is negative. Let the time when the switch is moved from a to b be at t = 0. Which pair of choices below best describes 5 the situation at t = T , where T is the period 8 of oscillations in LC circuit? and B2 and B3 4. A2 and B1 5. A2 and B2 6. A2 Sb and B1 3. A1 C 1. A1 2. A1 L and B3 7. A3 and B1 8. A3 and B2 9. A3 and B3 a E R What is the maximum current? 1. Imax E√ = LC R 2. Imax = E 3. Imax L C √ = E LC 4. Imax = E 5. Imax = E R 6. Imax = E R 1 LC 7. Imax = E 8. Imax = E R L C C L C L Part 2 of 2 Consider the following statements: A1. The current flow is counterclockwise. A2. The current is zero. A3. The current flow is clockwise. B1. The charge on the left plate of C is positive. 172 Chapter 33, section 9, Power in an AC Circuit Holt SF 22Rev 27 33:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 The maximum current that can pass through a light bulb filament is 0.909 A when its resistance is 182 Ω. What is the rms current conducted by the filament of the bulb? Part 2 of 3 What is the rms potential difference across the bulb’s filament? 173 Which of the following statements is true? All energy is dissipated in R . 1. True 2. False 3. Cannot be determined Part 2 of 3 The electric potential across C and L are 180◦ out of phase. 1. False 2. True Part 3 of 3 How much power does the light bulb use? Holt SF 22Rev 28 33:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A 996 W hair dryer is designed to carry a maximum current of 11.8 A. How large is the rms current in the hair dryer? 3. Cannot be determined Part 3 of 3 The source E does no net work, since energy lost in R is compensated by energy stored in C and L . 1. False 2. True 3. Cannot be determined Part 2 of 2 What is the rms potential difference across the hair dryer? RLC TF Questions 02 33:09, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 This RLC circuit is driven by an oscillating emf E . C L R E Chapter 33, section 13, The Transformer and Power Transmission 174 twice the primary voltage? Conceptual 18 Q15 33:13, highSchool, multiple choice, < 1 min, fixed. 1. twice the current in the primary 2. half the current in the primary Consider a transformer. What is true? 3. the same as the current in the primary 1. A transformer does not work with direct current. 4. Sometimes these two currents are not related to each other. 2. A transformer works with direct current. Hewitt CP9 25 E29 33:13, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 25 E21 33:13, highSchool, multiple choice, < 1 min, fixed. Can an efficient transformer step up energy? Why does a transformer require alternating voltage? 1. Yes; stepping up voltage is the same as stepping up energy. 1. Due to economic reasons; alternating voltage is cheaper to produce. 2. Yes, provided that the transformer is made of special material such as amino acid or other organic compounds. 2. If we apply a constant voltage to the primary coil, it will burn out due to a short circuit. 3. No; there is no such thing as an “efficient transformer.” 3. Energy can be transferred more efficiently if alternating voltage is used. 4. No; energy is conserved and cannot be stepped up. 4. No specific reason; constant voltage would work just as well. 5. Alternating voltage leads to electromagnetic induction which is necessary for the transformer to work. 6. The magnetic field produced by the primary coil can reach the secondary coil more easily. Hewitt CP9 25 E22 33:13, highSchool, multiple choice, < 1 min, fixed. How does the current in the secondary of the transformer compare with the current in the primary when the secondary voltage is 5. It cannot be determined. 6. Theoretically yes, but it is hard to build such transformers in practice. Hewitt CP9 25 P01 33:13, highSchool, numeric, < 1 min, normal. The primary coil of a step-up transformer draws 100 W. Find the power provided by the secondary coil. Hewitt CP9 25 P02 33:13, highSchool, numeric, < 1 min, normal. Part 1 of 3 An ideal transformer has 50 turns in its pri- Chapter 33, section 13, The Transformer and Power Transmission mary coil and 250 turns turns in its secondary coil. 12 Vac is connected to the primary coil. Find the ac voltage available at the secondary coil. Part 2 of 3 Find the current in a 10 Ω device connected to the secondary. Part 3 of 3 Find the power supplied to the primary. Hewitt CP9 25 P03 33:13, highSchool, numeric, < 1 min, normal. A model electric train requires 6 V to operate. If the primary coil of its transformer has 240 turns windings, how many windings should the secondary have if the primary is connected to a 120 V household circuit? Holt SF 22D 01 33:13, highSchool, numeric, < 1 min, normal. A step-down transformer providing electricity for a residential neighborhood has exactly 2680 turns in its primary. When the potential difference across the primary coil is 5850 V, the potential difference across the secondary is 120 V. How many turns are in the secondary? (Round the answer to the nearest whole number.) Holt SF 22D 02 33:13, highSchool, numeric, < 1 min, wordingvariable. A step-up transformer used in an automobile has a potential difference across the primary of 12 V and a potential difference across the secondary of 2.0 × 104 V. There are 21 turns in the primary coil. How many turns are in the secondary? Holt SF 22D 03 33:13, highSchool, numeric, < 1 min, normal. 175 A step-up transformer for long-range transmission of electric power is used to create a potential difference of 119340 V across the secondary. The potential difference across the primary is 117 V and the secondary has 25500 turns. How many turns are in the primary? Holt SF 22D 04 33:13, highSchool, numeric, < 1 min, wordingvariable. A potential difference of 0.750 V is needed to provide a large current for arc welding. The potential difference across the primary of a step-down transformer is 117 V. How many turns must be on the primary for each turn on the secondary? Holt SF 22D 05 33:13, highSchool, numeric, < 1 min, normal. A television picture tube requires a high potential difference, which in older models is provided by a step-up transformer. The transformer has 12 turns in its primary and 2550 turns in its secondary. A potential difference of 120 V is placed across the primary. What is the output potential difference? Holt SF 22D 06 33:13, highSchool, numeric, < 1 min, normal. A step-down transformer has 525 turns in its secondary and 12500 turns in its primary. The potential difference across the primary is 3510 V. What is the potential difference across the secondary? Holt SF 22Rev 35 33:13, highSchool, numeric, < 1 min, wordingvariable. A transformer is used to convert 120 V to 9.0 V for use in a portable CD player. The primary coil connected to the outlet has 640 turns. How many turns does the secondary have? Chapter 33, section 13, The Transformer and Power Transmission Holt SF 22Rev 36 33:13, highSchool, numeric, < 1 min, normal. 176 33:13, highSchool, numeric, < 1 min, wordingvariable. A transformer has 22 of wire in its primary and 88 in its secondary. A potential difference of 110 V ac is applied to the primary. What is the output potential difference? A ideal transformer shown in the figure below having a primary with 20 turns and secondary with 12 turns. The load resistor is 50 Ω. The source voltage is 105 Vrms . Holt SF 22Rev 41 33:13, highSchool, numeric, < 1 min, wordingvariable. The potential difference in the lines that carry electric power to homes is typically 20.0 kV. How many turns must be on the primary for each turn on the secondary if the output potential difference is 117 V? (Round the answer to the nearest whole ratio.) Holt SF 22Rev 43 33:13, highSchool, numeric, > 1 min, normal. Part 1 of 2 A generator supplies 5000 kW of power. The output potential difference is 4500 V before it stepped up to 510 kV . The electricity travels 410 miles (644000 m) through a transmission line that has a resistance per unit length of 0.00045 Ω/m . How much power is lost through transmission of the electrical energy along the line? Part 2 of 2 How much power would be lost through transmission if the generator’s output potential difference were not stepped up? Holt SF 22Rev 45 50 Ω StepDown Transformer 03 33:13, highSchool, numeric, > 1 min, normal. 12 turns Holt SF 22Rev 40 33:13, highSchool, numeric, < 1 min, normal. 20 turns A pair of adjacent coils has a mutual inductance of 1.06 H. The current in the primary circuit decreases by 9.50 A in a time interval of 0.0336 s. Determine the average emf induced in the secondary circuit. 105 Vrms A transformer is used to convert 120 V to 17 V in order to power a toy electric train. There are 480 turns in the primary. How many turns should there be in the secondary? What is the rms electric potential across the 50 Ω load resistor? Chapter 34, section 2, Plane Electromagnetic Waves Conceptual 19 09 34:02, highSchool, numeric, > 1 min, fixed. Part 1 of 2 If the frequency of an electromagnetic wave is 1 × 106 Hz what is the wavelength? Part 2 of 2 What type of electromagnetic wave is this? 1. radio wave 2. microwave 3. infrared 4. visible light 5. ultraviolet 6. X-rays 7. gamma rays Conceptual 19 Q02a 34:02, highSchool, multiple choice, < 1 min, fixed. In what way are sound waves and radio waves similar? 1. Both are traveling disturbances. 2. Both travel at the same speed. 3. Both require a medium. 4. Neither requires a medium. 177 Chapter 34, section 3, Speed of Electromagnetic Waves Conceptual 19 01 34:03, highSchool, numeric, > 1 min, normal. Radio and TV transmissions are being emitted into space, so Star Trek episodes are streaming out into the universe. The nearest star is 9.5 × 1017 m meters away. If civilized life exists on a planet near this star, how long will they have to wait for the next episode? 178 How long is the wavelength of the radiation at the end of the range? Conceptual 19 05 34:03, highSchool, numeric, > 1 min, fixed. What is the frequency of a microwave from a typical microwave oven? Conceptual 19 07 34:03, highSchool, numeric, > 1 min, fixed. Conceptual 19 02 34:03, highSchool, numeric, > 1 min, normal. If an X-ray has a wavelength of 5 nm, what is its frequency? Part 1 of 2 If the frequency of the wave used by your favourite station is 94.1 Megahertz, what is the wavelength? Conceptual 19 Q03 34:03, highSchool, multiple choice, < 1 min, fixed. Part 2 of 2 If the station is 50 km away, how long does it take for the radio waves to reach you from the station? Conceptual 19 03 34:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 The FM radio band in most places goes from frequencies of about 88 MHz to 108 MHz. How long is the wavelength of the radiation at the beginning of the range? Part 2 of 2 How long is the wavelength of the radiation at the end of the range? Conceptual 19 04 34:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 The AM radio band in a particular area has a frequency range of 535 KHz to 1610 KHz. How long is the wavelength of the radiation at the beginning of the range? Part 2 of 2 Suppose a sound wave and a light wave have the same frequency. Which of the following is true? 1. The light wave has a longer wavelength and has the greater speed. 2. The light wave has a longer wavelength and has the slower speed. 3. The light wave has a shorter wavelength and has the greater speed. 4. The light wave has a shorter wavelength and has the slower speed. 5. The sound wave has a longer wavelength and has the greater speed. 6. The sound wave has a longer wavelength and has the slower speed. 7. The sound wave has a shorter wavelength and has the greater speed. Hewitt CP9 26 E11 34:03, highSchool, multiple choice, < 1 min, fixed. At what speed does the radio wave travel? Chapter 34, section 3, Speed of Electromagnetic Waves 1. at the speed of light 2. at the speed of sound 3. at a speed between the speed of light and the speed of sound 4. faster than visible light 5. slower than the sound 179 3. There is no difference between the speed of light in glass and in a vacuum. 4. It cannot be judged because we don’t know what kind of glass it is. 5. For colorless glass, the light speed is higher than in a vacuum; for colored glass, the light speed is lower than in vacuum. Holt SF 14A 01 34:03, highSchool, numeric, > 1 min, fixed. 6. More information is needed. Hewitt CP9 26 R13 34:03, highSchool, multiple choice, < 1 min, fixed. How is the wavelength of light related to its frequency? 1. Waves of low frequency have long wavelengths. 2. Waves of high frequency have long wavelengths. 3. Sometimes waves of low frequency have long wavelengths; sometimes waves of high frequency have long wavelengths. 4. For visible light wavelength has an inverse relationship with frequency; for invisible light, it has a direct relationship. 5. There is no relationship between frequency and wavelengths at all. Hewitt CP9 26 R21 34:03, highSchool, multiple choice, < 1 min, fixed. How does the average speed of light in glass compare with its speed in a vacuum? 1. The speed of light in glass is higher. 2. The speed of light in glass is lower. Gamma-ray bursters are objects in the universe that emit pulses of gamma rays with high energies. The frequency of the most energetic bursts has been measured at around 3.0 × 1021 Hz. The speed of light is 3 × 108 m/s. What is the wavelength of these gamma rays? Holt SF 14A 02 34:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 FM radio bands range from 88 MHZ through 108 MHz. The speed of light is 3 × 108 m/s. What is the wavelength for the FM radio band at 88 MHz? Part 2 of 2 What is the wavelength for the FM radio band at 108 MHz? Holt SF 14A 03 34:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Shortwave radio is broadcast between 3.50 MHz and 29.7 MHz . The speed of light is 3 × 108 m/s. What is the wavelength at 3.50 MHz ? Part 2 of 2 What is the wavelength at 29.7 MHz ? Chapter 34, section 3, Speed of Electromagnetic Waves Holt SF 14A 04 34:03, highSchool, numeric, > 1 min, wordingvariable. 4. a function of the distance from the source. 5. a function of the size of the source. What is the frequency of an electromagnetic wave if it has a wavelength of 1.0 km? The speed of light is 3 × 108 m/s. Holt SF 14Rev 10 34:03, highSchool, numeric, > 1 min, fixed. Part 1 of 2 The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between 7.5 × 1014 Hz and 1.0 × 1015 Hz. The speed of light is 3 × 108 m/s. What is the largest wavelength to which these frequencies correspond? Part 2 of 2 What is the smallest wavelength? Holt SF 14Rev 11 34:03, highSchool, numeric, > 1 min, wordingvariable. The brightest light detected from the star Antares has a frequency of about 3.0 × 1014 Hz. The speed of light is 3 × 108 m/s. What is the wavelength of this light? Maxwells Prediction 34:03, highSchool, multiple choice, < 1 min, fixed. According to Maxwell’s equation, the speed of light in a vacuum is 1. greater for visible light than for radio waves. 2. greater for radio waves than for visible light. 3. independent of frequency. 180 Chapter 34, section 4, Energy Carried by Electromagnetic Waves: Poynting Vector 181 fixed. Concept 30 05 34:04, highSchool, multiple choice, < 1 min, fixed. If we double the frequency of light, we double the energy of each of its photons. If we instead double the wavelength of light, what happens to the photon energy? 1. Doubled 2. Halved 3. Quadrupled 4. No change Concept 30 14 34:04, highSchool, multiple choice, < 1 min, fixed. Which has the greatest energy? 1. A photon of infrared light 2. A photon of visible light 3. A photon of ultraviolet light 4. They have the same energy. Conceptual 19 08 34:04, highSchool, multiple choice, < 1 min, fixed. Which has the greatest energy among the following? Part 1 of 2 Compare the energy of visible light and ultraviolet light. 1. Visible light has more energy than ultraviolet light. 2. Visible light has less energy than ultraviolet light. 3. They have same energy. Part 2 of 2 What determines the energy of electromagnetic waves? 1. The higher the frequency of the radiation the greater its energy 2. The lower the frequency of the radiation the greater its energy Figuring Physics 32 34:04, highSchool, multiple choice, > 1 min, wording-variable. Maxwell’s equations tell us that a changing magnetic field induces a changing electric field, and vice versa in turn, to produce an electromagnetic wave. Such field induction depends on changes both with respect to time and with respect to distance — so it depends on speed. The speed of propagation of fields inducing and re-inducing each other is c , the speed of light. E 1. a wavelength of 90 nm 2. a wavelength of 2 nm 3. a wavelength of 45 nm B 4. a wavelength of 23 nm Conceptual 19 Q09 34:04, highSchool, multiple choice, < 1 min, Are propagation speeds faster than c consistant with conservation of energy? Chapter 34, section 4, Energy Carried by Electromagnetic Waves: Poynting Vector 1. no, because the each changing field would produce an ever-increasing field strength. 2. no, because of special relativity. 3. no, because of general relativity. 4. no, because in a vacuum light has to travel at a velocity less than or equal to c to conserve energy. Incandescent Lamp Filament 01 34:04, highSchool, numeric, > 1 min, normal. The filament of an incandescent lamp has a 150 Ω resistance and carries a direct current of 1 A. The filament is 8 cm long and 0.9 mm in radius. Calculate the Poynting vector at the surface of the filament. Poynting Vector again 34:04, highSchool, multiple choice, < 1 min, fixed. For an electromagnetic wave the direction of the vector E × B gives the direction of 1. the electric field. 182 Part 2 of 2 What is the total power radiated by the sun? Traveling EMwave M 34:04, highSchool, multiple choice, > 1 min, fixed. A snapshot at time t = 0 of the electric field for a plane electromagnetic wave with angular velocity ω traveling in the y direction at velocity c is shown. propagation direction E z y x What is the accompanying magnetic field at time t if the electric field has amplitude E0 ? 1. B = − E0 ˆ cos(k y − ω t) k . c 2. B = +c E0 sin(k y − ω t) ˆ. ı ˆ 3. B = +c E0 sin(k y + ω t) k . 2. the magnetic field. 3. wave propagation. 4. B = − E0 cos(k y − ω t) ˆ. ı c 4. the electromagnetic force on a proton. 5. B = + E0 cos(k y − ω t) ˆ. ı c 5. the emf induced by the wave. Solar EM Waves 34:04, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Use the radius of the sun 7 × 108 m and the distance to the Earth of 1 AU= 1.5 × 1011 m to determine the amplitude of the electric field at the surface of the sun from the solar radiation content of 1400 W/m2 measured at the surface of the Earth. Travelling EMwave 34:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 4 A snapshot at time t = 0 of the electric field for a plane electromagnetic wave with angular velocity ω traveling in the y direction at velocity c is shown. Chapter 34, section 4, Energy Carried by Electromagnetic Waves: Poynting Vector E z propagation direction y What happens to the the wavelength of the wave if the angular velocity ω of the wave is decreased? 1. λ increases. x 2. λ decreases. 3. λ remains the same. What is the accompanying magnetic field at time t if the electric field has amplitude E0 ? 1. B = − E0 ˆ cos(k y − ω t) k . c 2. B = +c E0 sin(k y − ω t) ˆ. ı ˆ 3. B = +c E0 sin(k y + ω t) k . 4. B = − E0 cos(k y − ω t) ˆ. ı c 5. B = + E0 cos(k y − ω t) ˆ. ı c Part 2 of 4 What happens to the ratio of the electric to magnetic field if the angular velocity ω of the wave is decreased? E0 increases. B0 E0 2. decreases. B0 E0 remains the same. 3. B0 1. Part 3 of 4 What happens to the velocity of the wave if the angular velocity ω of the wave is decreased? 1. v increases. 2. v decreases. 3. v remains the same. Part 4 of 4 183 Chapter 34, section 5, Momentum and Radiation Pressure O r n = 1.33 D Find the intensity I of the incident light at D. 1. I = 2. I = 3. I = 4. I = 5. I = 6. I = 7. I = 8. I = 9. I = 10. I = Part 1 of 2 A polymer film with a refraction index of 1.33 is impinged by a laser light from the left. Right interface Part 1 of 2 A point source at O emits light isotropically. Denote the power which the point source radiates by P . A small flat surface is placed at D, which is a distance r from O. This surface has an area A and is perpendicular to the radial vector OD. Laser on a polymer film 34:05, highSchool, multiple choice, > 1 min, fixed. Left interface Intensity from a light source 34:05, highSchool, numeric, > 1 min, normal. 184 P 4 π r2 P 2 π r2 P π r2 P 3 π r2 P 6 π r2 P A P 2A P 3A 2P 3A P 4A Part 2 of 2 Consider the setup described in Part 1, where 1 the surface absorbs of the light. 3 If P = 120 W, r = 1 m, and A = 1 mm2 , find the average pressure on the surface. Assuming the film is 100% transparent, what will be the direction of forces? 1. → ← 2. no forces on either interfaces 3. → → 4. ← → 5. ← ← 6. left no force, right → 7. left ←, right no force 8. left →, right no force 9. left no force, right ← Part 2 of 2 Now the left interface is coated with a thin metal film to provide 50% reflectivity. The right interface remains completely transparent. What will be the direction of forces on the two interfaces? 1. → ← Chapter 34, section 5, Momentum and Radiation Pressure 185 2. No forces on either interface 3. There will be a rightward force on the polymer 3. → → 4. ← → 4. There will be a leftward force on the polymer 5. ← ← 6. left no force, right → 7. left ←, right no force 8. left →, right no force 9. left no force, right ← Momentum and Transmission 34:05, highSchool, multiple choice, < 1 min, fixed. A narrow beam of light passes through a transparent plastic polymer with refractive index 2.0. Consider the case in which there is only one interface between the light and the polymer. Furthermore, consider the case in which there is 0% reflection at the interface between the polymer and the air: the polymer is 100 Upon entering the surface, the light’s wavelength, and thus, its momentum changes. Using what you know about momentum, determine what effect the shining of the light will have upon the polymer. n = 1. 0 n = 2. 0 total transmission 1. There will be a upward force on the polymer 2. There will be a downward force on the polymer 5. There will be a force on the polymer directed out of the page 6. There will be a force on the polymer directed into the page 7. There will be no force on the polymer– the light does not reflect, and thus does not interact 8. The interaction of the light and the polymer cannot be determined 9. There will be no force on the polymer– the angle of incidence must be nonzero in order for a force to result Chapter 34, section 7, The Production of Electromagnetic Waves by an Antenna Electron in a magnetic field 34:07, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 An electron in a uniform magnetic field B in the z direction describes a cyclotron orbit in the xy plane. A physicist along the y axis at point O is trying to detect electromagnetic radiation from the circulating electron using an electric dipole antenna connected in series to an inductor L, variable capacitor C and light bulb of resistance R. As she reorients the antenna and tunes the capacitor the light bulb suddenly lights up. z B receiving antenna C R O R2 m . eBL e2 B 2 L . 4. C = m2 3. C = 5. Need the electron’s velocity Oscillating Current 01 34:07, highSchool, multiple choice, > 1 min, fixed. A radio transmitter drives an oscillating current driven back and forth along the z axis in the aerial antenna wire as shown below. z I y x y e V II L x 186 antenna can be oriented in any direction Along which direction should she orient the antenna to maximize the brightness of the bulb? 1. along the ˆ direction ı 2. along the ˆ direction ˆ 3. along the k direction 4. at any orientation perpendicular to the ˆ direction ˆ 5. at any orientation perpendicular to the k direction Part 2 of 2 How does she tune the capicitor to maximize the bulb’s brightness? eB R . m m2 2. C = 2 2 . eBL 1. C = IV transmitter III Five linear receiving antennas are positioned with their centers at equal distances d from the center of the transmitter as follows I. Horizontal orientation, perpendicular to ˆ the antenna, positioned at d, in the +k direction. II. Vertical orientation, parallel to the antenna, positioned at d, in the +ˆ direcı tion. III. Horizontal orientation, perpendicular to the antenna, positioned at d, in the −ˆ direction. IV. Vertical orientation, parallel to the antenna, positioned at d, in the −ˆ direcı tion. V. Horizontal orientation, perpendicular to Chapter 34, section 7, The Production of Electromagnetic Waves by an Antenna the antenna, positioned at d, in the +ˆ direction. Which antennas receive the strongest signal? 1. I IV. Positioned at d, in the −ˆ direction, facı ing along z . ˆ V. Positioned at d, in the +ˆ direction, fac ing along x. ˆ Which antennas receive the strongest signal? 2. I, II, and IV 1. II and V 3. II, IV, V, and III 2. I 4. V and III 3. II 5. II and IV 4. IV Oscillating Current 02 34:07, highSchool, multiple choice, > 1 min, fixed. 5. V A radio transmitter drives an oscillating current back and forth along the z axis in the aerial antenna wire as shown below. z I y x 7. II and IV V II transmitter IV III Five circular receiving antennas are positioned with their centers at equal distances d from the center of the transmitter as follows ˆ I. Positioned at d, in the +k direction, facing along x. ˆ II. Positioned at d, in the +ˆ direction, facı ing along y . ˆ III. Positioned at d, in the −ˆ direction, fac ing along y . ˆ 187 6. III 8. I, II, V and III 9. II and III 10. I and V Chapter 34, section 8, Properties of Electromagnetic Waves 188 and sound waves do not. Concept 20 06 34:08, highSchool, multiple choice, < 1 min, fixed. 3. Sound waves travel faster than radio waves. Suppose a sound wave and an electromagnetic wave have the same frequency. Which has the longer wavelength? Conceptual 19 Q05 34:08, highSchool, multiple choice, < 1 min, fixed. 1. the electromagnetic wave 2. the sound wave Why would walking down a flight of stairs be very hazardous if our eyes detected only infrared? (Hint: What does the amount of infrared light emitted by an object indicate?) 3. They have the same wavelength. 4. It depends on the speed of the sound wave. 1. because infrared is an indicator of an object’s temperature. 2. because infrared cannot travel far. Conceptual 19 Q01 34:08, highSchool, multiple choice, < 1 min, fixed. Compare waves on a pond and electromagnetic waves. 1. A wave on a pond is a mechanical wave which requires a medium to travel. 2. A wave on a pond is a mechanical wave which doesn’t require a medium to travel. 3. A wave on a pond is an electromagnetic wave which requires a medium to travel 4. A wave on a pond is an electromagnetic wave which doesn’t require a medium to travel. Conceptual 19 Q02 34:08, highSchool, multiple choice, < 1 min, fixed. Conceptual 19 Q10 34:08, highSchool, multiple choice, < 1 min, fixed. A person is just as likely to get sunburned on a cloudy day as on a sunny day. Does this evidence support the hypothesis that ultraviolet light, not visible light, causes sunburn? 1. No. 2. Yes. Conceptual 19 Q12 34:08, highSchool, multiple choice, < 1 min, fixed. If someone asked you to prove that electromagnetic waves travel in a vacuum, what would you say? 1. We see stars and planets in the sky. In what way do sound waves differ from radio waves? 1. Sound waves require a medium to travel and radio waves do not. 2. We can see polarized light. 3. We can see diffracted light. 4. We can see refracted light. 2. Radio waves require a medium to travel Chapter 34, section 8, Properties of Electromagnetic Waves Conceptual 20 Q07 34:08, highSchool, multiple choice, < 1 min, fixed. 189 4. IV only 5. I and II only In a nighttime infrared image of a heated house, the windows glow brightly. However, textbooks claim that glass is opaque to infrared radiation. This would be 6. I and III only 7. II and IV only 8. III and IV only I) II) III) IV) due to warm windows; due to cold walls; due to people’s heat signature; due to detection of fire place from the window; 1. I and II only 9. All of these 10. None of these Conceptual 20 Q16 34:08, highSchool, multiple choice, < 1 min, fixed. 2. I and III only 3. II and III only 4. I only 5. IV only 6. None of these Conceptual 20 Q14 34:08, highSchool, multiple choice, < 1 min, fixed. Why do people wear light-colored clothing in summer and dark-colored clothing in winter? Which of these are NOT true about stainedglass windows at night? I) Stained glass absorbs certain colors selectively. II) No light comes through from the outside so it looks gray. III) A red pane looks red when light shines through it. IV) Stained-glass windows look bright from the outside. V) Dark light that passes through stainedglass windows makes it look gray. 1. I only 2. II only I) Dark clothing absorbs more light so it can keep you warmer; II) The absorbed light is converted to kinetic energy of the atoms in the clothing; III) Dark clothing is usually thicker; IV) Light clothing is lighter. 3. III only 4. IV only 5. V only 6. I and IV only 1. I only 7. IV and V only 2. II only 8. III and IV only 3. III only Chapter 34, section 8, Properties of Electromagnetic Waves 9. I and V only 10. None of these 190 4. None of these 5. All of these Conceptual 20 Q18 34:08, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 26 E03 34:08, highSchool, multiple choice, < 1 min, fixed. What kind of electromagnetic radiation can be detected by a human body? What is the fundamental source of electromagnetic radiation? I) II) III) IV) visible light infrared light ultra-violet light all other light 1. any charge 2. current 3. voltage 1. I only 4. an accelerating charge 2. II only 5. None of these 3. III only 4. I and II only Hewitt CP9 26 R03 34:08, highSchool, multiple choice, < 1 min, fixed. 5. I and III only What produces an electromagnetic wave? 6. I, II and III only 1. charges 7. III and IV only 2. static magnetic field 8. II, III and IV only 3. light 9. I and IV only 4. static electronic field 10. All of these 5. electricity Figuring Physics 24 34:08, highSchool, multiple choice, < 1 min, fixed. Which of these continually emits electromagnetic radiation? 1. a un-lit flashlight bulb 2. a hot steam radiator 3. a tray of ice cubes 6. None of these Chapter 34, section 9, The Spectrum of Electromagnetic Waves 191 fixed. Concept 30 03 34:09, highSchool, multiple choice, < 1 min, fixed. Green light is emitted when electrons in a substance make a particular energy-level transition. If blue light were instead emitted from the same substance, would it correspond to a greater or smaller change of energy in an atom? Part 1 of 2 White light is the combination of all frequencies of electromagnetic waves in the visible spectrum. In a vacuum, all the frequencies of light travel at the same speed. Suppose for a moment that lower frequencies traveled slower than higher frequencies. What would a distant star look like? 1. brighter than before 1. Greater energy change 2. dimmer than before 2. Smaller energy change 3. same 3. The same energy change 4. More information is needed. Conceptual 19 06 34:09, highSchool, multiple choice, < 1 min, wording-variable. Part 2 of 2 If the star suddenly disappeared, what would be the color of the last light that you would see from the star? 1. red 2. yellow Part 1 of 2 What is the wavelength for orange light? 3. green 1. 620 nm 4. blue 2. 530 nm 5. violet 3. 700 nm 6. indigo 4. 580 nm 7. orange Part 2 of 2 Convert this to meters. 1. 6.2 × 10−7 m 2. 5.3e − 07 m 3. 7e − 07 m 4. 5.8e − 07 m Conceptual 19 Q04 34:09, highSchool, multiple choice, < 1 min, Conceptual 19 Q06 34:09, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 An object that looks white when exposed to sunlight reflects all colors of light. What does a white object look like when it is exposed to red light? 1. A white object will look red when exposed to red light. Chapter 34, section 9, The Spectrum of Electromagnetic Waves 2. A white object will look yellow when exposed to red light. 3. A white object will look the same when exposed to red light. Part 2 of 2 What does a red object look like when it is exposed to blue light? 1. A red object will appear dark when exposed to blue light 2. A red object will appear bright when exposed to blue light 192 2. Radiowaves have lower frequency, same speed, and longer wavelength than ultraviolet light. 3. Radiowaves have higher frequency, same speed, and longer wavelength than ultraviolet light. 4. Radiowaves have lower frequency, faster speed, and shorter wavelength than ultraviolet light. Conceptual 19 Q11 34:09, highSchool, multiple choice, < 1 min, fixed. Conceptual 19 Q07 34:09, highSchool, multiple choice, < 1 min, fixed. Part 1 of 3 Compare radio waves and sound waves. Comparing microwaves and visible light, which of the following is true? 1. electromagnetic wave; it travels at the speed of light 1. Microwaves have lower frequency, slower speed, and longer wavelength than visible light. 2. electromagnetic wave; it does not travel at the speed of light 2. Microwaves have lower frequency, same speed, and longer wavelength than visible light. 3. Microwaves have higher frequency, same speed, and longer wavelength than visible light. 4. Microwaves have lower frequency, faster speed, and shorter wavelength than visible light. Conceptual 19 Q08 34:09, highSchool, multiple choice, < 1 min, fixed. Comparing radio waves and ultraviolet light, which of the following is true? 1. Radiowaves have lower frequency, slower speed, and longer wavelength than ultraviolet light. 3. mechanical wave; it travels at the speed of light 4. mechanical wave; it does not travel at the speed of light Part 2 of 3 What kind of wave is a sound wave? 1. electromagnetic wave; it travels at the speed of light. 2. electromagnetic wave; it does not travel at the speed of light. 3. mechanical wave; it travels at the speed of light. 4. mechanical wave; it does not travel at the speed of light. Part 3 of 3 What is the difference between radio waves Chapter 34, section 9, The Spectrum of Electromagnetic Waves and light waves? 1. The light waves have shorter wavelength. 193 7. violet light. Hewitt CP9 26 E04 34:09, highSchool, multiple choice, < 1 min, fixed. 2. The light waves have longer wavelength. What has the longest wavelength? 3. The light waves travels faster. 1. light waves 4. The radio waves are mechanical waves. 2. X rays Conceptual 19 Q13 34:09, highSchool, multiple choice, < 1 min, fixed. 3. radio waves 4. ultraviolet light waves What is the difference between gamma rays and infrared rays? 1. Gamma rays have a higher frequency and shorter wavelength. 2. Gamma rays have a lower frequency and shorter wavelength. 3. Gamma rays have a higher frequency and longer wavelength. 5. gama rays Hewitt CP9 26 E05 34:09, highSchool, multiple choice, < 1 min, fixed. What has the highest frequency? 1. ultraviolet light 2. infrared light 4. Gamma rays have a lower frequency and longer wavelength. 3. X ray EM Waves 34:09, highSchool, multiple choice, < 1 min, fixed. 4. visible light Of the following which type of electromagnetic wave has the longest wavelength? 6. radio wave 1. X-rays. 5. gamma ray Hewitt CP9 26 R08 34:09, highSchool, multiple choice, < 1 min, fixed. 2. AM radio waves. 3. red light. 4. Gamma rays. What is the principal difference between a radio wave and visible light? 1. Radio waves have lower frequencies than visible light waves. 5. microwaves. 6. FM radio waves. 2. Radio waves are not electromagnetic waves. Chapter 34, section 9, The Spectrum of Electromagnetic Waves 3. Radio waves are sound waves. 4. Light is more powerful than radio waves. 5. They travel at different speeds. Hewitt CP9 26 R11 34:09, highSchool, multiple choice, < 1 min, fixed. What color does visible light of the lowest frequency appear? Of the highest? 194 Hewitt CP9 27 E11 34:09, highSchool, multiple choice, < 1 min, fixed. A spotlight is coated so that it won’t transmit yellow light from its white-hot filament. What color is the emerging beam of light? 1. blue 2. red 3. green 1. red for lowest; blue for highest 4. yellow 2. yellow for lowest; green for highest 4. black 3. red for lowest; violet for highest 4. green for lowest; red for highest Hewitt CP9 27 E20 34:09, highSchool, multiple choice, < 1 min, fixed. 5. violet for lowest; red for highest 6. blue for lowest; green for highest Hewitt CP9 27 E08 34:09, highSchool, multiple choice, < 1 min, fixed. Part 1 of 3 What color is obtained when you mix yellow light and blue light? 1. green 2. white The radiation curve of the sun shows that the brightest light from the sun is yellowgreen. Why then do we see the sun as whitish instead of yellow-green? 3. cyan 4. red 5. magenta 1. The yellow-green light has very strong intensity, so when it arrives at our eyes, we can only feel it as strong white light. 6. blue 7. yellow 2. All colors mix to produce the white light we see. 3. When sunlight passes through the air, yellow-green components are absorbed by the air. 4. Outside the Earth you will see yellowgreen light of the sun. Part 2 of 3 What color should be combined with green light to produce white light? 1. green 2. white 3. cyan Chapter 34, section 9, The Spectrum of Electromagnetic Waves 195 34:09, highSchool, numeric, > 1 min, normal. 4. red The portion of the visible spectrum that appears brightest to the human eye is around 560 nm in wavelength, which corresponds to yellow-green. The speed of light is 3 × 108 m/s. What is the frequency of 560 nm light? 5. magenta 6. blue 7. yellow Part 3 of 3 What color is the mixture of magenta, yellow and cyan light? Holt SF 14A 06 34:09, highSchool, numeric, > 1 min, normal. What is the frequency of highly energetic ultraviolet radiation that has a wavelength of 125 nm? The speed of light is 3 × 108 m/s. 1. green 2. white 3. cyan Holt SF 14Rev 12 34:09, highSchool, numeric, > 1 min, wordingvariable. 4. red 5. magenta What is the wavelength of an FM radio signal if the number on the dial reads 99.5 MHz? The speed of light is 3 × 108 m/s. 6. blue 7. yellow Holt SF 14Rev 13 34:09, highSchool, numeric, > 1 min, normal. Hewitt CP9 27 R01 34:09, highSchool, multiple choice, < 1 min, fixed. What is the relationship between the frequency of light and its color? 1. Lights of different frequencies are perceived as different colors. 2. The lowest-frequency light we detect appears to most people as the color violet. 3. The highest-frequency light we detect appears to most people as the color red. 4. There is no relationship between the frequency of light and its color. 5. None of these Holt SF 14A 05 What is the wavelength of a radar signal that has a frequency of 33 GHz? The speed of light is 3 × 108 m/s. Chapter 35, section 1, The Nature of Light Concept 20 07 35:01, highSchool, multiple choice, < 1 min, fixed. 196 we can still see it. What differences in the properties of sound and light does this indicate? 1. The bell jar is a good absorber of sound. From the stands of a race track why do you notice smoke from the starter’s gun before you hear it fire? 1. The response time of eyes is shorter than that of ears. 2. The gun smokes before making sound. 2. The bell jar is a good light transmitter. 3. Sound needs a material medium for its transmission, while light does not. 4. Light needs a material medium for its transmission, while sound does not. 3. Light travels about a million times faster than sound in air. 5. There is a frequency shift of sound waves when it passes through a vacuum. 4. Sound has a much longer wavelength than light. Concept 20 24 35:01, highSchool, multiple choice, < 1 min, fixed. 5. Smoke spreads out quickly. Concept 20 08 35:01, highSchool, multiple choice, < 1 min, fixed. At Olympic competition, a microphone picks up the sound of the starter’s gun and sends an electric signal to speakers at every runner’s starting block. Why? 1. There is a lot of noise in the stadium, so the runners have difficulty hearing the gun fire. 2. The electronic starting gun does not rely on time for sound to travel through air. 3. There is no unique reason for that. 4. Electric signals travel about a million times faster than sound in air. What two physics mistakes occur in a science fiction movie that shows a distant explosion in outer space, where you see and hear the explosion at the same time? 1. In outer space there is no material to carry light; if there were, the sound would reach you before the light. 2. In outer space there is no air to carry sound; if there were, the faster-moving light would reach you before the sound. 3. The explosion cannot occur in outer space; if it could, the faster-moving light would reach you before the sound. 4. The explosion cannot occur in outer space; if it could, the sound would reach you before the light. 5. None of these Concept 20 12 35:01, highSchool, multiple choice, < 1 min, fixed. If a bell rings inside a bell jar, we can no longer hear it when the air is pumped out, but Concept 20 25 35:01, highSchool, multiple choice, < 1 min, fixed. A rule of thumb for estimating the distance Chapter 35, section 1, The Nature of Light in kilometers between an observer and a lightning stroke is to divide the number of seconds in the interval between the flash and the sound by 3. Is this rule correct? 197 (invisible infrared light or heat). 3. The missing energy strengthens the intensity of the light emitted. 4. None of these 1. No; the speed of light must be considered in this problem. 2. No; the speed of sound varies rapidly with altitude. 3. Yes; the speed of light is much greater than the speed of sound. Conceptual 20 Q15 35:01, highSchool, multiple choice, < 1 min, wording-variable. What is the frequency range of light seen when you look at a white object? 1. all visible colors 4. Yes; the sound waves are longitudinal waves. 2. no visible colors Concept 29 01 35:01, highSchool, multiple choice, < 1 min, fixed. 3. ultra violet colors Why can the sunlight that illuminates the Earth be approximated by plane waves, whereas the light from a nearby lamp cannot? 5. All possible colors 1. The sunlight is much stronger than the light from a nearby lamp. 2. The Sun is much farther away from us than the nearby lamp. 3. The light from a lamp is circular polarized while the light from the Sun is not. 4. None of these Concept 30 19 35:01, highSchool, multiple choice, < 1 min, fixed. 4. infra-red colors 6. No possible colors Conceptual 20 Q19 35:01, highSchool, multiple choice, < 1 min, fixed. Why don’t planets twinkle the way stars do? I) The light coming from a planet is larger in diameter. II) The planets are larger than stars. III) The view of the stars are obstructed by other stars. IV) The thermal fluctuation in the atmosphere distorts the light of the stars. 1. II only If atoms of a substance absorb ultraviolet light and emit red light, what becomes of the “missing” energy? 2. III only 3. I and III only 1. The missing energy becomes the nuclear energy of the substance. 2. The missing energy is light of other colors 4. I and IV only 5. II and III only Chapter 35, section 1, The Nature of Light 198 5. None of these 6. III and IV only 7. I, II and III only Hewitt CP9 26 E02 35:01, highSchool, multiple choice, < 1 min, fixed. 8. II, III and IV only 9. All of these Conceptual 21 Q01 35:01, highSchool, multiple choice, < 1 min, fixed. The leaves of a tree are bright green. What does a leaf’s absorption spectrum look like? 1. The leaf would absorb all colors except green. 2. The leaf would reflect all colors except green. 3. The leaf would absorb sunlight. 4. The leaf would reflect sunlight. An excited atom emits a photon of a certain frequency. Then two photons of this frequency fly towards the atom. Which of the following is likely to happen next? 1. The atom will absorb both photons and will become more excited than it originally was. 2. The atom will absorb one of the photons and will return to its excited state. 3. One of the two photons will knock an electron out leaving an ion behind. 4. An atom will emit another photon of the same frequency. Hewitt CP9 26 P08 35:01, highSchool, numeric, > 1 min, normal. 5. None of these Conceptual 21 Q02 35:01, highSchool, multiple choice, < 1 min, fixed. Consider objects that appear red. Which is not true? 1. The red marker will be sharply peaked in red as compared to other spectrum. 2. The red laser will be sharply peaked in the red, with no other colors emitted. 3. The red coal will be peaked in the infrared, with some overlap into the visible spectrum. 4. The red sweater will have a peak in the red, but not quite as sharp as the laser. Part 1 of 2 A certain blue-green light has a wavelength of 600 nm in air. What is its wavelength in water, where light travels at 75 % of its speed in air? Part 2 of 2 What is its wavelength in Plexiglas, where light travels at 67 % of its speed in air? Hewitt CP9 27 E01 35:01, highSchool, multiple choice, < 1 min, fixed. In a dress shop with only fluorescent lighting, a customer insists on taking dresses into the daylight at the doorway to check their color. Is she being reasonable? 1. No; the light in the dress shop is enough Chapter 35, section 1, The Nature of Light for her to see the effect. 2. Yes; in sunlight she can see much more clearly. 199 2. Red for a hot day and yellow for a cold day. 3. Green for a hot day and white for a cold day. 3. Yes; under fluorescent lighting, blue colors will be accented. Colors appear quite different in sunlight. 4. Yellow for a hot day and blue for a cold day. 4. No; if all customers make this kind of request, the shop will lose control. 5. Green for a hot day and magenta for a cold day. Hewitt CP9 27 E02 35:01, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 27 E04 35:01, highSchool, multiple choice, < 1 min, fixed. Why will the leaves of a red rose be heated more than the petals when illuminated with red light? Why do we not list black and white as colors? 1. The petals of a red rose will reflect red light while the green leaves absorb red light. The energy absorbed by the leaves tends to increase their temperature. 1. People usually think black and white should only reflect dark and light in a image. They cannot represent the colorful world. 2. We have a subjective mind. 2. The cells in leaves are different from those in petals. They are more likely to absorb heat. 3. Black should not be regarded as a color; an early mistake in theory caused white to be regarded as a color. 3. Red light will distort the DNA in leaves and make it easy to receive energy, but for petals this cannot happen. 4. Black means low intensity; white is the result of an additive mixture of all the colors. 4. If the petals are illuminated with red light, they will dry immediately and cannot absorb additional light. Hewitt CP9 28 R18 35:01, highSchool, numeric, < 1 min, fixed. Which travels most slowly in glass? Hewitt CP9 27 E03 35:01, highSchool, multiple choice, < 1 min, fixed. 1. Red light 2. Blue light If sunlight were somehow green instead of white, what color garment would be most advisable on an uncomfortable hot day? On a very cold day? 1. Blue for a hot day and green for a cold day. 3. Violet light 4. Yellow light 5. Orange light 6. Brown light Chapter 35, section 1, The Nature of Light 7. Green light 200 Chapter 35, section 4, Reflection 201 3. Illuminated with green light Hewitt CP9 27 E06 35:04, highSchool, multiple choice, < 1 min, fixed. 4. Illuminated with blue light 5. Illuminated with orange light Fire engines used to be red. Now many of them are yellow-green. Why was the color changed? Hewitt CP9 27 R32 35:04, highSchool, multiple choice, < 1 min, fixed. 1. Red color makes people feel nervous. Why does water appear cyan? 2. They are most likely to be noticed if they are yellow-green; the eye is most sensitive to that color. 1. Blue light from the sky is reflected by the surface of water. 3. Red color is not easy to notice among fires. 2. Water molecules absorb more blue light than any other light. 4. People got tired of the red color and a color change was advised. 3. Water molecules resonate somewhat in the visible red, causing red light to be absorbed easieer than blue light in water. Hewitt CP9 27 E09 35:04, highSchool, multiple choice, < 1 min, fixed. 4. At normal temperature water gives out more blue light than any other light. What color would red cloth appear if it were illuminated by sunlight or by cyan light only? 5. Water molecules strongly absorb infrared light, which makes water appear cyan. 1. red and cyan correspondingly 2. red and blue correspondingly 3. blue and red correspondingly 4. red and red correspondingly Hewitt CP9 28 E04 35:04, highSchool, multiple choice, < 1 min, fixed. Trucks often have signs on their backs that says: “If you can’t see my mirrors, I can’t see you.” Explain the physics here. 4. red and black correspondingly Hewitt CP9 27 E23 35:04, highSchool, multiple choice, < 1 min, fixed. In which of these cases will a ripe banana appear black? 1. The truck is too big to let the mirror be seen. 2. They all might have a bad mirror. 3. Light that takes a path from point A to point B will take the same reverse path in going from point B to point A. 1. Illuminated with red light 2. Illuminated with yellow light 4. If you are good driver, you may not need a mirror. Chapter 35, section 4, Reflection Hewitt CP9 28 R05 35:04, highSchool, numeric, < 1 min, fixed. What is the law of reflection? in the figure. A light ray strikes the horizontal mirror, reflects off the horizontal mirror, impinges on the raised mirror, reflects off the raised mirror, and proceeds in the right-hand direction. 1. Reflection is not consistent from an irregular surface. φ 2. The critical angle is 90 degrees. 3. The angle of incidence equals the angle of refraction. 4. The angle of refraction equals the angle of reflection. 5. The angle of reflection equals the angle of incidence. 6. A faster light in the media results in a larger reflective angle. Hinged Mirrors 01 35:04, highSchool, numeric, > 1 min, wordingvariable. The reflecting surfaces of two intersecting flat mirrors are at an angle of 56◦ , as shown in the figure. A light ray strikes the horizontal mirror at an angle of 53◦ with respect to the mirror’s surface. φ 56◦ 53◦ Figure is not drawn to scale. Calculate the angle φ. Holt SF 14Rev 53 35:04, highSchool, numeric, > 1 min, normal. The reflecting surfaces of two intersecting flat mirrors are at an angle of 57 ◦ , as shown 202 57◦ Figure is not drawn to scale. Calculate the angle φ. Chapter 35, section 5, Transmission and Refraction Air Liquid Interface 01 35:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Consider a light ray which enters from air to a liquid, where the index of refraction of √ the liquid is given by n = 2. Consider the following three ratios, where each is defined by the specified quantity in the liquid, λ , f , and v , to that in the air, λ, f, and c. light ray n=1 n= √ 2 Air 1. 2. 3. 4. 5. λ λ λ λ λ λ λ λ λ λ λ ? λ =1 = 1 2 √ Air Liquid Interface 02 35:05, highSchool, numeric, < 1 min, normal. Part 1 of 3 Consider a light ray which enters from air to a liquid, where the index of refraction of the liquid is given by n = 1.41421. Consider the following three ratios, where each is defined by the specified quantity in the liquid, λ , f , and v , to that in the air, λ, f, and c. light ray Air 1.41421 1 =√ 2 = f =2 f n=1 Liquid What is the ratio of their wavelengths, 5. 203 Liquid What is the ratio of their wavelengths, Part 2 of 3 What is the ratio of their frequencies of oscilf lations, ? f Part 3 of 3 2 =2 Part 2 of 2 What is the ratio of their frequencies of oscilf lations, ? f f 1. =1 f f 1 2. =√ f 2 f 1 3. = f 2 √ f 4. =2 f λ ? λ What is the ratio of the traveling speeds, v ? c Air Liquid Interface 03 35:05, highSchool, multiple choice, < 1 min, fixed. Consider a light ray which enters from air to a liquid, where the index of refraction of √ the liquid is given by n = 2. light ray n=1 n= √ 2 What is the ratio the liquid) Air Liquid v (where v is defined in c Chapter 35, section 5, Transmission and Refraction 1. 2. 3. 4. 5. v c v c v c v c v c 204 1 =√ 2 mond? The speed of light in a vacuum is 3 × 108 m/s. =1 Conceptual 20 Q31 35:05, highSchool, multiple choice, < 1 min, fixed. = = 1 2 √ 2 =2 Concept 28 E09 35:05, highSchool, multiple choice, < 1 min, fixed. A person in a dark room looking through a window can clearly see a person outside in the daylight. Why can the person outside not see the person inside? 1. Window glass typically transmits about 92% of incident light, and the two surfaces reflect about 8%. 2. The reflected outside light is more intense than the inside light transmitted out. 3. People inside the room are more sensitive to light than people outside. 4. Light is easier to transmit into the room than transmit out. It sometimes happens that in cities located on a coast a hazy white layer can be seen over the city, but the layer is much less pronounced, or even absent, over the water. Why does this happen? 1. the water is cooler than the city 2. the water is warmer than the city 3. due to reflection 4. due to refraction 5. None of these Figuring Physics 23 35:05, highSchool, multiple choice, < 1 min, fixed. Light rays bend as they pass from air into water at an angle (not 90 degrees). This is refraction. Incident ray Normal Conceptual 20 02 35:05, highSchool, numeric, < 1 min, fixed. Air Water If the speed of light through material Z is 2.5 × 108 m/s, what is this material’s index of refraction? The speed of light in a vacuum is 3 × 108 m/s. Conceptual 20 03 35:05, highSchool, numeric, < 1 min, fixed. Diamond has a high index of refraction at about 2.4, which helps account for its sparkle. How fast does light travel through a dia- Refracted ray Which quantity doesn’t change when light refracts? 1. average speed of light 2. index of refraction of the material Chapter 35, section 5, Transmission and Refraction 205 3. frequency of light 4. wavelength of light Hewitt CP9 26 E18 35:05, highSchool, multiple choice, < 1 min, fixed. Is glass opaque to light of frequencies that match its own natural frequencies? 1. No; the frequencies of glass are in magnitudes that no light frequencies will match. 2. No; the frequencies of glass are related to the movements of glass atoms, which are almost not affected by the frequencies of light. 3. Yes; the electrons in the glass will be excited by the incident light, the frequecies of which match the natural frequencies of the glass. 4. Yes; the energy of light will be totally converted into the energy of electrons in the glass when the frequencies of light match the natural frequencies of the glass. 5. More information is needed. Hewitt CP9 27 R29 35:05, highSchool, multiple choice, < 1 min, fixed. When light strikes the surface between glass and air perpendicularly, about 4% is reflected. What is the percentage of light transmitted through a plane of window glass? Hewitt CP9 28 P06 35:05, highSchool, numeric, < 1 min, normal. No glass is perfectly transparent. Mainly because of reflections, about 92 % of light passes through an average sheet of clear windowpane. The 8% loss is not noticed through a single sheet, but through several sheets it is apparent. How much light is transmitted by a “double-glazed” window (one with two sheets of glass)? Hewitt CP9 28 R14 35:05, highSchool, multiple choice, < 1 min, fixed. What causes refraction? 1. the existence of different colors of light 2. the difference in the speed of light in different transparent media 3. the speed of light being higher than c in some media 4. reflection What part of the electromagnetic spectrum is most absorbed by water? 1. infrared 2. radio wave 3. red 4. microwave 5. ultraviolet Hewitt CP9 28 P05 35:05, highSchool, numeric, < 1 min, normal. 5. None of these Light enters from air to liquid 35:05, highSchool, multiple choice, > 1 min, fixed. Consider a light ray which enters from air to a liquid, where the index of refraction of √ the liquid is given by n = 2. Chapter 35, section 5, Transmission and Refraction light ray n=1 n= √ 2 Air Liquid Denote the wavelength and the frequency in the liquid by λ and f and those in the air by λ and f . Choose the correct pair of ratios: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ √ 1 f =, =2 2 f √ f 1 =√ , =2 f 2 √ f = 1, =2 f √ √ f = 2, =2 f √ f = 2, =2 f 1 f =, =1 2 f f 1 =√ , =1 f 2 f = 1, =1 f √ f = 2, =1 f f = 2, =1 f 206 Chapter 35, section 6, The Law of Refraction 207 above, below or at the visible space station? Concept 28 E25 35:06, highSchool, multiple choice, > 1 min, fixed. 1. Above 2. Directly at While standing on a bank you wish to spear a fish in front of you. Would you aim above, below, or directly at the observed fish to make a direct hit? If, on the other hand, you wished to zap the fish with a laser beam of the same color as the fish, how would you aim? 1. Below; above 2. Below; directly at 3. Above; above 3. Below 4. It depends on the movement of the space station. Concept 28 E38 35:06, highSchool, multiple choice, < 1 min, fixed. When your eyes are submerged in water, do light rays coming from water to your eyes bend more, less, or the same as in air? 4. Above; below 1. More 5. None of these 2. Less Concept 28 E26 35:06, highSchool, multiple choice, > 1 min, fixed. If while standing on a bank you wished to zap a small blue fish out in front of you with red laser beam, would you aim above, below, or directly at the observed fish to make a direct hit? 1. Slightly below the position 2. Slightly above the position 3. Directly at the fish 4. It depends on the movement of the water. 3. The same 4. It depends on the speed of the water. Conceptual 20 Q26 35:06, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 In movies that involve a character lost in the wilderness somewhere, you often see the hero vainly try to spear a fish in a river or tidal basin. Even if his aim is good, how should he aim to spear the fish? 1. below the fish 2. above the fish Concept 28 E30 35:06, highSchool, multiple choice, < 1 min, fixed. 3. on the heart 4. at the tail If you were to send a beam of laser light to a space station above the atmosphere and just above the horizon, would you aim the laser Part 2 of 2 Due to refraction, how deep is the fish in Chapter 35, section 6, The Law of Refraction relation to its image? 1. deeper 2. shallower 3. at the point of the image Hewitt CP9 26 E21 35:06, highSchool, multiple choice, < 1 min, fixed. Your friend says that you can get a sunburn on a cloudy day but you cannot get a sunburn even on a sunny day if you are behind glass. Is he correct? 1. Yes; most of the solar spectrum can pass through clouds. 2. No; clouds are full of water, which can block most of the sunlight. 3. Yes; clouds are transparent to ultraviolet light, which is the major reason for sunburn. 4. No; glass is transparent to ultraviolet light, which is the major reason for sunburn. 5. None of these 208 of refraction. Part 2 of 3 b) If the light travels from air to some medium with an angle of incidence of 14.5◦ and an angle of refraction of 9.80◦ , find the refractive index of the unknown medium. Part 3 of 3 c) If the light travels from air to diamond (n = 2.419) at an angle of incidence of 31.6◦ , find the angle of refraction. Holt SF 15A 03 35:06, highSchool, numeric, < 1 min, wordingvariable. A ray of light of vacuum wavelength 550 nm traveling in air enters a slab of transparent material. The incoming ray makes an angle of 40.0◦ with the normal, and the refracted ray makes an angle of 26.0◦ with the normal. Find the index of refraction of the transparent material. (Assume that the index of refraction of air for light of wavelength 550 nm is 1.00.) Holt SF 15Rev 10 35:06, highSchool, numeric, < 1 min, wordingvariable. Holt SF 15A 01 35:06, highSchool, numeric, < 1 min, wordingvariable. Light passes from air into water at an angle of incidence of 42.3◦ . Find the angle of refraction in the water. Find the angle of refraction for a ray of light that enters a bucket of water (n = 1.333) from air at an angle of 25.0◦ to the normal. Holt SF 15Rev 11 35:06, highSchool, numeric, < 1 min, wordingvariable. Holt SF 15A 02 35:06, highSchool, numeric, < 1 min, wordingvariable. A ray of light enters the top of a glass of water at an angle of 36.0◦ with the vertical. What is the angle between the refracted ray and the vertical? Part 1 of 3 An incoming ray of light has a vacuum wavelength of 589 nm. a) If the light travels from flint glass (n = 1.66) to crown glass (n = 1.52) with an angle of incidence of 25.0◦ , find the angle Holt SF 15Rev 12 35:06, highSchool, numeric, < 1 min, wordingvariable. A narrow ray of yellow light from glowing Chapter 35, section 6, The Law of Refraction sodium (λ 0 = 589 nm) traveling in air strikes a smooth surface of water at an angle θi = 35.0◦ . Find the angle of refraction, θr . Holt SF 15Rev 13 35:06, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 A ray of light traveling in air strikes a flat 2.00 cm thick block of glass (n = 1.50) at an angle of 30.0 ◦ with the normal. a) Trace the light ray through the glass, and find the angle of refraction for light passing from air to glass. Part 2 of 2 b) Find the angle of refraction for light passing from glass to air. Holt SF 15Rev 14 35:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The light ray shown in the figure makes an angle of 20.0◦ with the normal line at the boundary of linseed oil and water. θ1 Air ◦ 20 Linseed oil θ2 Water a) Find the angle θ1 . Note that n = 1.48 for the linseed oil. Part 2 of 2 b) Find the angle θ2 . Holt SF 15Rev 39 35:06, highSchool, numeric, < 1 min, wordingvariable. 209 The angle of incidence and the angle of refraction for light going from air into a material with a higher index of refraction are 63.5◦ and 42.9◦ , respectively. What is the index of refraction of this material? Holt SF 15Rev 40 35:06, highSchool, numeric, < 1 min, wordingvariable. A person shines a light at a friend who is swimming underwater. If the ray in the water makes an angle of 36.2◦ with the normal, what is the angle of incidence? Holt SF 15Rev 41 35:06, highSchool, numeric, < 1 min, wordingvariable. What is the index of refraction of a material in which the speed of light is 1.85 × 108 m/s? Holt SF 15Rev 42 35:06, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 Light moves from flint glass (n = 1.66) into water at an angle of incidence of 28.7◦ . a) What is the angle of refraction? Part 2 of 2 b) At what angle would the light have to be incident to give an angle of refraction of 90.0◦ Holt SF 15Rev 49 35:06, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The index of refraction for red light in water is 1.331, and that for blue light is 1.340. a) If a ray of white light traveling in air enters the water at an angle of incidence of 83.0◦ , what is the angle of refraction for the red component of light? Chapter 35, section 6, The Law of Refraction Part 2 of 2 b) What is the angle of refraction for the blue component of light? Holt SF 15Rev 50 35:06, highSchool, numeric, > 1 min, wordingvariable. A ray of light traveling in air strikes the surface of mineral oil at an angle of 23.1◦ with the normal to the surface. If the light travels at 2.17 × 108 m/s through the oil, what is the angle of refraction? Holt SF 15Rev 51 35:06, highSchool, numeric, > 1 min, wordingvariable. A ray of light traveling in air strikes the surface of a liquid. If the angle of incidence is 30.0◦ and the angle of refraction is 22.0◦ , find the critical angle for light traveling from the liquid back into the air. Holt SF 15Rev 52 35:06, highSchool, numeric, < 1 min, wordingvariable. The laws of refraction and reflection are the same for sound and for light. The speed of sound is 340 m/s in air and 1510 m/s in water. If a sound wave that is traveling in air approaches a flat water surface with an angle of incidence of 12.0◦ , what is the angle of refraction? Holt SF 15Rev 54 35:06, highSchool, numeric, < 1 min, wordingvariable. A ray of light traveling in air strikes the surface of a block of clear ice (n = 1.309) at an angle of 40.0◦ with the normal. Part of the light is reflected and part is refracted. Find the angle between the reflected and the refracted light. 210 Holt SF 15Rev 60 35:06, highSchool, numeric, > 1 min, wordingvariable. A flashlight on the bottom of a 4.00 m deep swimming pool sends a ray upward and at an angle so that the ray strikes the surface of the water 2.00 m from the point directly above the flashlight. What angle (in air) does the emerging ray make with the water’s surface? Holt SF 15Rev 61 35:06, highSchool, numeric, > 1 min, wordingvariable. A submarine is 325 m horizontally out from the shore and 115 m beneath the surface of the water. A laser beam is sent from the submarine so that it strikes the surface of the water at a point 205 m m from the shore. If the beam strikes the top of a building standing directly at the water’s edge, find the height of the building. Chapter 35, section 7, Dispersion and Prisms 211 9. None of these Conceptual 20 Q09 35:07, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Diamonds have a very high index of refraction. How does this help to account for their sparkle? 1. dispersion of light Conceptual 20 Q11 35:07, highSchool, multiple choice, < 1 min, fixed. If the atmosphere did not scatter light, what would you see when you looked at the daytime sky? I) The sky would be dark; II) Sunlight would pass right through atmosphere; III) Light would be scattered to your eyes. 2. refraction 1. I and II only 3. light emitted by the diamond. 2. II and III only 4. None of these 3. I and III only 4. All of these 4. All of these Part 2 of 2 The cutting of diamonds into facets increase the sparkle you see. Consider the following statements. I) Internal reflection of light increases; II) More light is transmitted with dispersion; III) It enhances the appearance; IV) Refraction occurs. Which is/are NOT true? 5. None of these Conceptual 20 Q12 35:07, highSchool, multiple choice, < 1 min, fixed. If the atom and molecules in the sky had about 10 times their present size, what would you expect the daytime sky to be? 1. much whiter 1. I only 2. blue 2. II only 3. dark 3. III only 4. red 4. IV only 5. None of these 5. I and II only 6. II and III only Conceptual 20 Q17 35:07, highSchool, multiple choice, < 1 min, wording-variable. 7. I and IV only 8. II and IV only For a house window to be as energy efficient as possible, to which wavelengths of the electromagnetic spectrum should it be trans- Chapter 35, section 7, Dispersion and Prisms parent? 1. visible light 2. all except visible light 3. ultra violet light 212 Hewitt CP9 27 E34 35:07, highSchool, multiple choice, < 1 min, fixed. If the sky on a certain planet in the solar system were normally orange, what color would sunset be? 4. infra-red light 1. red 5. All light 2. blue Conceptual 20 Q30 35:07, highSchool, multiple choice, < 1 min, fixed. 3. yellow Which parts of the electromagnetic spectrum, if any, scatter all wavelengths equally from atoms and molecules? 5. white 1. gamma rays 2. alpha rays 3. beta rays 4. ultra-violet rays 4. orange 6. black Hewitt CP9 27 E35 35:07, highSchool, multiple choice, < 1 min, fixed. Volcanic emissions put fine ashes in the air that scatter red light. What color does a full moon appear through these ashes? 5. infrared rays 1. red Hewitt CP9 27 E27 35:07, highSchool, multiple choice, < 1 min, fixed. 2. cyan 3. yellow Why does the sky appear darker blue when you are at high altitudes? 1. There is less sunshine at high altitudes than at lower altitudes. 4. orange 5. brown 6. gray 2. There is less air above you and consequently less scattering of sunlight. 3. There are more red-absorbing molecules in the air at high altitudes. 4. There is less air above you and consequently more scattering of sunlight. Hewitt CP9 27 E38 35:07, highSchool, multiple choice, < 1 min, fixed. If the atomosphere of the Earth were several times thicker, what color would the ordinary snowfall seem? Chapter 35, section 7, Dispersion and Prisms 1. red 2. blue 213 enter a glass block normal to its surface at the same time. After passing through the block, which pulse exits first? 3. white 1. Red light 4. green 2. Blue light 5. black 3. Yellow light 6. gray 4. Green light Hewitt CP9 27 R25 35:07, highSchool, multiple choice, < 1 min, fixed. Why does the sun look red at sunrise and sunset but not at noon? 1. Red light is easily transmitted through the air since its frequency is the lowest. At noon, sunlight travels through the least amount of atmosphere with little scattering of high-frequency light to the surface. 2. Red light is easily scattered through the air since its frequency is the lowest. At noon, sunlight travels through the least amount of atmosphere with little transmission of highfrequency light to the surface. 3. The sun is colder at sunrise and sunset than at noon. 4. The temperature at noon is warmer than at sunrise and sunset. 5. Our eyes are more sensitive to the red light at sunrise and sunset than at noon. 6. The sun itself is red at sunrise and sunset, but is yellow at noon; it has nothing to do with the effect of the atmosphere. Hewitt CP9 28 E21 35:07, highSchool, multiple choice, < 1 min, fixed. A pulse of red light and a pulse of blue light 5. Violet light Hewitt CP9 28 E22 35:07, highSchool, multiple choice, < 1 min, fixed. During a lunar eclipse, the moon is not completedly dark, but is often a deep red in color. Why? 1. During the sunset, the Sun transfers some red light to the moon. 2. High frequencies pass more easily through the long grazing path through the Earth’s atmosphere to be refracted finally onto the moon. 3. Low frequencies pass more easily through the long grazing path through the Earth’s atmosphere to be refracted finally onto the moon. Chapter 35, section 8, Huygens’ Principle 214 4. none of these Huygens Reflection Analysis 35:08, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 The figure below shows Christian Huygens’ analysis of the reflection from the surface of a mirror. The two arcs are Huygens’ wavelets that were emitted simultaneously from points A and B at t = 0 . Assume: Medium 1 is a vacuum and Medium 2 has an index of refraction greater than 1. Part 3 of 3 According to Huygens’ principle, which of the following would NOT be a property of the wave front AB after it had propagated from time t from the position shown in the figure? The new (reflected) wave front would 1. be tangent to the wavelet centered at A. 2. pass through the point D. 3. form an angle equal to θ with the mirror surface. 4. form an angle equal to θ with the surface normal. θ nt ide nt inc fro ve wa B A 6. form a right angle with the reflected ray. mirror surface D The angle of incidence θ is equal to which angle? 1. θ = B DA 2. θ = B AD 3. θ = ABD 4. none of these Part 2 of 3 The radius rA of the wavelet centered at A must be equal to 1. rA = AD 2. rA = AB 3. rA = BD 5. touch the wavelet centered at A at a point that is exactly distance AB away from point D. 7. none of these. Huygens Refraction Analysis 35:08, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 The figure below shows Christian Huygens’ analysis of the refraction of a wave front AB upon entering Medium 2 from Medium 1. The two arcs are Huygens’ wavelets that were emitted from points A and B at t = 0 . Assumre: Medium 1 is a vacuum and Medium 2 has an index of refraction greater than 1. Chapter 35, section 8, Huygens’ Principle nt y Ra e av W fro 3. sin θ1 = 4. sin θ1 = θ1 5. sin θ1 = B 6. sin θ1 = t v1 A D v 2t 7. sin θ1 = Medium 1 Medium 2 θ2 Ray C According to Huygens, the index of refraction of Medium 2 is equal to the ratio of which two line segments? 1. n = 2. n = 3. n = 4. n = 5. n = 6. n = 7. n = 8. n = AB CD AC BD CD AB BD AC AB AD BD AD AC AD CD AD AB AD BD 2. sin θ1 = AB 1. n = 2. n = 4. n = 5. n = 6. n = 7. n = 8. n = CD AD AC sin θ2 = CD sin θ2 = sin θ2 = sin θ2 = sin θ2 = sin θ2 = sin θ2 = sin θ2 = AC AD AC AB AB AD BD AC BD AD BD AB Part 3 of 3 The conclusion of Huygen’s analysis is that the index of refraction of Medium 2 is equal to the ratio of the sines of which two angles? 3. n = Part 2 of 3 The sines of the angles θ1 and θ2 are equal, respectively to 1. sin θ1 = 8. sin θ1 = BD AD BD CD CD AD AB CD AC AD AC CD 215 B AD ABD B DA DAC ADC DAC B DA B AD C AD ADC B AD ADC ABD ACD B DA ADC Chapter 35, section 9, Total Internal Reflection Conceptual 20 27 35:09, highSchool, multiple choice, < 1 min, fixed. In many weapons systems, including aircraft, fiber optics is used to transmit information. Why might fiber optics be particular useful in a military application such as a battlefield environment? I) Fiber optics are very light. II) Fiber optics are very compact. III) Fiber optics are flexible. IV) Fiber optics can carry more information than a copper wire. 216 Conceptual 20 Q29 35:09, highSchool, multiple choice, < 1 min, fixed. A polar bear actually has translucent colorless fur and black skin. What are the benefits it derives from this? 1. It acts like a fibre optic cable. 2. It gives the fur white in color. 3. It makes the fur shiny. 4. All of these 5. None of these 1. I only 2. II only Conceptual 20 Q32 35:09, highSchool, multiple choice, < 1 min, fixed. 3. III only 4. IV only 5. I and II only 6. II and III only If you swim just below the surface of a pool and look straight up, you will see the sky. However, if you look at a glancing angle to the surface of the water, you will see a reflection of the bottom of the pool. What caused this to happen? 7. I and IV only 1. total internal reflection 8. I, II and IV only 2. to reflection 9. I, III and IV only 3. refraction 10. All of these 4. None of these Conceptual 20 Q28 35:09, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 27 E05 35:09, highSchool, multiple choice, < 1 min, fixed. If you left a glass fiber-optic cable unshielded by any plastic covering, should the light still be able to travel through the cable? Why are the interiors of optical instruments black? 1. Yes 2. No 1. The interior coating absorbs rather than reflects light, and therefore appears black. 2. The interior should be black in order to keep cool. Chapter 35, section 9, Total Internal Reflection 217 3. There is nothing inside optical instruments. Holt SF 15Rev 37 35:09, highSchool, numeric, < 1 min, fixed. 4. In light the interiors look black, but in a dark environment, they can emit light. Hewitt CP9 28 R25 35:09, highSchool, numeric, > 1 min, normal. Part 1 of 3 Light with a wavelength of λ = 589 nm travels from a certain material to air. a) Calculate the critical angle for zircon (n = 1.923) when it is surrounded by air. What is the critical angle of light in glass if the index of refraction of glass is 1.4 and the index of refraction of air is 1.05? Part 2 of 3 b) Calculate the critical angle for fluorite (n = 1.434) when it is surrounded by air. Holt SF 15C 01 35:09, highSchool, numeric, < 1 min, fixed. Part 3 of 3 c) Calculate the critical angle for ice (n = 1.309) when it is surrounded by air. Find the critical angle for light traveling from glycerine (n = 1.473) into air. Holt SF 15C 02 35:09, highSchool, numeric, < 1 min, fixed. Calculate the critical angle for light traveling from glycerine (n = 1.473) into water (n = 1.333). Holt SF 15C 03 35:09, highSchool, numeric, < 1 min, fixed. Holt SF 15Rev 38 35:09, highSchool, numeric, < 1 min, fixed. Light traveling in air enters the flat side of a prism made of crown glass (n = 1.52), as shown in the figure. 45◦ Find the critical angle for light traveling from ice (n = 1.309) into air. Holt SF 15C 04 35:09, highSchool, numeric, < 1 min, fixed. Part 1 of 2 a) Find the critical angle in air for diamond (n = 2.419). Part 2 of 2 b) Find the critical angle in air for cubic zirconia (n = 2.20). Holt SF 15Rev 36 35:09, highSchool, numeric, < 1 min, fixed. Calculate the critical angle for light going from glycerine (n = 1.473) into air. What is the critical angle? Holt SF 15Rev 53 35:09, highSchool, numeric, > 1 min, wordingvariable. A jewel thief decides to hide a stolen diamond by placing it at the bottom of a crystalclear fountain. He places a circular piece of wood on the surface of the water and anchors it directly above the diamond at the bottom of the fountain. Chapter 35, section 9, Total Internal Reflection 218 30.0◦ d 60◦ 2m 60◦ If the fountain is 2.00 m deep, find the minimum diameter, d of the piece of wood that would prevent the diamond from being seen from outside the water. Holt SF 15Rev 56 35:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A fiber-optic cable used for telecommunications has an index of refraction of 1.53. a) For total internal reflection of light inside the cable, what is the minimum angle of incidence to the inside wall of the cable if the cable is in air? Part 2 of 2 b) What is the minimum angle of incidence to the inside wall of the cable if the cable is in water? 60◦ a) Trace the path of the light ray through the glass and find the angle of incidence of the ray at the bottom of the prism. Part 2 of 2 b) Calculate the critical angle corresponding to total internal reflection. Holt SF 15Rev 58 35:09, highSchool, numeric, < 1 min, wordingvariable. Light strikes the surface of a prism, n = 1.80, as shown in the figure. 45◦ Holt SF 15Rev 57 35:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A ray of light traveling in air strikes the midpoint of one face of an equiangular glass prism (n = 1.55) at an angle of exactly 30.0◦ . If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism? Holt SF 15Rev 59 35:09, highSchool, numeric, < 1 min, wordingvariable. A fiber-optic rod consists of a central strand of material surrounded by an outer coating. The interior portion of the rod has an index of refraction of 1.60. Chapter 35, section 9, Total Internal Reflection If all rays striking the interior walls of the rod with incident angles greater than 59.5◦ are subject to total internal reflection, what is the index of refraction of the coating? Holt SF 15Rev 62 35:09, highSchool, numeric, > 1 min, wordingvariable. A laser beam traveling in air strikes the midpoint of one end of a slab of material with index of refraction 1.48 as shown in the figure below. 42 cm ◦ 50 3.1 mm Find the number of internal reflections of the laser beam before it finally emerges from the opposite end of the slab. 219 Chapter 35, section 10, Fermat’s Principle Hewitt CP9 28 R04 35:10, highSchool, multiple choice, < 1 min, fixed. What does Fermat’s principle say? 1. Light is visible. 2. Nothing in the world can travel with the speed greater than the speed of light. 3. Light can be reflected. 4. Light can be refracted. 5. Out of all possible paths that light might take to get from one point to another, it takes the path that requires the shortest time. 220 Chapter 35, section 12, Luminous Intensity Concept 09 15 35:12, highSchool, multiple choice, < 1 min, fixed. The intensity of light from a central source varies inversely as the square of the distance. If you lived on a planet only half as far from the Sun as our Earth, how would the intensity compare with that on Earth? 1. Two times 2. Three times 3. Four times 4. Eight times Hewitt CP9 09 R11 35:12, highSchool, multiple choice, < 1 min, fixed. excites their electrons into a higher energy level. 3. No; light energy is related to the wavelength of the light, rather than the intensity. 4. No; light intensity gets weaker with distance, but the total amount of light over a spherical surface is the same at all distances from the source. 5. More information is needed. Hewitt CP9 26 E37 35:12, highSchool, multiple choice, < 1 min, fixed. The planet Jupiter is more than five times as far from the Sun as the Earth. How does the brightness of the Sun appear at this greater distance? 1. 5 times the brightness on Earth How does the brightness of light change when a point source of light is brought twice as far away? 2. 1/5 of the brightness on Earth 3. 1/25 of the brightness on Earth 1. same 4. 25 times the brightness on Earth 2. double 5. the same as the brightness on Earth 3. four times brighter than before 6. More information is needed. 4. one fourth darker than before 5. The distance is needed. Hewitt CP9 26 E35 35:12, highSchool, multiple choice, < 1 min, fixed. The intensity of light falls off as the inverse square of the distance from the source. Does this mean that light energy is lost? 1. Yes; the energy of light is proportional to the intensity. 2. Yes; light interacts with air atoms and 221 Chapter 36, section 2, Images Formed by Flat Mirrors 222 Conceptual 20 Q01 36:02, highSchool, multiple choice, > 1 min, fixed. Hewitt CP9 28 E03 36:02, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 How does the smoothness of a mirror affect the clarity of the image you see? 1. The image becomes clear. Cowboy Joe wishes to shoot his assailant by ricocheting a bullet off a mirrored metal plate. To do so, should he simply aim at the mirrored image of his assailant? 2. The image becomes blur. 1. No; if he does so, he will miss the target. 3. There is no change in the image. Part 2 of 2 What is the difference between a set of parallel rays reflected off a very smooth mirror and the same rays reflected off a more bumpy mirror made of the exact material? 2. Yes; the ricocheting bullet will follow the same change in direction upon impact that light follows when reflecting from a plane surface. 3. No; light is refracted in metal. 4. No; an image is not a reliable target. 1. smooth; stay parallel; bumpy; can scatter 2. smooth; can scatter; bumpy; stay parallel 3. Both stay parallel 4. Both can scatter Conceptual 20 Q05 36:02, highSchool, multiple choice, < 1 min, normal. As you walk toward a full-length plane mirror, your image walks towards you. What is the speed of your image if your speed is 1 m/s? 1. 1 m/s 2. 4.5 m/s 3. 6 m/s 4. 1.25 m/s 5. None of these Hewitt CP9 28 E11 36:02, highSchool, multiple choice, < 1 min, fixed. Why is it difficult to see the roadway in front of you when driving on a rainy night? 1. The road is covered with water which acts like a plane mirror. 2. Lightning may prevent you from seeing the roadway clearly. 3. There is no moon to light the roadway. 4. It is much darker outside than on a clear night. Hewitt CP9 28 E12 36:02, highSchool, multiple choice, < 1 min, fixed. What must be the minimum length of a plane mirror in order for you to see a full view of yourself? 1. One fourth of your height Chapter 36, section 2, Images Formed by Flat Mirrors 2. Half of your height 3. Twice of your height 223 How tall will the wiped area be compared with the vertical dimension of your face? 1. The wiped area will be half as tall as your face. 4. One third of your height Hewitt CP9 28 E13 36:02, highSchool, multiple choice, < 1 min, fixed. What effect does your distance from the plane mirror that is half your height have? 1. If you are too far away from the mirror, you cannot see your image. 2. The closer you are to the mirror, the more you can see of your body. 3. The farther you are from the mirror, the more you can see of your body. 4. A half-height mirror works at any distance. Hewitt CP9 28 E14 36:02, highSchool, multiple choice, < 1 min, fixed. Hold a pocket mirror at almost an arm’s length from your face and note the amount of your face you can see. To see more of your face, should you hold the mirror closer or farther, or would you have to have a larger mirror? 2. The wiped area will be one fourth as tall as your face. 3. The wiped area will be one third as tall as your face. 4. The wiped area will twice as tall as your face. 4. The wiped area will the same tall as your face. Hewitt CP9 28 E16 36:02, highSchool, multiple choice, < 1 min, fixed. A diagram shows a person and her twin at equal distances on opposite sides of a thin wall. Suppose a window is to be cut in the wall so each twin can see a complete view of the other. Find the size of the smallest window that can be cut in the wall to do the job. 1. one fourth the height of the person or her twin 2. one third the height of the person or her twin 3. half the height of the person or her twin 1. You have to have a larger mirror. 4. twice the height of the person or her twin 2. You can hold the mirror closer. 3. You can hold the mirror farther. 5. the same the height of the person or her twin Hewitt CP9 28 E15 36:02, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 28 P02 36:02, highSchool, multiple choice, < 1 min, normal. On a steamy mirror wipe away just enough to see your full face. A butterfly at eye level is 20 cm in front of a plane mirror. You are behind the butterfly, Chapter 36, section 2, Images Formed by Flat Mirrors 50 cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror? Hewitt CP9 28 P03 36:02, highSchool, numeric, < 1 min, normal. 224 4. 5 5. 4 6. 10 7. 12 If you take a photograph of your image in a plane mirror, how many meters away should you set your focus if you are 2 m in front of the mirror? Hewitt CP9 28 P04 36:02, highSchool, numeric, < 1 min, normal. Suppose you walk toward a mirror at 2 m/s. How fast do you and your image approach each other? Reflections in Mirrors 01 36:02, highSchool, multiple choice, > 1 min, wording-variable. Hint: Often it is easier to make a rough drawing the determine the answer to what might appear to be a tedious question. In a clothing store two flat mirrors are hinged at one edge (for you to view the clothes you desire to purchase). You (as indicated by an L shaped object) are standing in the 47 ◦ wedge formed by two mirrors. A view from above is shown below. 8. 3 9. 7 Reflections in Mirrors 02 36:02, highSchool, multiple choice, > 1 min, wording-variable. Hint: Make a rough drawing to check your answer. Often in a clothing store two flat mirrors are hinged at one edge (for you to view the clothes you desire to purchase). You (as indicated by an L shaped object) are standing in the 45 ◦ wedge formed by two mirrors. A view from above is shown below. 45 ◦ How many images can you see in the hinged mirrors? 1. 7 47 ◦ 36 ◦ 2. 5 3. 9 How many images can you see in the hinged mirrors? 34 ◦ 4. 11 1. 6 5. 3 2. 8 6. 4 3. 9 7. 6 8. 8 Chapter 36, section 2, Images Formed by Flat Mirrors 9. 10 225 Chapter 36, section 3, Images Formed by Concave Mirrors 226 and inverted. Concave mirror image 36:03, highSchool, multiple choice, < 1 min, fixed. The goal of this problem is to describe the image of an object as the object moves towards a concave mirror of radius R from a far distance. The figure shows a graph of s vs s, 1 1 1 from the equation + = , for a given rass f dius R, where R = 2f . From the graph you can obtain the answer to the following question. s' 3f s'=sf/(s-f) R=2 f Holt SF 14B 01 36:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 Consider a concave mirror with a focal length of 10.00 cm. a) Find the image distance when the object distance is 10.00 cm. (Answer with −1000 if the image does not exist.) (2 f, 2 f) 2f Part 2 of 4 b) Find the image distance when the object distance is 5.00 cm. (Answer with −1000 if the image does not exist.) f concave mirror 7. s < 0; the image is larger than the object and erect. f 2f 3f s -f s' s' =s When the object is at 0 < s < f , then Part 3 of 4 c) Find the magnification of the image for part b). (Answer with −1000 if the image does not exist.) Part 4 of 4 d) Describe the image for part b). 1. None of these 1. real, inverted, larger 2. s < 0; the image is larger than the object and inverted. 2. virtual, inverted, larger 3. real, upright, larger 3. s < 0; the image is smaller than the object and erect. 4. virtual, upright, larger 5. real, inverted, smaller 4. s < 0; the image is smaller than the object and inverted. 6. virtual, inverted, smaller 7. real, upright, smaller 5. s > 0; the image is larger than the object and erect. 8. virtual, upright, smaller 9. None of these 6. s > 0; the image is larger than the object Chapter 36, section 3, Images Formed by Concave Mirrors 227 Holt SF 14B 02 36:03, highSchool, numeric, > 1 min, normal. Part 2 of 3 b) Calculate the magnification of the image. Part 1 of 3 A concave shaving mirror has a focal length of 33 cm. a) Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. (Answer with −1000 if the image does not exist.) Part 3 of 3 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger Part 2 of 3 b) Calculate the magnification of the image. (Answer with −1000 if the image does not exist.) Part 3 of 3 c) Describe the image. 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 1. real, inverted, larger 8. virtual, upright, smaller 2. virtual, inverted, larger 9. None of these 3. real, upright, larger 4. virtual, upright, larger Holt SF 14B 04 36:03, highSchool, numeric, > 1 min, wordingvariable. 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller Part 1 of 5 A pen placed 11.0 cm from a concave spherical mirror produces a real image 13.2 cm from the mirror. a) What is the focal length of the mirror? 8. virtual, upright, smaller 9. None of these Holt SF 14B 03 36:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A concave makeup mirror is designed so that a person 25.0 cm in front of it sees an upright image at a distance of 50.0 cm behind the mirror. a) What is the radius of curvature of the mirror? Part 2 of 5 b) Calculate the magnification of the image. Part 3 of 5 Assume the pen is placed 27.0 cm from the mirror. c) What is the position of the new image? (Answer with −1000 if the image does not exist.) Part 4 of 5 d) What is magnification of the new image? (Answer with −1000 if the image does not exist.) Chapter 36, section 3, Images Formed by Concave Mirrors Part 5 of 5 e) Describe the new image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 228 8. virtual, upright, smaller 9. None of these Part 3 of 6 c) Find the magnification of the image when an upright pencil is placed 25.0 cm from the mirror. (Answer with −1000 if the image does not exist.) Part 4 of 6 d) Describe the image. 1. real, inverted, larger 7. real, upright, smaller 8. virtual, upright, smaller 2. virtual, inverted, larger 3. real, upright, larger 9. None of these 4. virtual, upright, larger Holt SF 14Rev 34 36:03, highSchool, numeric, > 1 min, wordingvariable. 5. real, inverted, smaller 6. virtual, inverted, smaller Part 1 of 6 A concave shaving mirror has a radius of curvature of 25.0 cm. a) Find the magnification of the image when an upright pencil is placed 45.0 cm from the mirror. (Answer with −1000 if the image does not exist.) Part 2 of 6 b) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Part 5 of 6 e) Find the magnification of the image when an upright pencil is placed 5.00 cm from the mirror. (Answer with −1000 if the image does not exist.) Part 6 of 6 f) Describe the image. 3. real, upright, larger 4. virtual, upright, larger 1. real, inverted, larger 2. virtual, inverted, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 3. real, upright, larger 4. virtual, upright, larger 7. real, upright, smaller Chapter 36, section 3, Images Formed by Concave Mirrors 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Holt SF 14Rev 35 36:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A concave spherical mirror can be used to project an image onto a sheet of paper, allowing the magnified image of an illuminated real object to be accurately traced. a) If you have a concave mirror with a focal length of 8.5 cm, where would you place a sheet of paper so that the image projected onto it is twice as far from the mirror as the object is? 229 Holt SF 14Rev 49 36:03, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A glowing electric light bulb placed 15 cm from a concave spherical mirror produces a real image 8.5 cm from the mirror. The light bulb is moved to a position 25 cm from the mirror. a) What is the image position? (Answer with −1000 if the image does not exist.) Part 2 of 4 b) Find the magnification of the first image. Part 3 of 4 c) Find the magnification of the final image. (Answer with −1000 if the image does not exist.) Part 4 of 4 d) Describe the two images. 1. real, inverted, larger Part 2 of 3 b) What is the magnification of the image? Part 3 of 3 c) Describe the image. 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 1. real, upright, larger 5. real, inverted, smaller 2. real, inverted, larger 6. virtual, inverted, smaller 3. virtual, upright, larger 7. real, upright, smaller 4. virtual, inverted, larger 8. virtual, upright, smaller 5. real, upright, smaller 9. None of these 6. real, inverted, smaller 7. virtual, upright, smaller Holt SF 14Rev 52 36:03, highSchool, numeric, > 1 min, wordingvariable. 8. virtual, inverted, smaller 9. None of these Part 1 of 3 An object is placed 10.0 cm in front of a mirror and an image of the object is formed Chapter 36, section 3, Images Formed by Concave Mirrors on a wall 2.00 m away from the mirror. a) What is the radius of curvature of the mirror? 230 6. p = −2q 7. q = 2p Part 2 of 3 b) Find the magnification of the image. Part 3 of 3 c) Describe the image. 1. real, upright, larger 8. q = −2p 9. None of these. Holt SF 14Rev 57 36:03, highSchool, numeric, > 1 min, wordingvariable. 2. real, inverted, larger 3. virtual, upright, larger 4. virtual, inverted, larger Part 1 of 2 An object 2.70 cm tall is placed 12.0 cm in front of a mirror, which creates an upright image that is 5.40 cm in height. a) What is the magnification of the image? 5. real, upright, smaller 6. real, inverted, smaller Part 2 of 2 b) What is the radius of curvature of the mirror? 7. virtual, upright, smaller 8. virtual, inverted, smaller Holt SF 14Rev 58 36:03, highSchool, multiple choice, > 1 min, fixed. 9. None of these Holt SF 14Rev 54 36:03, highSchool, numeric, > 1 min, fixed. A flat mirror can be treated as a special type of spherical mirror that has an “infinite” radius of curvature. If the equation 2 11 =+ R pq is applied to a flat mirror, which is the correct relationship between p and q ? 1. p = 0, q = ∞ 2. p = ∞, q = 0 A “floating coin” illusion consists of two parabolic mirrors, each with a focal length of 7.5 cm, facing each other so that their centers are 7.5 cm apart (See the following figure). Small hole Parabolic mirrors Coins Place a few coins on the lower mirror. An image of the coins forms due to the mirror system. Determine which of the following statements is true. 4. p = −q 1. The virtual and inverted image is located right on the lower mirror with the magnification of −1. 5. p = 2q 2. The real and upright image is located 3. p = q Chapter 36, section 3, Images Formed by Concave Mirrors right in the top mirror opening with the magnification of +1. 3. The real and inverted image is located 7.5 cm on top of the top mirror opening with the magnification of −1. 4. The virtual and inverted image is located 7.5 cm on top of the top mirror opening with the magnification of −2. 5. The virtual and upright image is located 7.5 cm on top of the top mirror opening with the magnification of 1. 6. The real and upright image is located 7.5 cm on top of the top mirror opening with the magnification of 2. 7. The real and inverted image is located 7.5 cm below the lower mirror with the magnification of −1. 8. The virtual and upright image is located 7.5 cm below the lower mirror with the magnification of 1. 231 Chapter 36, section 4, Images Formed by Convex Mirrors 232 3. II and IV only Conceptual 20 Q21 36:04, highSchool, multiple choice, < 1 min, fixed. 4. I and IV only 5. II and III only Part 1 of 2 What shape are the security mirrors often placed high in the corners of stores? 1. Bowed outward 6. All of these Holt SF 14C 01 36:04, highSchool, numeric, > 1 min, wordingvariable. 2. Bowed inward 3. flat Part 2 of 2 Why are the security mirrors shaped that way? I) to capture a wide field of view as possible II) to focus the cash register III) to focus the people Part 1 of 4 The image of a crayon appears to be 23.0 cm behind the surface of a convex mirror and is 1.70 cm tall. The mirror’s focal length is 46.0 cm. a) How far in front of the mirror is the crayon positioned? Part 2 of 4 b) Calculate the magnification of the image. 1. I only 2. II only Part 3 of 4 c) Describe the image. 3. III only 1. real, inverted, larger 4. All of these 2. virtual, inverted, larger Conceptual 20 Q22 36:04, highSchool, multiple choice, < 1 min, fixed. Some of the mirrors you might see in an amusement park make some parts of you seem large, while at the same time making other parts seem smaller. How is this accomplished? I) II) III) IV) The mirrors are curved outward The mirrors are curved inward The mirrors are flat The mirrors are distorted 1. I and II only 2. I and III only 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Part 4 of 4 d) How tall is the actual crayon? Holt SF 14C 02 36:04, highSchool, numeric, > 1 min, wording- Chapter 36, section 4, Images Formed by Convex Mirrors 233 variable. Part 1 of 4 A convex mirror with a focal length of 0.26 m forms a 0.081 m tall image of an automobile at a distance of 0.25 m behind the mirror. a) How far from the mirror is the car located? Part 3 of 4 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger Part 2 of 4 b) What is the magnification of the image? Part 3 of 4 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Part 4 of 4 d) What is the height of the car? Holt SF 14C 03 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A convex mirror of focal length 33 cm forms an image of a soda bottle at a distance of 19 cm behind the mirror. The height of the image is 7.0 cm. a) Where is the object located? Part 4 of 4 d) How tall is the object? Holt SF 14C 04 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A convex mirror with a radius of curvature of 0.550 m is placed above the aisles in a store. a) Determine the image distance of a customer lying on the floor 3.1 m directly below the mirror. Part 2 of 3 b) What is the magnification of the image? Part 3 of 3 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger Part 2 of 4 b) What is the magnification of the image? 4. virtual, upright, larger Chapter 36, section 4, Images Formed by Convex Mirrors 5. real, inverted, smaller 6. virtual, inverted, smaller 234 Part 1 of 3 A candle is 49 cm in front of a convex spherical mirror that has a focal length of 35 cm. a) What is the image distance? 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Holt SF 14C 05 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 2 of 3 b) Calculate the magnification of the image. Part 3 of 3 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger Part 1 of 3 A spherical glass ornament is 6.00 cm in diameter. An object is placed 10.5 cm away from the ornament. a) Where will its image form? 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller Part 2 of 3 b) What is the magnification of the image? Part 3 of 3 c) Describe the image. 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 1. real, inverted, larger 9. None of these 2. virtual, inverted, larger 3. real, upright, larger Holt SF 14Rev 36 36:04, highSchool, numeric, > 1 min, wordingvariable. 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller Part 1 of 4 A convex mirror with a radius of curvature of 45.0 cm forms a 1.70 cm tall image of a pencil at a distance of 15.8 cm behind the mirror. a) Find the object distance for the pencil. Part 2 of 4 b) Find the magnification of the image. 9. None of these Holt SF 14C 06 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 3 of 4 c) Describe the image. 1. real, inverted, larger Chapter 36, section 4, Images Formed by Convex Mirrors 235 2. virtual, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger 3. real, upright, larger 4. virtual, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 5. real, inverted, smaller 6. virtual, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 7. real, upright, smaller 8. virtual, upright, smaller 8. virtual, upright, smaller 9. None of these 9. None of these Part 4 of 4 d) What is the height of the object? Holt SF 14Rev 48 36:04, highSchool, numeric, > 1 min, wordingvariable. A child holds a candy bar 15.5 cm in front of the convex side-view mirror of an automobile. The image height is reduced by one half. What is the radius of curvature of the mirror? Holt SF 14Rev 50 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A convex mirror is placed on the ceiling at the intersection of two hallways. If a young man stands directly underneath the mirror, his shoe, which is a distance of 195 cm from the mirror, forms an image that appears 12.8 cm behind the mirror’s surface. a) What is the mirror’s focal length? Part 2 of 3 b) What is the magnification of the image? Part 3 of 3 c) Describe the image. 1. real, inverted, larger Holt SF 14Rev 51 36:04, highSchool, numeric, < 1 min, wordingvariable. The side-view mirror of an automobile has a radius of curvature of 11.3 cm. The mirror produces a virtual image one third the size of the object. How far is the object from the mirror? Holt SF 14Rev 55 36:04, highSchool, numeric, < 1 min, wordingvariable. A real object is placed at the zero end of a meter stick. A large concave mirror at the 100.0 cm end of the meterstick forms an image of the object at the 70.0 cm position. A small convex mirror placed at the 20.0 cm position forms a final image at the 10.00 cm point. What is the radius of curvature of the convex mirror? Holt SF 14Rev 56 36:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 A dedicated sports-car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image Chapter 36, section 4, Images Formed by Convex Mirrors of his face 30.0 cm behind the hubcap. He then turns the hubcap over and sees another image of his face 10.0 cm behind the hubcap. a) How far is his face from the hubcap? Part 2 of 4 b) What is the radius of curvature of the hubcap? Part 3 of 4 c) What is the magnification for the first image? Part 4 of 4 d) What is the magnification for the second image? Holt SF 14Rev 59 36:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Use the mirror equation and the equation for magnification to determine which of the following statements is true for the image of a real object formed by a convex mirror. 1. always upright, real, larger than the object. 236 object. 9. None of these Part 2 of 2 Use the mirror equation and the equation for magnification to determine which of the following statements is true for the image of a real object formed by any spherical mirror with p < |f |. 1. always upright, real. 2. always inverted, real. 3. always upright, virtual. 4. always inverted, virtual. 5. None of these Mirrors 36:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 Consider a concave mirror with radius R. An upright object is placed in between the interval R/2 and R. 2. always inverted, real, larger than the object. R R/2 3. always upright, virtual, larger than the object. The image is 4. always inverted, virtual, larger than the object. 5. always upright, real, smaller than the object. 1. real, inverted, enlarged. 2. real, inverted, reduced. 3. real, upright, enlarged. 6. always inverted, real, smaller than the object. 7. always upright, virtual, smaller than the object. 4. real, upright, reduced. 5. virtual, inverted, enlarged. 6. virtual, inverted, reduced. 8. always inverted, virtual, smaller than the Chapter 36, section 4, Images Formed by Convex Mirrors 7. virtual, upright, enlarged. 8. virtual, upright, reduced. 9. real, upright, same size. 10. virtual, upright, same size. Part 2 of 3 Hint: A sketch may help you answer the questions. Consider a new situation for the following two questions. The light rays from an upright object, when reflected by a spherical mirror, form a virtual image. The absolute value of the magnification of this image is less than one. 1. The mirror can only be concave. 2. The mirror can only be convex. 3. The mirror can either be concave or convex. Part 3 of 3 Consider a same situation in the previous question, that is The light rays from an upright object, when reflected by a spherical mirror, form a virtual image. The absolute value of the magnification of this image is less than one. 1. The virtual image is upright and behind the mirror. 2. The virtual image is inverted and behind the mirror. 3. The virtual image is upright and in front of the mirror. 4. The virtual image is inverted and in front of the mirror. 237 Chapter 36, section 5, Spherical Mirrors: Ray Tracing Mirror Convergent Diagram 36:05, highSchool, multiple choice, > 1 min, wording-variable. 238 2. f Hint: The convergent mirror in this problem is a part of a lens/mirror system so the object in this problem may be either real or virtual. Construct a ray diagram. Given: A virtual object is located to the right of a convergent mirror. The object’s distance from the mirror and its focal length are shown in the figure below. 0 19 19 f f 31 12 19 f0 31 19 f 12 3. f f 19 f 12 Which diagram correctly shows the image? 0 4. f 1. f 0 19 f0 31 19 f 12 19 19 f f 31 12 Mirror Divergent Diagram 36:05, highSchool, multiple choice, > 1 min, wording-variable. Hint: The convergent mirror in this problem is a part of a lens/mirror system so the object in this problem may be either real or virtual. Construct a ray diagram. Given: A virtual object is located to the right of a divergent mirror. The object’s distance from the mirror and its focal length are Chapter 36, section 5, Spherical Mirrors: Ray Tracing 239 shown in the figure below. 3. f f 19 −19 f f 12 7 0 19 f 12 Which diagram correctly shows the image? 0 4. f 1. f −19 f 7 19 −19 f f 12 7 0 f Spherical Mirror A 01 36:05, highSchool, numeric, > 1 min, wordingvariable. h q 0 19 f 12 Part 1 of 2 A concave spherical mirror has a radius of curvature of 30.2 cm . The object distance is 27.4 cm . 2. −19 f 7 0 19 f 12 Rp f h Scale: 10 cm = Find the magnitude of the image distance. Part 2 of 2 Find the magnification. Chapter 36, section 5, Spherical Mirrors: Ray Tracing Spherical Mirror A 02 36:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A convex spherical mirror has a radius of curvature of 30.6 cm . The object distance is 14 cm . 240 Part 2 of 2 Find the magnification. Spherical Mirror B 01 36:05, highSchool, numeric, > 1 min, wordingvariable. A concave spherical mirror forms a real image 2.36 times the size of the object. The object distance is 21.5 cm . h q h p q f h p R R f h Scale: 10 cm = Scale: 10 cm = Find the magnitude of the image distance. Part 2 of 2 Find the magnification. Spherical Mirror A 03 36:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A concave spherical mirror has a radius of curvature of 30.6 cm . The object distance is 4.8 cm . Find the magnitude of the radius of curvature of the mirror. Spherical Mirror B 02 36:05, highSchool, numeric, > 1 min, wordingvariable. A convex spherical mirror forms a virtual image 0.52 times the size of the object. The object distance is 13.7 cm . h h R f h h q p p f R q Scale: 10 cm = Scale: 10 cm = Find the magnitude of the image distance. Find the magnitude of the radius of curvature of the mirror. Spherical Mirror B 03 Chapter 36, section 5, Spherical Mirrors: Ray Tracing 36:05, highSchool, numeric, > 1 min, wordingvariable. image 1.91 times the size of the object. The distance between object and image is 28.2 cm . A concave spherical mirror forms a virtual image 1.46 times the size of the object. The object distance is 4.8 cm . h h R p f f p q h h R 241 q Scale: 10 m = Find the magnitude of the radius of curvature of the mirror. Scale: 10 cm = Find the magnitude of the radius of curvature of the mirror. Spherical Mirror C 02 36:05, highSchool, numeric, > 1 min, wordingvariable. A convex spherical mirror forms a virtual image 0.52 times the size of the object. The distance between object and image is 21 cm . h h q p f R Scale: 10 cm = Find the magnitude of the radius of curvature of the mirror. Spherical Mirror C 03 36:05, highSchool, numeric, > 1 min, wordingvariable. A concave spherical mirror forms a virtual Chapter 36, section 8, Images Formed by Thin Lenses Conceptual 20 Q23 36:08, highSchool, multiple choice, < 1 min, fixed. Compare a lens used to capture an image to the lens used to project that image back onto a screen for viewing. 1. Different types 2. Same types Conceptual 20 Q25 36:08, highSchool, multiple choice, < 1 min, fixed. 242 36:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 An object is placed 20.0 cm in front of a converging lens of focal length 10.0 cm. a) Find the image distance. Part 2 of 3 b) Find the magnification. Part 3 of 3 c) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger Why is the image projected onto the back of the retina in your eyes upside down? 3. real, upright, larger 1. The eye is a converging lens. 4. virtual, upright, larger 2. The focal length of the eye is very long. 5. real, inverted, smaller 3. The eye is a diverging lens. 6. virtual, inverted, smaller 4. None of these 7. real, upright, smaller Hewitt CP9 01 P06 36:08, highSchool, multiple choice, < 1 min, fixed. Poke a hole in a piece of cardboard and hold the cardboard in the sunlight. Note the image of the sun that is cast below. Try a square hole; what is the image of the sun? 1. triangular 8. virtual, upright, smaller 9. None of these Holt SF 15B 03 36:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 An object is placed 20.0 cm in front of a diverging lens of focal length 10.0 cm. a) Find the image distance. 2. round Part 2 of 3 b) Find the magnification. 3. square 4. pentagon Part 3 of 3 c) Describe the image. 5. hexagon Holt SF 15B 01 1. real, inverted, larger Chapter 36, section 8, Images Formed by Thin Lenses 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 243 0.50. g) Find the image distance if the object distance is 5.0 cm. Part 8 of 8 h) Find the focal length. 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Holt SF 15B 04 36:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 8 Consider a converging lens with focal length 6.0 cm. a) Find the object distance if the image distance is −3.0 cm. Part 2 of 8 b) Find the magnification. Part 3 of 8 Consider a converging lens with focal length 2.9 cm. c) Find the object distance if the image distance is 7.0 cm. Holt SF 15Rev 24 36:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 6 An object is placed in front of a diverging lens with a focal length of 20.0 cm. a) Find the image distance for an object distance of 40.0 cm. Part 2 of 6 b) Find the magnification. Part 3 of 6 c) Find the image distance for an object distance of 20.0 cm. Part 4 of 6 d) Find the magnification. Part 5 of 6 e) Find the image distance for an object distance of 10.0 cm. Part 6 of 6 f) Find the magnification. Part 4 of 8 d) Find the magnification. Holt SF 15Rev 25 36:08, highSchool, numeric, < 1 min, wordingvariable. Part 5 of 8 Consider a diverging lens of focal length 6.0 cm. e) Find the image distance if the object distance is 4.0 cm. Part 1 of 2 A person looks at a gem using a converging lens with a focal length of 12.5 cm. The lens forms a virtual image 30.0 cm from the lens. a) Find the magnification. Part 6 of 8 f) Find the magnification. Part 2 of 2 b) Describe the image. Part 7 of 8 Consider a diverging lens of magnification 1. real, inverted, smaller Chapter 36, section 8, Images Formed by Thin Lenses 2. real, upright, smaller 244 Where must an object be placed to have a magnification of 2.00 in front of a converging lens of focal length 12.0 cm? 3. virtual, upright, smaller 4. virtual, inverted, smaller Holt SF 15Rev 46 36:08, highSchool, numeric, < 1 min, wordingvariable. 5. real, inverted, larger 6. real, upright, larger 7. virtual, upright, larger A diverging lens is used to form a virtual image of an object. The object is 80.0 cm in front of the lens, and the image is 40.0 cm in front of the lens. Find the focal length of the lens. 8. virtual, inverted, larger Holt SF 15Rev 26 36:08, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 4 An object is placed in front of a converging lens with a focal length of 20.00 cm. a) Find the image distance for an object distance of 40.00 cm. Part 2 of 4 b) Find the magnification. Part 3 of 4 c) Find the image distance for an object distance of 10.00 cm. Part 4 of 4 d) Find the magnification. Holt SF 15Rev 44 36:08, highSchool, numeric, < 1 min, wordingvariable. The image of one kind of United States postage stamp is 1.50 times the size of the actual stamp in front of a lens. Find the focal length of the lens if the distance from the lens to the stamp is 2.84 cm. Holt SF 15Rev 45 36:08, highSchool, numeric, < 1 min, wordingvariable. Holt SF 15Rev 47 36:08, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A microscope slide is placed in front of a converging lens with a focal length of 2.44 cm. The lens forms an image of the slide 12.9 cm from the lens. a) How far is the lens from the slide if the image is real? Part 2 of 2 b) How far is the lens from the slide if the image is virtual? Holt SF 15Rev 48 36:08, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 a) Where must an object be placed to form an image 30.0 cm from a diverging lens with a focal length of 40.0 cm? Part 2 of 2 b) Find the magnification of the image. Holt SF 15Rev 55 36:08, highSchool, numeric, < 1 min, wordingvariable. An object’s distance from a converging lens is 10.0 times the focal length. How far is the image from the lens? Express Chapter 36, section 8, Images Formed by Thin Lenses 245 the answer in terms of the focal length. 4. virtual, erect, and larger. Holt SF 15Rev 63 36:08, highSchool, numeric, > 1 min, wordingvariable. 5. virtual, inverted, and larger. 6. real, erect, and smaller. Part 1 of 2 A nature photographer is using a camera that has a lens with a focal length of 4.80 cm. The photographer is taking pictures of ancient trees in a forest and wants the lens to be focused on a very old tree that is 10.0 m away. a) How far must the lens be from the film in order for the resulting picture to be clearly focused? 7. virtual, erect, and smaller. 8. virtual, inverted, and smaller. Part 2 of 3 The image distance q to the right of the lens is 1. q = Part 2 of 2 b) How much would the lens have to be moved to take a picture of another tree that is only 1.75 m away? 2. q = Single Lens 01 36:08, highSchool, multiple choice, > 1 min, wording-variable. 4. q = Part 1 of 3 Hint: You may wish to construct a ray diagram. 11 Given: A real object is located at “ p = f” 6 to the left of a convergent lens with a focal length f as shown in the figure below. 6. q = 3. q = 5. q = 7. q = 8. q = 9. q = 10. q = f f 11 f. 5 13 f. 5 5 f. 2 15 f. 7 11 f. 6 8 f. 3 13 f. 6 7 f. 3 15 f. 8 15 f. 4 Part 3 of 3 Using this lens, the magnification is 11 6 The image is (× f ) 0 1. real, inverted, and larger. 2. real, inverted, and smaller. 3. real, erect, and larger. 6 1. M = − . 5 5 2. M = − . 2 5 3. M = − . 3 7 4. M = − . 8 Chapter 36, section 8, Images Formed by Thin Lenses 7 5. M = − . 5 6 6. M = − . 7 7 7. M = − . 4 5 8. M = − . 6 8 9. M = − . 7 8 10. M = − . 5 13 f. 4 11 f. 9. q = 4 13 10. q = f. 7 8. q = Single Lens 03 36:08, highSchool, multiple choice, > 1 min, wording-variable. Hint: Construct a ray diagram. 11 f” Given: A real object is located at “ p = 6 to the left of a convergent lens with a focal length f as shown in the figure below. f f 11 0 6 The image distance q to the right of the lens (× f ) is 1. q = 2. q = 3. q = 4. q = 5. q = 6. q = 7. q = 11 f. 5 11 f. 6 5 f. 2 13 f. 6 8 f. 3 7 f. 3 7 f. 2 246 Chapter 36, section 9, Combinations of Lenses and Mirrors f1 = 5m Double Lenses all versions 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5.2 m . Another concave lens is placed 5.53 m behind the first lens with a focal length −9.7 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. f2 = f1 = 5. 2 m − 9. 7 m f1f2 f1 f2 p1 10 m 0 5 15 f2 = 6.3 m f1 f2 f2 p1 10 m 0 5 20 m 10 15 20 25 30 35 40 45 At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? 5.53 m 10 f1 247 20 25 At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Double Lenses version 1 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another convex lens is placed 20 m behind the first lens with a focal length 6.3 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Double Lenses version 2 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another convex lens is placed 4 m behind the first lens with a focal length 7.3 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. f1 = f2 = 5m 7.3 m f1 f2 f1 f2 p1 10 m 0 5 4m 10 15 20 Chapter 36, section 9, Combinations of Lenses and Mirrors At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Double Lenses version 3 36:09, highSchool, numeric, > 1 min, wordingvariable. when compared to the initial object? Double Lenses version 4 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another concave lens is placed 5 m behind the first lens with a focal length −8.6 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. f1 = f2 = 5 m −8.6 m f1 f2 Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another convex lens is placed 15 m behind the first lens with a focal length 12 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. f1 = f2 = 5m 12 m f1 p1 0 5 15 f2 p1 10 m 0 5 5m 10 15 20 25 At what distance is the first image from the first lens? Part 3 of 4 At what distance is the second image from the second lens? 15 m 10 f1 Part 2 of 4 What isfthe magnification of the first image? 2 f2 f1 10 m 248 20 25 At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? Part 4 of 4 What is the magnification of the final image, Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Double Lenses version 5 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another concave lens is placed 18 m behind the first lens with a focal length −12 m (see the figure below). Chapter 36, section 9, Combinations of Lenses and Mirrors Note: Make a ray diagram sketch in order to check your numerical answer. f1 = f2 = −12 m 5m f1 f1 = 5m f1 p1 f1 2 f p1 0 5 18 m 10 15 20 0 25 At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Double Lenses version 6 36:09, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 An object is placed 10 m before a convex lens with focal length 5 m . Another concave lens is placed 5 m behind the first lens with a focal length −3.4 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. f2 = −3.4 m f2 f1 f2 f2 10 m 10 m 249 5 5m 10 15 20 At what distance is the first image from the first lens? Part 2 of 4 What is the magnification of the first image? Part 3 of 4 At what distance is the second image from the second lens? Part 4 of 4 What is the magnification of the final image, when compared to the initial object? Chapter 36, section 10, Thin Lenses: Ray Tracing Lens A 01 36:10, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A convergent lens has a focal length of 6.7 cm . The object distance is 10.8 cm . h p 250 Part 2 of 2 Find the magnification. Lens A 03 36:10, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A convergent lens has a focal length of 20.3 cm . The object distance is 9.7 cm . q f f h h h fq p f Scale: 10 cm = Find the distance of the image from the center of the lens. Scale: 10 cm = Part 2 of 2 Find the magnification. Find the distance of the image from the center of the lens. Lens A 02 36:10, highSchool, numeric, > 1 min, wordingvariable. Part 2 of 2 Find the magnification. Part 1 of 2 A divergent lens has a focal length of 20 cm . The object distance is 18.2 cm . Lens B 01 36:10, highSchool, numeric, > 1 min, wordingvariable. A convergent lens forms a real image 1.64 times the size of the object. The object distance is 10.8 cm . h h fp q f h p q f f h Scale: 10 cm = Find the distance of the image from the center of the lens. Scale: 10 cm = Find the distance of the focal point from Chapter 36, section 10, Thin Lenses: Ray Tracing 251 the center of the lens. variable. Lens B 02 36:10, highSchool, numeric, > 1 min, wordingvariable. A convergent lens forms a real image 1.64 times the size of the object. The distance between object and image is 28.4 cm . A divergent lens forms a virtual image 0.52 times the size of the object. The object distance is 18.7 cm . h q p f f h h h fp q f Scale: 10 cm = Find the distance of the focal point from the center of the lens. Scale: 10 cm = Find the distance of the focal point from the center of the lens. Lens C 02 36:10, highSchool, numeric, > 1 min, wordingvariable. Lens B 03 36:10, highSchool, numeric, > 1 min, wordingvariable. A divergent lens forms a virtual image 0.52 times the size of the object. The distance between object and image is 27.7 cm . A convergent lens forms a virtual image 1.92 times the size of the object. The object distance is 9.6 cm . h h fp q f h h fq p f Scale: 10 cm = Find the distance of the focal point from the center of the lens. Scale: 10 cm = Find the distance of the focal point from the center of the lens. Lens C 03 36:10, highSchool, numeric, > 1 min, wordingvariable. Lens C 01 36:10, highSchool, numeric, > 1 min, wording- A convergent lens forms a virtual image 1.92 times the size of the object. The distance Chapter 36, section 10, Thin Lenses: Ray Tracing 252 between object and image is 8.8 cm . 1. f h f h fq p f 19 f 12 19 f 7 0 Scale: 10 cm = Find the distance of the focal point from the center of the lens. 2. Lens Convergent Diagram 36:10, highSchool, multiple choice, > 1 min, wording-variable. Hint: The convergent lens in this problem is a part of a lens system so the object in this problem may be either real or virtual. Construct a ray diagram. Given: A real object is located to the left of a divergent lens. The object’s distance and image’s distance from the lens and the lens’ focal length are shown in the figures below. f 19 f 7 19 f 12 f 0 3. f f f f 19 f 12 19 f 0 12 Which diagram correctly shows the image? 0 19 f 7 Chapter 36, section 10, Thin Lenses: Ray Tracing 253 1. 4. f 19 f 7 f 19 f 12 f f 19 19 f f0 12 31 0 Lens Divergent Diagram 36:10, highSchool, multiple choice, > 1 min, wording-variable. Hint: The convergent lens in this problem is a part of a lens system so the object in this problem may be either real or virtual. Construct a ray diagram. Given: A real object is located to the left of a divergent lens. The object’s distance and image’s distance from the lens and the lens’ focal length are shown in the figures below. f f 19 f 0 12 Which diagram correctly shows the image? 2. f 19 f 12 f 0 19 f 31 3. f 19 19 f f0 12 31 f Chapter 36, section 10, Thin Lenses: Ray Tracing 4. f 19 f 12 f 0 19 f 31 254 Chapter 36, section 11, Lensmaker’s Equation 255 tive. Lens Maker Formula 02 36:11, highSchool, numeric, > 1 min, wordingvariable. 5. non-focusing since the focal length is zero. The cross-section of a glass lens with an index of refraction “1.33”, is shown below. 6. non-focusing since the focal length is infinite. 0.9 cm 0.7 cm Hint: Include both the magnitude and sign, which indicates whether this is a divergent or convergent lens. Determine the focal length f using the small angle approximation. Lens Maker Formula 03 36:11, highSchool, multiple choice, > 1 min, wording-variable. The cross-section of a glass lens with an index of refraction “1.33”, is shown below. Lens Maker Formula 04 36:11, highSchool, multiple choice, < 1 min, wording-variable. Part 1 of 2 A thin composite lens is shown in the figure, 1 where |R1 | = R , |R2 | = R , and n2 > n1 . 2 Hint: In considering the choice, one may set n2 = n and n1 = 1. R1 R2 n1 The lens has focal length 1. f = 2. f = 0.9 cm 0.7 cm 3. f = 4. f = 5. f = This lens is 1. divergent since the focal length is negative. 2. convergent since the focal length is positive. 3. divergent since the focal length is positive. 4. convergent since the focal length is nega- n2 6. f = 7. f = 8. f = 9. f = 10. f = n1 R. n1 − n 2 2 n1 R. n2 − n 1 2 n1 R. n1 − n 2 n1 R. n2 − n 1 n1 R. 2 (n 2 − n 1 ) n1 R. 2 (n 1 − n 2 ) 2 n2 R. n2 − n 1 n2 R. n2 − n 1 n2 R. 2 (n 2 − n 1 ) n2 R. 2 (n 1 − n 2 ) Part 2 of 2 The lens is Chapter 36, section 11, Lensmaker’s Equation 1. divergent and the focal length is negative. 256 8. E, G, X, and K 9. Q, G, and X 2. convergent and the focal length is positive. 3. divergent and the focal length is positive. 4. convergent and the focal length is negative. 5. cannot be determined since the focal length is zero. 10. Y, X, and E Thin Lens 06 36:11, highSchool, multiple choice, > 1 min, fixed. The magnitudes of the radii of curvature for the spherical surfaces A and B are, respectively, |RA | = a and |RB | = 3 a. The material of which the lens is made has an index of refraction n = 1.5. 6. non-focusing since the focal length is infinite. Lens Selection 36:11, highSchool, multiple choice, > 1 min, wording-variable. A Find the focal length of the following thin lens 1. f = 3 a 2. f = 4 a 3. f = −4 a 4. f = 2 a Q G K X Y D E Which of the glass lenses above, when placed in air, will cause parallel rays of light to diverge? 5. f = a 6. f = −a 1. G, D, and E 7. f = −2 a 2. D, K, and Y 8. f = −3 a 3. Q, G, and D 4. D, Y, and E 5. K, Q, and Y 6. E, G, and K 7. K, Y, G, and E B Chapter 36, section 12, The Camera Concept 28 E42 36:12, highSchool, multiple choice, < 1 min, fixed. Cover the top half of a camera lens. What effect does this have on the pictures taken? 1. The picture becomes darker. 2. The picture has only the top half of the original image. 3. The picture has only the bottom half of the original image. 4. The picture becomes smaller. Conceptual 20 Q24 36:12, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 When you focus an optical instrument such as a camera or microscope, what are you actually doing to the lens? 1. One lens is moving while other lens is stationary. 2. Both lenses are moving with respect to each other. 3. Lens aperture changes. 4. None of these Part 2 of 2 What happens to the focal point of the image? 1. Remains the same 2. Changes 257 Chapter 36, section 13, The Eye and Corrective Lenses Eyeglasses for farsighted 36:13, highSchool, numeric, > 1 min, normal. A far-sighted student has a near point of 100 cm. Calculate the focal length of the glasses needed so the near point will be normal (25 cm). Neglect the space between the eyes and the eye-glasses. Holt SF 15Rev 64 36:13, highSchool, numeric, < 1 min, wordingvariable. The distance from the front to the back of your eye is approximately 1.90 cm. If you can see a clear image of a book when it is 35.0 cm from your eye, what is the focal length of the lens/cornea system? Holt SF 15Rev 65 36:13, highSchool, numeric, < 1 min, wordingvariable. Suppose you look out the window and see your friend, who is standing 15.0 m away. To what focal length must your eye muscles adjust the lens of your eye so that you may see your friend clearly? Remember that the distance from the front to the back of your eye is about 1.90 cm. 258 Chapter 36, section 14, The Simple Magnifier Holt SF 15B 02 36:14, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Sherlock Holmes examines a clue by holding his magnifying glass (with a focal length of 15.0 cm) 10.0 cm away from an object. a) Find the image distance. Part 2 of 3 b) Find the magnification. Part 3 of 3 c) Describe the image that he observes. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these Holt SF 15Rev 43 36:14, highSchool, numeric, < 1 min, wordingvariable. A magnifying glass has a converging lens of focal length 15.0 cm. At what distance from a nickel should you hold this lens to get an image with a magnification of +2.00? 259 Chapter 36, section 16, The Telescope Holt SF 14Rev 46 36:16, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 4 The real image of a tree is magnified −0.085 times by a telescope’s primary mirror. The tree’s image forms 35 cm in front of the mirror. a) What is the distance between the mirror and the tree? Part 2 of 4 b) What is the focal length of the mirror? Part 3 of 4 c) What is the value for the mirror’s radius of curvature? Part 4 of 4 d) Describe the image. 1. real, inverted, larger 2. virtual, inverted, larger 3. real, upright, larger 4. virtual, upright, larger 5. real, inverted, smaller 6. virtual, inverted, smaller 7. real, upright, smaller 8. virtual, upright, smaller 9. None of these 260 Chapter 37, section 1, Conditions for Interference Concept 29 23 37:01, highSchool, multiple choice, < 1 min, fixed. Will the light from two very close stars produce an interference pattern? 1. Yes; if they are very close to each other, the light has large overlapping area. 2. Yes; strong light from the two stars creates very clear interference patterns. 3. No; light from two very close stars is not likely to have the same frequency. 4. No; the light is too strong to produce a discernable interference pattern. 261 Chapter 37, section 2, Double Slit Interference: Young’s Experiment Concept 29 10 37:02, highSchool, multiple choice, < 1 min, fixed. Light illuminates two closely spaced thin slits and produces an interference pattern on a screen behind. How will the distance between the fringes of the pattern differ for red light and blue light? 1. Closer for red light 2. Farther apart for red light 3. The same spacing for both Concept 29 11 37:02, highSchool, multiple choice, < 1 min, fixed. A double slit arrangement produces an interference fringe for yellow sodium light. To produce narrower-spaced fringes, should red light or blue light be used? 262 37:02, highSchool, multiple choice, < 1 min, fixed. Why is Young’s experiment more effective with slits than with the pinholes he first used? 1. Pinholes can only be used in diffraction experiments because light transmitting through two pinholes do not interfere with each other. 2. It is hard to create pinholes with the same size, which is important to the quality of the interference pattern. 3. Slits form parallel straight-line fringes, which produce clearer interference patterns than overlapping circular fringes. 4. None of these Holt SF 16A 01 37:02, highSchool, numeric, < 1 min, wordingvariable. A double-slit interference experiment is performed with light from a laser. The separation between the slits is 0.50 mm, and the first-order maximum of the interference pattern is at an angle of 0.059◦ from the center of the pattern. What is the wavelength of the laser light? 1. Blue 2. Red 3. Either Concept 29 14 37:02, highSchool, multiple choice, < 1 min, fixed. What happens to the distance between interference fringes if the separation between two slits is increased? 1. Increases Holt SF 16A 02 37:02, highSchool, numeric, > 1 min, wordingvariable. Light falls on a double slit with slit separation of 2.02 × 10−6 m, and the first bright fringe is seen at an angle of 16.5◦ relative to the central maximum. What is the wavelength of the light? 2. Decreases 3. Remains unchanged Holt SF 16A 03 37:02, highSchool, numeric, > 1 min, wordingvariable. 4. The fringes disappear. Concept 29 15 A pair of narrow parallel slits separated by a distance of 0.250 mm are illuminated by the Chapter 37, section 2, Double Slit Interference: Young’s Experiment green component from a mercury vapor lamp (λ = 546.1 nm). What is the angle from the central maximum to the first bright fringe on either side of the central maximum? 4. 546.173 nm Holt SF 16A 04 37:02, highSchool, numeric, > 1 min, wordingvariable. 263 7. Unable to determine. A pair of narrow parallel slits separated by a distance of 0.250 mm are illuminated by the green component from a mercury vapor lamp (λ = 546.1 nm). What is the angle from the central maximum to the second dark fringe on either side of the central maximum? Holt SF 16Rev 09 37:02, highSchool, numeric, > 1 min, wordingvariable. Light falls on two slits spaced 0.330 mm apart. The angle between the first dark fringe and the central maximum is 0.0800◦ . What is the wavelength of the light? Holt SF 16Rev 10 37:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A sodium-vapor street lamp produces light that is nearly monochromatic. If the light shines on a wooden door in which there are two straight, parallel cracks, an interference pattern will form on a distant wall behind the door. The slits have a separation of 0.3096 mm, and the second-order maximum occurs at an angle of 0.21800◦ from the central maximum. a) Determine the wavelength of the light. 1. 659.235 nm 2. 588.984 nm 3. 588.984 nm 5. None of these. 6. 656.326 nm Part 2 of 3 b) Determine the angle of the third-order maximum. Part 3 of 3 c) Determine the angle of the fourth-order minimum. Holt SF 16Rev 11 37:02, highSchool, numeric, > 1 min, wordingvariable. All but two gaps within a set of venetian blinds have been blocked off to create a double-slit system. These gaps are separated by a distance of 3.2 cm. Infrared radiation is then passed through the two gaps in the blinds. The angle between the central and the second-order maxima in the interference pattern is 0.56◦ . What is the wavelength of the radiation? Holt SF 16Rev 28 37:02, highSchool, numeric, > 1 min, wordingvariable. A double-slit interference experiment is performed using blue light from a hydrogen discharge tube (λ = 486 nm). The fifth-order bright fringe in the interference pattern is 0.578◦ from the central maximum. How far apart are the two slits separated? Holt SF 16Rev 29 37:02, highSchool, numeric, > 1 min, wordingvariable. A beam containing light of wavelengths of λ1 and λ2 passes through a set of parallel slits. In the interference pattern, the fourth bright line of the λ1 light occurs at the same position Chapter 37, section 2, Double Slit Interference: Young’s Experiment as the fifth bright line of the λ2 light. If λ1 is known to be 540.0 nm, what is the value of λ2 ? Holt SF 16Rev 31 37:02, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 In an arrangement to demonstrate doubleslit interference, λ = 643 nm, θ = 0.737◦ , and d = 0.150 mm. a) For light from the two slits interfering at this angle, what is the path difference in millimeters? Part 2 of 3 b) What is the path difference in terms of the number of wavelengths? Part 3 of 3 c) Will the interference correspond to a maximum, a minimum, or an intermediate condition? 1. maximum 2. minimum 3. intermediate 4. None of these 5. Unable to determine 264 Chapter 37, section 4, Intensity Distribution of the Double-Slit Interference Double Slits 01 37:04, highSchool, numeric, > 1 min, normal. θ 19 mm S1 viewing screen 0.092 mm Part 1 of 2 Two narrow parallel slits are illuminated with light of wavelength 700 nm. S2 15 m What is the phase difference between the two interfering waves on a screen at a point 19 mm from the central bright fringe? Part 2 of 2 What is the ratio of the intensity at this point to the intensity at the center of a bright fringe? 265 Chapter 37, section 5, Phasor Addition of Waves MultiSlits 01 37:05, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 3 Given: The setup of a six slit diffraction experiment shown in the figure. y 2 3 4 δ L Figure: Not drawn to scale. Find the path difference difference between two rays from adjacent slits which gives rise to the first minimum. 2. δ = 3. δ = 4. δ = 6. δ = 7. δ = 8. δ = 5. φ = 2. φ = 4. φ = 7. φ = 6 5. δ = 1. φ = 6. φ = 5 1. δ = rays from adjacent slits which gives rise to the first minimum. 3. φ = 1 1 λ 6 1 λ 4 1 λ 5 2 λ 5 3 λ 4 3 λ 5 2 λ 3 1 λ 2 9. δ = 2 λ 8. φ = 1 π 3 1 π 2 2 π 5 1 π 4 3 π 4 3 π 5 1 π 5 2 π 3 9. φ = 2 π 10. φ = π Part 3 of 3 What is the phase angle difference between two adjacent rays, at the principal maximum? 1. φ = 2 π 2. φ = 3. φ = 4. φ = 5. φ = 6. φ = 7. φ = 8. φ = 10. δ = λ 9. φ = Part 2 of 3 Find the phase angle difference between two 266 1 π 3 2 π 3 1 π 4 1 π 2 3 π 4 2 π 5 3 π 5 4 π 5 10. φ = π Chapter 37, section 5, Phasor Addition of Waves 267 two adjacent rays, at the principal maximum? MultiSlits 02 37:05, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 2 Given: The setup of a six slit diffraction experiment shown in the figure. 1. φ = 2 π 2. φ = 3. φ = 4. φ = 1 y 2 3 5. φ = 6. φ = 4 7. φ = 5 6 8. φ = δ L Figure: Not drawn to scale. Find the path difference difference between two rays from adjacent slits which gives rise to the first minimum. 1. δ = 5. δ = 2. δ = 3. δ = 4. δ = 6. δ = 7. δ = 8. δ = 1 λ 6 1 λ 4 1 λ 5 2 λ 5 3 λ 4 3 λ 5 2 λ 3 1 λ 2 9. δ = 2 λ 10. δ = λ Part 2 of 2 What is the phase angle difference between 9. φ = 1 π 3 2 π 3 1 π 4 1 π 2 3 π 4 2 π 5 3 π 5 4 π 5 10. φ = π MultiSlits 03 37:05, highSchool, multiple choice, > 1 min, wording-variable. Given: The setup of a four slit diffraction experiment shown in the figure. y 1 2 3 4 δ L Figure: Not drawn to scale. Find the path difference difference between two rays from adjacent slits which gives rise to the first minimum. 1. δ = 1 λ 4 Chapter 37, section 5, Phasor Addition of Waves 5. δ = 2. δ = 3. δ = 4. δ = 6. δ = 7. δ = 8. δ = 2. φ = 1 λ 5 1 λ 6 2 λ 5 3 λ 4 3 λ 5 2 λ 3 1 λ 2 3. φ = 4. φ = 6. φ = 7. φ = 8. φ = 268 2 π 5 1 π 4 3 π 4 3 π 5 1 π 5 2 π 3 9. φ = 2 π 10. φ = π 9. δ = 2 λ MultiSlits 05 37:05, highSchool, multiple choice, > 1 min, wording-variable. 10. δ = λ MultiSlits 04 37:05, highSchool, multiple choice, > 1 min, wording-variable. Given: The setup of a six slit diffraction experiment shown in the figure. Given: The setup of a five slit diffraction experiment is shown in the figure below. 1 y 2 1 y 2 3 3 4 5 4 δ 5 L 6 δ L Figure: Not drawn to scale. Find the phase angle difference between two rays from adjacent slits which gives rise to the first minimum. 1 π 3 1 5. φ = π 2 1. φ = Figure: Not drawn to scale. Find the phase angle difference and the path difference between each pair of adjacent rays which gives rise to the first minimum. 2 π 5 1 2. φ = π 3 1 3. φ = π 2 2 4. φ = π 5 1. φ = and and and and 1 5 1 δ= 5 1 δ= 5 1 δ= 6 δ= λ λ λ λ Chapter 37, section 5, Phasor Addition of Waves 5. φ = 6. φ = 7. φ = 8. φ = 9. φ = 1 π 3 1 π 2 2 π 5 1 π 3 1 π 2 10. φ = π and δ = and δ = and δ = and δ = and δ = and δ = 1 6 1 6 1 4 1 4 1 4 1 λ 2 λ λ λ λ λ 269 Chapter 37, section 6, Change of Phase Due to Reflection Hewitt CP9 28 P08 37:06, highSchool, numeric, < 1 min, normal. 30 cm 30 cm Consider two ways that light might hypothetically get from its starting point S to its final point F by being reflected by a mirror at either point A or point B. Since light travels at a fixed speed in air, the path of the least time will also be the path of the least distance. S F ⊗ ⊗ 40 cm A 40 cm B C Find the difference in the path lengths SAF and SBF. 270 Chapter 37, section 7, Interference in Thin Films An Optical Coating 37:07, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 A light ray is traveling in a medium with an index of refraction n1 and it is reflected at the boundary of a second medium with an index of refraction n2 . Considering the change of the relative phases ∆φ due to their reflections, which of the following conditions is correct? a wavelength λ = 500 nm and incident angle θ ≈ 0, what is the minimum nonzero thickness t of the coating? 1. t = 2. t = 3. t = 4. t = 5. t = 1. If n1 > n2 , then ∆φ = 0 and if n1 < n2 , then ∆φ = 0. 6. t = 2. If n1 > n2 , then ∆φ = 0 and π if n1 < n2 , then ∆φ = . 2 7. t = 3. If n1 > n2 , then ∆φ = 0 and if n1 < n2 , then ∆φ = π . 8. t = π and 2 π if n1 < n2 , then ∆φ = . 2 π 5. If n1 > n2 , then ∆φ = and 2 if n1 < n2 , then ∆φ = π . 9. t = 4. If n1 > n2 , then ∆φ = λ 8n λ 4n λ 2n 3λ 4n λ n nλ 8 nλ 4 nλ 2 3nλ 4 10. t = n λ An Optical Coating S 37:07, highSchool, multiple choice, > 1 min, fixed. 6. If n1 > n2 , then ∆φ = π and if n1 < n2 , then ∆φ = π . Part 2 of 2 Consider the optical coating on a glass lens where the index of refraction of the coating is n, where n is greater than the index of refraction of the air. 12 θ ≈ 0◦ θ air t 271 n lens Assume: The index of refraction of the lens is greater than that of the coating. To minimize the reflection of a ray with A light ray is traveling in air with an index of refraction of unity and it is reflected at the boundary of a second medium with an index of refraction n. Consider the optical coating on a glass lens where the index of refraction of the coating is n, where n is greater than the index of refraction of the air. 12 θ ≈ 0◦ θ air t n lens Assume: The index of refraction of the lens is greater than that of the coating. Chapter 37, section 7, Interference in Thin Films To minimize the reflection of a ray with a wavelength 500 nm and incident angle θ ≈ 0, what is the minimum nonzero thickness of the coating? 1. t = 2. t = 3. t = 4. t = 5. t = 6. t = 7. t = 8. t = 9. t = λ 8n λ 4n λ 2n 3λ 4n λ n nλ 8 nλ 4 nλ 2 3nλ 4 10. t = n λ Coating on a Camera Lens 1 37:07, highSchool, numeric, > 1 min, normal. A thin film of cryolite ( nc = 1.35 ) is applied to a camera lens ( ng = 1.5 ). The coating is designed to reflect wavelengths at the blue end of the spectrum and transmit wavelengths in the near infrared. What minimum thickness gives high transmission at λ = 900 nm? Concept 29 25 37:07, highSchool, multiple choice, < 1 min, fixed. Because of wave interference a film of oil on water seems to be yellow to observers directly above in an airplane. What color does it appear to a scuba diver directly below? 1. yellow 2. blue 3. black 4. none of these Thin Film thickness 37:07, highSchool, multiple choice, > 1 min, fixed. A material with index of refraction n = 1.3 is used to coat a piece of glass (nglass = 1.5). What should be the minimum thickness of this film in order to minimize reflection of light, which has a wavelength λ in vacuum? 1. 2. 3. 4. 5. Coating on a Camera Lens 2 37:07, highSchool, numeric, > 1 min, normal. A thin film of cryolite ( nc = 1.35 ) is applied to a camera lens ( ng = 1.5 ). The coating is designed to reflect wavelengths at the blue end of the spectrum and transmit wavelengths in the near infrared. What minimum thickness gives high reflectivity at 450 nm? 272 6. 7. 8. 9. λ 2 λ 3 λ 4 λn 2 λn 3 λn 4 λ n λ 2n λ 3n Chapter 37, section 7, Interference in Thin Films 10. λ 4n 273 Chapter 38, section 1, Diffraction 274 TV signal in lower numbered channels. Concept 29 02 38:01, highSchool, multiple choice, < 1 min, fixed. In our everyday environment, diffraction is much more evident for sound waves than for light waves. Why is this so? 2. Low frequency signals can carry more information than high frequency signals. 3. Low frequency signals encounter less resistance from the air than high frequency signals while traveling. 4. None of these 1. Light waves travel much faster than sound waves. 2. Light waves have much shorter wavelength than sound waves. 3. We see light more often than we hear sound in our everyday environment. Hewitt CP9 29 R03 38:01, highSchool, multiple choice, < 1 min, fixed. Is diffraction more pronounced through a small or a large opening? 1. small 4. None of these 2. large Concept 29 03 38:01, highSchool, multiple choice, < 1 min, fixed. Why do radio waves diffract around buildings, while light waves do not? 1. Radio waves travel much slower than light waves. 2. Radio waves are electromagnetic waves while light waves are not. 3. Radio waves have a much longer wavelengths than light waves. 4. None of these Concept 29 05 38:01, highSchool, multiple choice, < 1 min, fixed. Why can TV channels of lower numbers give better pictures in regions of poor TV reception? (Lower channel numbers represent lower carrier frequencies.) 1. Diffraction around buildings is easier for 3. It depends on the frequency of the light. Chapter 38, section 12, The Diffraction Grating Concept 30 08 38:12, highSchool, multiple choice, < 1 min, fixed. If we use a prism or a diffraction grating to compare the red light from a common neon tube and the red light from a helium neon laser, what striking difference do we see? 1. The light from a common neon tube is brighter. 2. The light from a common neon tube will be diffracted into several shades of red light while the light from a helium neon laser is monochromatic. 3. The light from heilum neon laser is too strong to be diffracted. 4. None of these Holt SF 16B 01 38:12, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 A diffraction grating with 2.500 × 103 lines/cm is used to examine the sodium spectrum. a) Calculate the angular separation of the two closely spaced yellow lines of sodium (588.995 nm and 589.592 nm) in the first order. 275 A diffraction grating with 4525 lines/cm is illuminated by direct sunlight. The first-order solar spectrum is spread out on a white screen hanging on a wall opposite the grating. a) At what angle does the first-order maximum for blue light with a wavelength of 422 nm appear? Part 2 of 2 b) At what angle does the first-order maximum for red light with a wavelength of 655 nm appear? Holt SF 16B 03 04 38:12, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A grating with is illuminated with light of wavelength 565 nm. a) What is the highest-order number that can be observed if the grating has 1605 lines/cm? (Hint: Remember that sin θ can never be greater than 1.) Part 2 of 2 b) What is the highest-order number that can be observed if the grating has 16050 lines/cm? Holt SF 16B 05 38:12, highSchool, numeric, > 1 min, normal. Part 2 of 3 b) Calculate the angular separation for the two lines in the second order. A diffraction grating is calibrated by using the 546.1 nm line of mercury vapor. The first-order maximum is found at an angle of 21.2◦ . Calculate the number of lines per centimeter on this grating. Part 3 of 3 c) Calculate the angular separation for the two lines in the third order. Holt SF 16Rev 19 20 38:12, highSchool, numeric, > 1 min, wordingvariable. Holt SF 16B 02 38:12, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Light with a wavelength of 707 nm is passed through a diffraction grating with 795 slits/cm. a) Find the angle at which one would ob- Part 1 of 2 Chapter 38, section 12, The Diffraction Grating serve the first-order maximum. Part 2 of 2 b) If the wavelength of the light were 353 nm, at what angle would the second-order maximum appear? Holt SF 16Rev 21 38:12, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 6 By attaching a diffraction-grating spectroscope to an astronomical telescope, one can measure the spectral lines from a star and determine the star’s chemical composition. Assume the grating has 3661 slits/cm. The wavelengths of the star’s light are λ1 = 478.500 nm, λ2 = 647.400 nm, and λ3 = 696.400 nm. a) Find the angle at which the first-order spectral line for λ1 occurs. Part 2 of 6 b) Find the angle at which the first-order spectral line for λ2 occurs. Part 3 of 6 c) Find the angle at which the first-order spectral line for λ3 occurs. Part 4 of 6 d) Find the angle at which the second-order spectral line for λ1 occurs. Part 5 of 6 e) Find the angle at which the second-order spectral line for λ2 occurs. Part 6 of 6 f) Find the angle at which the second-order spectral line for λ3 occurs. Holt SF 16Rev 26 38:12, highSchool, numeric, > 1 min, normal. The 546.1 nm line in mercury is measured at an angle of 81◦ in the third-order spectrum of a diffraction grating. 276 Calculate the number of lines per milimeter for the grating. Holt SF 16Rev 30 38:12, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Visible light from an incandescent light bulb ranges from 400.0 nm to 700.0 nm. When this light is focused on a diffraction grating, the entire first-order spectrum is seen, but none of the second-order spectrum is seen. a) What is the maximum spacing between lines on this grating? Part 2 of 2 b) What is the minimum spacing between lines on this grating? Chapter 39, section 3, Postulates: Speed of Light 277 1. Yes. Concept 35 04 39:03, highSchool, multiple choice, < 1 min, fixed. Suppose that a person riding on the top of a freight car shines a searchlight beam in the direction in which the train is traveling. How does the speed of the light beam relative to the ground compare to the speed of beam when the train is at rest? 1. Faster 2. No. Concept 35 10 39:03, highSchool, multiple choice, < 1 min, fixed. Suppose that the light bulb in the rocket ship (shown in the figures below) is closer to the front than to the rear of the compartment, so that the observer in the ship sees the light reaching the front before it reaches the back. 2. Slower 3. No change Concept 35 07 39:03, highSchool, multiple choice, < 1 min, fixed. Light travels more slowly in glass than in air. Does this contradict the theory of relativity? 1. Yes; the theory of relativity cannot be applied in a transparent medium. 2. Yes; but the theory of relativity is correct in air. 3. No; another theory supports the contradiction. 4. No; the speed of light in space is constant. Concept 35 08 39:03, highSchool, multiple choice, < 1 min, fixed. If two lightning bolts hit exactly the same place at exactly the same time in one frame of reference, is it possible that observers in other frames will see the bolts hitting at different times or at different places? Is it still possible that an outside observer will see the light reaching the back first? 1. Yes 2. No Concept 35 12 39:03, highSchool, multiple choice, < 1 min, fixed. Can an electron beam sweep across the face of a cathode-ray tube at a speed greater than the speed of light, and why? 1. Yes; though no material nor information can travel faster than light. 2. Yes; some material moves faster than light. 3. No; nothing is faster than light. 4. No; only an electron travel faster than light. Conceptual 28 03 39:03, highSchool, multiple choice, < 1 min, Chapter 39, section 3, Postulates: Speed of Light fixed. Astronomers have routinely observed distant galaxies moving away from the Milky Way galaxy at speeds over 10% of the speed of light (30,000 km/s). At what speed does this distant light reach astronomers? 1. 60000 km/s 2. 30000 km/s 3. 15000 km/s 4. 10000 km/s 5. 7500 km/s Conceptual 28 Q18 39:03, highSchool, multiple choice, < 1 min, normal. Someone shines a light while moving toward you at 1000 m/s. With what speed will the light strike you? (The speed of light is 300,000,000 m/s) 278 Chapter 39, section 4, The Michelson-Morley Experiment Concept 35 05 39:04, highSchool, multiple choice, < 1 min, fixed. Why did Michelson and Morley at first consider their experiment a failure? 1. They ignored the experimental errors. 2. They did not have the equipment they originally wanted. 3. They did not confirm the expected result. 4. They did not measure the exact quantities. 279 Chapter 39, section 5, Consequences of Special Relativity Concept 35 01 39:05, highSchool, multiple choice, < 1 min, fixed. The idea that force causes acceleration doesn’t seem strange. This and other ideas of Newtonian mechanics are consistent with our everyday experience. Why do the ideas of relativity seem strange? 1. The effects of relativity become apparent only at very high speeds very uncommon to everyday experience. 2. The principles of relativity apply outside Earth. 280 fires a gun pointed forward. Relative to the ground, is the bullet moving faster or slower when the train is moving than when it is standing still? Relative to the freight car, is the bullet moving faster or slower when the train is moving than when the train is standing still? 1. Faster; faster 2. Faster; the same 3. Faster; slower 4. Slower; faster 5. Slower; the same 6. The same; the same 3. For the effects of relativity to become apparent large masses are needed. 7. The same; faster 4. Earth’s rotation doesn’t let us observe relativity that applies to systems moving in straight trajectories. Concept 35 06 39:05, highSchool, multiple choice, < 1 min, fixed. Concept 35 02 39:05, highSchool, multiple choice, < 1 min, fixed. When you drive down the highway you are moving through space. What else are you moving through? If you were in a smooth-riding train with no windows, could you sense the difference between uniform motion and rest or between accelerated motion and rest? 1. Time 2. Dimension 3. Length 1. Only accelerated motion can be sensed. 4. Speed 2. Only uniform motion can be sensed. 3. Both acclerated and uniform motion can be sensed. 4. No motion can be sensed. Concept 35 03 39:05, highSchool, multiple choice, < 1 min, fixed. Concept 35 09 39:05, highSchool, multiple choice, < 1 min, fixed. Event A occurs before event B in a certain frame of reference. How could event B occur before event A in some other frame of reference? 1. It’s impossible. A person riding on the roof of a freight train Chapter 39, section 5, Consequences of Special Relativity 2. Its a matter of relative distance. 3. The spaces are distorted. 4. It’s a matter of relative velocity. Concept 35 11 39:05, highSchool, multiple choice, < 1 min, fixed. The speed of light is a speed limit in the universe, at least for the four-dimensional universe we comprehend. No material particle can attain or surpass this limit even when a continuous, unremitting force is exerted on it. Why is this so? 1. The momentum of an object has a limit. 2. It is contradictory to the theory of relativity. 281 things. 3. The moving points are imaginary. 4. This is an exception of the theory of special relativity. Concept 35 18 39:05, highSchool, multiple choice, < 1 min, fixed. Is it possible for a son or daughter to be biologically older than his or her parents? 1. Yes if the parents travel very long time in a high-speed space ship. 2. Yes if the child travels very long time in a high-speed space ship. 3. No; children always stay younger than their parents. 3. The photon has a speed limit. 4. Time dilations makes it impossible. 4. Light vanishes when it travels faster than c. Concept 35 13 39:05, highSchool, multiple choice, < 1 min, xed. Consider the speed of the point where scissors blades meet when scissors are closed. The closer the blades are to being closed, the faster the point moves. The point could, in principle, move faster than light. Likewise for the speed of the point where an ax meets wood when the ax blade meets the wood almost horizontally. The contact point travels faster than the ax. Similarly, a pair of laser beams that are crossed and moved toward being parallel produce a point of intersection that can move faster than light. Why do these examples not contradict special relativity? Concept 35 19 39:05, highSchool, multiple choice, < 1 min, fixed. If you were in a rocket ship traveling away from the Earth at a speed close to the speed of light, what changes would you note in your pulse? In your volume? 1. Slower pulse and smaller volume 2. Faster pulse and larger volume 3. No changes; you observed yourself in the same reference frame. 4. No changes because of time dilation Concept 35 20 39:05, highSchool, multiple choice, < 1 min, fixed. 1. The moving points are not massive. 2. The moving points are not material If you were on Earth monitoring a person in a rocket ship traveling away from the Earth Chapter 39, section 5, Consequences of Special Relativity at a speed close to the speed of light, what changes would you note in his pulse? In his volume? 1. Slower pulse and smaller volume 2. Faster pulse and larger volume 3. No changes; you are in the different reference frame from him. 4. No changes because of time dilation Concept 35 22 39:05, highSchool, multiple choice, < 1 min, fixed. How does the measured density of a body in motion compare to its density at rest? 282 length decreases and vice versa. Concept 35 25 39:05, highSchool, multiple choice, < 1 min, fixed. Light is reflected from a moving mirror. How is the reflected light different from the incident light and how is it the same? 1. The frequency changes, and both the wavelength and the speed of light stay the same. 2. Both the frequency and the wavelength change, and the speed of light stays the same. 3. The wavelength changes, and both the frequency and the speed of light stay the same. 1. Increases 2. Decreases 3. The density cannot be measured when bodies move very fast. 4. No change in the frequency, the wavelength, nor the speed of light. Concept 35 30 39:05, highSchool, multiple choice, < 1 min, fixed. 4. No difference Concept 35 24 39:05, highSchool, multiple choice, < 1 min, fixed. The formula relating speed, frequency, and wavelength of electormagnetic waves, c = f ν , was known before relativity was developed. Relativity has not changed this equation but it has added which new feature to it? Part 1 of 3 Electrons end their trip down the Stanford accelerator with an energy thousands of times their rest energy. In theory, if you could travel with them, would you notice an increase in their energy? 1. Electrons would have the same increase in energy. 2. Electrons would have their rest energy. 1. The speed of light is a constant in all reference frames. 2. The frequency is dependent on the reference frames. 3. The wavelength is changed by the reference frames. 4. As the frequency increases, the wave- 3. Electrons would have zero energy. 4. Electrons’ energy would increase, but not as much as in the accelerator’s frame of reference. Part 2 of 3 Would you notice an increase in their momentum? Chapter 39, section 5, Consequences of Special Relativity 1. Electrons would have the same relativistic momentum. 2. Electrons would have zero momentum. 3. Electrons would have a classical non-zero momentum. 4. Electrons’ momentum would increase, but not as much as in the accelerator’s frame of reference. 283 Concept 35 32 39:05, highSchool, multiple choice, < 1 min, fixed. A chunk of radioactive material encased in an idealized perfectly insulating blanket gets warmer as its nuclei decay and release energy. How do the masses of the radioactive material and the blanket, respectively, change? 1. Decreases; decreases 2. Decreases; increases Part 3 of 3 In your moving frame of reference, what would be the approximate speed of the target they are about to hit? 1. Much less than the speed of light 2. Equal to the speed of light 3. Close to the speed of light 4. Greater than the speed of light Concept 35 31 39:05, highSchool, multiple choice, < 1 min, fixed. Two safety pins, identical except that one is latched and one is unlatched, are placed in identical acid baths. After the pins are dissolved, what, if anything, is the difference in the two acid baths? 1. The bath that dissolved the latched pin will be colder and more massive. 2. The bath that dissolved the unlatched pin will have more mass than that of latched pin. 3. The unlatched pin will not be dissolved, while the latched pin will be dissolved well. 4. The bath that dissolved the unlatched pin will be colder with no difference in mass. 3. Increases; increases 2. Increase; decrease Concept 35 33 39:05, highSchool, multiple choice, < 1 min, fixed. The electrons that illuminate the screen in a typical television picture tube travel at nearly one-fourth the speed of light and have nearly 3% more energy than hypothetical non-relativistic electrons traveling at the same speed. Does this relativistic effect tend to increase or decrease your electic bill? 1. Increases; the relativistic electrons require extra momentum and energy. 2. Decreases; the relativistic electrons travel very fast. 3. No effect; there is no change in momentum and energy of relativistic electrons. 4. Your bill is independent of the momentum and energy of electrons. Concept 35 34 39:05, highSchool, multiple choice, < 1 min, fixed. Can the idea of the correspondence principle be applied outside physical science? Chapter 39, section 5, Consequences of Special Relativity 284 cally. 1. Yes; it just makes good sense. 2. No; it does not work outside of physics. 3. No; it works only in the relativistic physics. 4. The correspondence principle is not valid these days. Concept 35 38 39:05, highSchool, multiple choice, < 1 min, fixed. One of the fads of the future might be “century hoping,” where occupants of high-speed spaceships would depart from the Earth for several years and return centuries later. What are the present-day obstacles to such a practice? 1. We are in the same frame of reference. 4. No; the theory does not show that time dilation has no limit. Concept 36 01 39:05, highSchool, multiple choice, < 1 min, fixed. An astronaut awakes in her closed capsule, which actually sits on the moon. Can she tell whether her weight is the result of gravitation or of accelerated motion? 1. She can tell her weight is the result of gravitation. 2. She knows her weight is caused by accelerated motion. 3. She can feel both of them. 4. She does not recognize the difference between them. 2. We cannot distort the time space. 3. We cannot live in the rocket which travels at the speed of light. 4. We do not have enough energy to accelerate to the speed of light. Concept 35 39 39:05, highSchool, multiple choice, < 1 min, fixed. Is the statement by the philosopher Kierkegaard that “Life can only be understood backwards; but it must be lived forwards” consistent with the theory of special relativity? Concept 36 02 39:05, highSchool, multiple choice, < 1 min, fixed. You wake up at night in your berth on a train to find yourself being “pulled” to one side of the train. You naturally assume that the train is rounding a curve but you are puzzled that you don’t hear any sounds of motion. Which of the following is NOT a possible explanation? 1. The train has stopped on a banked section of a track. 1. Yes; the theory shows that there are various frames of reference. 2. The train has stopped next to some superdense matter to which you are highly attracted. 2. Yes; the theory does not provide for traveling backward in time. 3. The car is leaning because of a derailment. 3. No; we can travel backward theoreti- 4. Only acceleration around a curve can Chapter 39, section 5, Consequences of Special Relativity cause their effect. Concept 36 03 39:05, highSchool, multiple choice, < 1 min, fixed. Since gravity can duplicate the effects of acceleration, it can also balance the effects of acceleration. How and when can an astronaut experience no net force (as measured by a scale) because of the canceling effects of gravity and acceleration? 1. When an astronaut is being launched, the effect of gravity and the effect of the thrust force of rocket cancel. 2. When an astronaut is in orbit, the effect of gravity and the effect of the frame’s acceleration cancel. 3. When an astronaut travels in a spaceship in the universe, no gravity acts on his or her body. 4. When an astronaut travels at the speed of light, he or she cannot feel any force. Concept 36 04 39:05, highSchool, multiple choice, < 1 min, fixed. An astronaut is provided a “gravity” when the ship’s engines are activated to accelerate the ship. This requires the use of fuel. Is there a way to accelerate and provide “gravity” without the sustained use of fuel? 1. If the ship travels with the constant acceleration, an astronaut in it feels “gravity”. 2. Once the ship reaches the speed of light, an astronaut feels “gravity” and there is no consumption of fuel. 3. If the ship is set into rotation, an astronaut experiences “gravity” without the consumption of fuel. 285 4. Any “gravity” requires the sustained use of fuel. Concept 36 05 39:05, highSchool, multiple choice, < 1 min, fixed. In his famous novel Journey to the Moon, Jules Verne stated that occupants in a spaceship would shift their orientation from up to down when the ship crossed the point where the moon’s gravitation became greater than the Earth’s. Is this correct? 1. Yes; the space ship travles with a constant acceleration, so the occupants recognize up or down. 2. Yes; the moon’s gravitation and the Earth’s one are the occupants recognize the up or down. 3. No; the occupants travel very fast near a huge gravitational object (the moon and the Earth) so they have no sense of up or down. 4. No; the occupants are in the state of free-fall and have no sense of up or down. Concept 36 06 39:05, highSchool, multiple choice, < 1 min, fixed. What happens to the separation distance between two people if they both walk north at the same rate from two different places on the Earth’s equator? And just for fun, where in the world is a step in every direction a step south? 1. Decrease; at the north pole. 2. Decrease; at the south pole. 3. Increase; at the north pole. 4. Increase; at the south pole. Chapter 39, section 5, Consequences of Special Relativity Concept 36 07 39:05, highSchool, multiple choice, < 1 min, fixed. We readily note the bending of light by reflection and refraction, but why is it we do not ordinarily notice the bending of light by gravity? 1. The Earth is too small to notice the effect. 2. Light travels too fast to notice the effect in our everyday life. 3. The gravities of the Sun, the Moon, and other planets make the effect vanish. 4. The gravity of the Earth is too weak for us to notice the effect. 286 its otherwise straight-line path in a gravitational field of 1 g . By what distance would a beam of light drop from its otherwise straight-line path if it traveled in a uniform field of 1 g for 1 s? Part 2 of 2 For 2 s? Concept 36 10 39:05, highSchool, multiple choice, < 1 min, fixed. Light changes its energy when it “falls” in a gravitational field. This change in energy is not evidenced by a change in speed, however. What is the evidence for this change in energy? 1. The polarization state is inverted. Concept 36 08 39:05, highSchool, multiple choice, < 1 min, fixed. 2. The electric field of light is changed. Why do we say that light travels in straight lines? Is it strictly accurate to say that a laser beam provides a perfectly straight line for purposes of surveying? 4. The light is red shifted. 1. Yes; the main character of a laser is that it travels in a perfect straight line. 2. Yes; the principle of the laser beam is based on the stimulated emission of radiation. 3. No; the laser beam travels in an almost straight line, not perfect. 4. No; the laser beam is distorted near very huge objects. Concept 36 09 39:05, highSchool, numeric, > 1 min, fixed. Part 1 of 2 At the end of 1 s, a horizontally fired bullet has dropped a vertical distance of 4.9 m from 3. The intensity of light is lowered. Concept 36 24 39:05, highSchool, multiple choice, < 1 min, fixed. Why does the gravitational attraction between the sun and Mercury vary? Would it vary if the orbit of Mercury were perfectly circular? 1. The orbit of Mercury about the sun is not perfect circle; no variation of the sun’s gravitational field. 2. The mass of Mercury charges during its orbit; no variation of the Sun’s gravitational field. 3. A comet travels near Mercury periodically; no variation of the Sun’s gravitational field. 4. Mercury is located very close to the sun; Chapter 39, section 5, Consequences of Special Relativity no variation of the sun’s gravitational field. Concept 36 27 39:05, highSchool, multiple choice, < 1 min, fixed. Based on what you know about the emission and absorption of electromagnetic waves, how are gravitational waves are emitted or absorbed? (Scientists seeking to detect gravitational waves must arrange for them to be absorbed.) 1. A gravitation field is distorted. 287 1. accelerated, uniformly moving, accelerated 2. uniformly moving, accelerated, accelerated 3. All are accelerated. 4. All are uniformly moving. 5. accelerated, uniformly moving, uniformly moving 6. uniformly moving, accelerated, uniformly moving 2. A radiation is detected. 3. Masses oscillate. 4. Charges oscillate. Conceptual 28 08 39:05, highSchool, numeric, < 1 min, normal. Calculate the Lorentz factor for objects traveling at 99.9% of the speed of light. Conceptual 28 09 39:05, highSchool, numeric, < 1 min, normal. What is the apparent mass of a 1-kg object that has been accelerated to 99% of light speed? Conceptual 28 Q01 39:05, highSchool, multiple choice, < 1 min, wording-variable. For each of the following situations specify whether you are in a uniformly moving reference frame or an accelerated reference frame, respectively. A. You are in your car, slowing down to make a stop; B. You are floating deep in space, far from the effects of gravity; C. You are standing still on the surface of the earth. 7. uniformly moving, uniformly moving, accelerated 8. accelerated, accelerated, uniformly moving Conceptual 28 Q02 39:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Imagine taking a ride on a perfectly quiet train that rides on a perfectly smooth and straight tracks. If the train is moving at a constant speed and you throw a ball straight up, it appears as though 1. it is falling straight back down 2. it is falling backwards 3. it is falling forward 4. it is not falling Part 2 of 2 If the train is accelerating forward, the ball 1. is falling straight back down 2. is falling backwards Chapter 39, section 5, Consequences of Special Relativity 288 3. is falling forward 2. the backward laser light moves faster. 4. is not falling 3. they both move at the same speed. Conceptual 28 Q03 39:05, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 You are riding on a flatbed truck moving at 50 kilometers per hour. You have two identical guns, one aimed forward and one aimed backward, and you fire them at the same time. According to an observer in the ground, 1. the forward bullet appears to move faster. 2. the backward bullet appears to move faster. 3. they both appear to move at the same speed. Part 2 of 2 According to an observer on the truck 1. the forward laser light moves faster. 2. the backward laser light moves faster. 3. they both move at the same speed. Conceptual 28 Q08 39:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Does relativity theoretically allow you to go backward in time into the past? 1. Yes 2. No Part 2 of 2 According to an observer on the truck, 1. the forward bullet appears to move faster. 2. the backward bullet appears to move faster. Part 2 of 2 An object travelling at the speed of light can be accelerated all the way to (or faster than) the speed of light. 1. true 2. false 3. they both appear to move at the same speed. Conceptual 28 Q04 39:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 You are riding on a flatbed truck moving at 100 kilometers per hour. You have two identical lasers, one aimed forward and one aimed backward. According to an observer in the ground, Conceptual 28 Q10 39:05, highSchool, multiple choice, < 1 min, wording-variable. As you ride in an elevator, when is the apparent acceleration smaller than the acceleration due to gravity outside the elevator (on the surface of the Earth)? 1. when the elevator is accelerating downward 2. when the elevator is at rest 1. the forward laser light moves faster. Chapter 39, section 5, Consequences of Special Relativity 3. when the elevator is accelerating upward Conceptual 28 Q11 39:05, highSchool, multiple choice, < 1 min, fixed. If you are in a spaceship far from the reaches of gravity, under what conditions will it feel to you as if the spaceship were sitting stationary on Earth’s surface? 1. when the tidal effects of sun is not present 2. when the spaceship is accelerating at 9.81 m/s2 3. when the spaceship is at rest 4. when the spaceship is influenced by the gravitational force of another planet Conceptual 28 Q14 39:05, highSchool, multiple choice, < 1 min, fixed. Why is it that we don’t ordinarily notice the bending of light? 1. Light travels at a very high speed. 2. Light doesn’t really bend. 3. What few light rays that bend are overpowered by those that do not bend. Conceptual 28 Q19 39:05, highSchool, numeric, < 1 min, normal. If you can do 39 pushups on the surface of Earth, how many can you do in a spaceship, far from gravity, accelerating at g ? 289 Chapter 39, section 6, The Lorentz Transformation for Displacements Concept 35 23 39:06, highSchool, multiple choice, < 1 min, fixed. If stationary observers measure the shape of a passing object to be exactly circular, what is the shape of the object according to observers traveling with it? 1. It depends on the speed of object. 2. It’s also circular. 3. It’s an ellipse (shorter in the direction of motion). 4. It’s an ellipse (longer in the direction of motion). Concept 35 29 39:06, highSchool, multiple choice, < 1 min, fixed. Why does the two-mile linear accelerator at Stanford University in California “appear” to be less than a meter long to the electrons that travel in it. 1. Electrons travel faster than the speed of light. 290 What is the width of the building as measured by a friend standing at rest next to the building? Part 2 of 2 What height of the building would be measured by the friend? Conceptual 28 Q13 39:06, highSchool, multiple choice, < 1 min, fixed. Due to the length contraction, you notice that a passing train appears to be shorter than when it is stationary. What do the people in the train observe about you? 1. They observe you to appear longer than when you are at stationary. 2. They observe you to appear as you are at stationary. 3. They observe you to appear shorter than when you are at stationary Problems 35 06 39:06, highSchool, numeric, < 1 min, normal. 2. The decrease in volume makes the electron smaller. A bus moving at 0.99 c is 70 feet long according to its passengers and driver. What is its length from your vantage point on a fixed planet? 3. Length contraction reduces the apparent length. Problems 35 08 39:06, highSchool, numeric, < 1 min, normal. 4. Time dilation makes the lifetime of electrons longer. A bus is 70 feet long according to its passengers and driver. If the bus driver decided to drive at 0.9999 c in order to make up some time, what would you measure the length of the bus to be? Conceptual 28 05 39:06, highSchool, numeric, < 1 min, normal. Part 1 of 2 Elliot is traveling by a building at 150000 km/s, moving along the width of the building. He measures the building to be 50 m wide and 100 m tall. Chapter 39, section 7, The Lorentz Transformation for Time 291 1. Possible only if he travels very long time formed high in the atmosphere by the interactions of cosmic rays with atomic nuclei in the upper atmosphere. They receive a lot of energy from the original cosmic ray and travel at speeds close to the speed of light. Muons have an average lifetime of about two millionths of a second and according to classical physics should decay before reaching the sea level. Laboratory measurements, however, show that muons in great number do reach the Earth’s surface. What is the explanation? 2. Possible only if he travels at the speed of light 1. Muons travel faster as they enter the lower atmosphere. 3. Impossible; only the speed of aging can change. 2. The timing in the muons’ frame of reference is different from ours. Concept 35 17 39:07, highSchool, multiple choice, < 1 min, fixed. A twin who makes a long trip at relativistic speeds returns younger than his twin sister who stayed at home. Could he return before his twin sister was born? 4. Time dilation makes it impossible. Concept 35 21 39:07, highSchool, multiple choice, < 1 min, fixed. If you lived in a world where people regularly traveled at speeds near the speed of light, why would it be risky to make a dental appointment for 10:00 AM next Thursday? 1. You and your dentist are in the different reference frames; your clock and his will indicate different times. 2. Spaces around you and your dentist are distorted; you cannot meet him. 3. You and your dentist will be in different time space, and your watches cannot be synchronized. 3. Muons interact with some particles in the air. 4. Experimental physics is wrong. Concept 35 37 39:07, highSchool, multiple choice, < 1 min, fixed. When we look out into the universe, we see the past. John Dobson, founder of the San Francisco Siderwalk Astronomers, says that we cannot even see the backs of our own hands now. In fact, we can’t see anything now. Do you agree? 1. Yes; there is always a finite time interval between an event and our perception of it. 2. Yes; we cannot see the future events. 3. No; our hands are very close to our eyes. 4. Time dilation confuses you and your dentist about the correct time. Concept 35 36 39:07, highSchool, multiple choice, < 1 min, fixed. Muons are elementary particles that are 4. No; we cannot recognize the time interval. Concept 36 11 39:07, highSchool, multiple choice, < 1 min, fixed. Chapter 39, section 7, The Lorentz Transformation for Time Would we notice a slowing down or speeding up of a clock if we carried it to the bottom of a very deep well? 1. The clock will run slower. 292 the center of a rotating kingdom. Charity goes to live at the edge of the kingdom for a time and then returns home. Which twin is older when they rejoin? (Ignore any time-dilation effects associated with travel to and from the edge.) 2. The clock will run faster. 1. Prudence 3. The clock will run the same as at the surface. Concept 36 15 39:07, highSchool, multiple choice, < 1 min, fixed. Will a clock at the equator run slightly faster or slightly slower than an identical clock at one of the Earth’s poles? 1. The clock runs slower. 2. The clock runs faster. 3. The clocks run the same. 4. The speed of clock depends on the position at the equator. Concept 36 16 39:07, highSchool, multiple choice, < 1 min, fixed. Splitting hairs, should a person who worried about growing old live at the top or at the bottom of a tall apartment building? 2. Charity 3. There will be no difference. 4. More information is needed. Conceptual 28 04 39:07, highSchool, numeric, < 1 min, normal. Anna is watching the stars late at night when she sees a spaceship pass at 80% of the speed of light; 10 seconds pass on Earth as she watches a clock on the spaceship. How much time passes on the spaceship clock? Conceptual 28 Q06 39:07, highSchool, multiple choice, < 1 min, fixed. You and a friend buy two identical watches. Some days later you see your friend travelling relative to you at 25% of the speed of light. Which watch is running factor? 1. friend’s 1. At the top 2. yours 2. At the bottom 3. same speed 3. There will be no difference. Conceptual 28 Q07 39:07, highSchool, numeric, < 1 min, normal. 4. It depends on the growth speed. Concept 36 17 39:07, highSchool, multiple choice, < 1 min, fixed. Prudence and Charity are twins raised at You take your pulse while sitting in your room and you measure 57 beats per minute (bpm). All else being equal, what would your pulse measure if you took it while on a fast-moving train? Chapter 39, section 7, The Lorentz Transformation for Time Conceptual 28 Q15 39:07, highSchool, multiple choice, < 1 min, fixed. To an outside observer, where would you appear to age faster? 1. on top of a mountain 2. at the sea level 3. 100 m below sea level 293 Conceptual 28 Q20 39:07, highSchool, multiple choice, < 1 min, fixed. You are jealous of your younger brother, who looks very young for his age. You are interested in reducing the rate at which you age relative to him. Having heard of general relativity and the effect of gravity on time, you decide that you need to spend more time at an altitude that makes you age more slowly relative to your brother. Using only gravity considerations, which job would meet your needs? 4. in the space station 1. park ranger high in the mountains Conceptual 28 Q16 39:07, highSchool, multiple choice, < 1 min, fixed. 2. a worker at a space station 3. a taxi cab driver at sea level You’ve decided to let your sister, a NASA astronaut, cook the Thanksgiving turkey this year. Normally the turkey takes 6 hours to cook, but your sister decides to cook it on her spaceship while travelling at close to the speed light. According to your watch, she was gone for 6 hours. What was the condition of the turkey? 1. The turkey was overcooked. 2. The turkey was undercooked. 3. The turkey was just right. Conceptual 28 Q17 39:07, highSchool, multiple choice, < 1 min, fixed. Because of relative motion, you notice a friend’s clock running slowly. How does your friend view your clock? 1. running faster than his clock 2. running slower than his clock 4. a miner at below sea level Problems 35 01 39:07, highSchool, multiple choice, < 1 min, fixed. Consider a high-speed rocket ship equipped with a flashing light source. If the frequency of flashes when the ship is approaching is twice what it was when the ship was a fixed distance away, by how much is the period (time interval between flashes) changed? Is this period constant for a constant relative speed? For accelerated motion? Defend your answer. 1. Each flash has less distance and the frequency increase more, and the period decrease more as well. 2. Each flash has the same distance and the frequency increase more, but the period is constnat. 3. Each flash has the same distance and the frequency and the period are also constant. 3. running the same 4. Each flash has more distance and the Chapter 39, section 7, The Lorentz Transformation for Time frqeuency decrease more, and the period increase more as well . Problems 35 04 39:07, highSchool, numeric, < 1 min, normal. A passenger on an interplanetary express bus traveling at v =0.99 c takes 5 minutes catnap by his watch. How long does the nap last from your vantage point on a fixed planet? Problems 35 07 39:07, highSchool, numeric, < 1 min, normal. A passenger on an interplanetary express bus traveling at 0.1 c takes 5 minutes catnap by his watch. How long would you measure the passenger’s catnap to be? Problems 35 09 39:07, highSchool, numeric, < 1 min, normal. Assume that rocket taxis of the future move about the solar system at 0.5 c . For a 1 hour trip as measured by a clock in the taxi, a driver is paid 10 stellars. The taxi driver’s union demands that pay be based on Earth time instead of taxi time. If their demand is met, what will be the new pay for the same trip? 294 Chapter 39, section 8, The Lorentz Transformation for Velocities Conceptual 28 06 39:08, highSchool, numeric, < 1 min, normal. An interplanetary spaceship has windows that are 3 meters wide. How fast must it pass by a planet so that an observer on that planet measures the width of the windows to be 1.5 meters? Conceptual 28 10 39:08, highSchool, numeric, < 1 min, fixed. If a moving clock appears to be ticking onehalf as fast as normal, at what percentage of light speed is traveling? 295 The starship Enterprise, passing the Earth at 0.8 c , sends a drone ship forward at 0.5 c relative to the Enterprise. What is the drone’s speed relative to the Earth? (Where, c is the speed of light) Problems 35 03 39:08, highSchool, numeric, < 1 min, fixed. Pretend that the starship Enterprise in the previous problem is somehow traveling at c with respect to the Earth, and it fires a drone forward a speed c with respect to itself. Using the equation for the relativistic addition of velocities, what is the speed of the drone with respect to the Earth? Figuring Physics 07 39:08, highSchool, multiple choice, < 1 min, fixed. 1. 0.5c Assume: The sun passes between the Earth and a pair of stars as shown below, and the moon passes in from of the sun and totally eclipses it so the stars are visible. 3. c 2. 0.98c 4. 2c Relative Speeds 39:08, highSchool, multiple choice, > 1 min, fixed. STAR STAR SUN MOON OBSERVER According to General Relativity, the stars will appear to be slightly 1. closer together. 2. farther apart. A flashbulb is placed in the middle of a bus. When the flashbulb goes off, light from the bulb strikes the rear and front of the bus simultaneously, as seen by an observer, Karl, sitting in the bus. As seen by another observer, Fred, standing on the curb as the bus moves past, the light 1. hits the front of the bus slightly before it hits the rear. 2. hits the rear of the bus slightly before it hits the front. 3. distorted, but not closer or farther apart. 3. hits the front and back of the bus simultaneously. Problems 35 02 39:08, highSchool, numeric, < 1 min, normal. 4. Not enough information to form a conclusion. Chapter 39, section 8, The Lorentz Transformation for Velocities Relativistic Speeds 02 39:08, highSchool, numeric, > 1 min, normal. Part 1 of 2 Our hero is fired upon by the dastardly space villain whose space howitzer has a muzzle velocity of 0.5 c . Moreover, the space villain is speeding toward our hero at 0.7 c when she fires her evil weapon? How fast does our hero see the projectile rushing at him (as a multiple of c)? Assume: The positive direction is from our hero towards the dastardly space villain. Part 2 of 2 Our hero sees the weapon fired from a mere 1 Gm away. How long does he have to raise his deflector screens? (Remember, it also takes some time for the light to get to him, and the projectile is already on its way.) The speed of light is 3 × 108 m/s. 296 Chapter 39, section 9, Relativistic Momentum and Relativistic Form of Concept 35 26 39:09, highSchool, multiple choice, < 1 min, fixed. As a meter stick moves past you, your measurments show its momentum to be twice its classical momentum and its length to be 1 m. In what direction is the stick pointing? 1. Along the direction of motion 2. Perpendicular to the direction of motion 3. 60◦ to the direction of motion 4. 30◦ to the direction of motion Concept 35 27 39:09, highSchool, multiple choice, < 1 min, fixed. If a meter stick is moving with a relativistic momentum that is twice its classical momentum in a direction along its length (like a properly thrown spear), how long will you measure its length to be? 1. 0.5 m 2. 0.87 m 3. 1 m 4. 2 m Problems 35 05 39:09, highSchool, numeric, < 1 min, normal. According to Newtonian mechanics, the momentum of a bus is p = mv. According the relativity, it is p = γ mv. How many times greater the actual momentum of the bus moving at 0.99 c compare with the momemtum it would have if classical mechanics were valid? 297 Chapter 39, section 10, Relativistic Energy Conceptual 12 01 39:10, highSchool, numeric, > 1 min, normal. Part 1 of 2 According to Einstein’s famous equation E = mc 2 how much energy is contained in 1 lb of feathers? Part 2 of 2 What relationship would the above energy E1 and the energy E2 of 1 lb of lead have? 1. E1 > E2 2. E1 < E2 3. E1 = E2 4. Unable to determine Conceptual 12 02 39:10, highSchool, numeric, < 1 min, normal. According to Einstein’s famous equation E = m c2 how much energy is contained in 100 kg of matter? Conceptual 12 07 39:10, highSchool, numeric, > 1 min, normal. Part 1 of 3 In the Sun, 1 g of hydrogen consumed in nuclear fusion reactions produce 0.9929 g of helium; the other 0.0071 g of material is converted into other forms of energy. How much energy does this process produce? Part 2 of 3 How high could you raise the Mt. Palomar 5-m telescope (of mass 450000 kg) with this energy? 298 Part 3 of 3 If you could convert 1 g of hydrogen into energy every second through nuclear fusion, the energy produced would be equivalant to how many 1-gigawatt power plants? Conceptual 28 12 39:10, highSchool, numeric, < 1 min, normal. Part 1 of 2 If you were able to extract 100% of the energy available in 1 kg of hydrogen, how much energy would you have? Part 2 of 2 How much energy would be available from 1 kg of uranium if the same 100% efficiency were attained in this extraction? Figuring Physics 33 39:10, highSchool, multiple choice, > 1 min, fixed. Einstein’s celebrated equation, E = m c2 states that energy is equal to the mass of an object multiplied by the speed of light squared. What the equation means is 1. energy and mass both travel at the speed of light. 2. when mass travels at the speed of light it becomes pure energy. 3. when mass travels at the speed of light squared it becomes pure energy. 4. mass and energy are related. 5. (all of these). 6. (none of these). Problems 35 10 39:10, highSchool, numeric, > 1 min, fixed. The fractional change of masses to energy in a fission reactor is about 0.1uranium that un- Chapter 39, section 10, Relativistic Energy dergoes fission, how much energy is released? If energy costs three cents per megajoule, how much is this energy worth in dollars? 299 Chapter 39, section 11, Mass as a Measure of Energy Concept 35 35 39:11, highSchool, multiple choice, < 1 min, fixed. What does the equation E = m c2 mean? 1. We cannot move faster than the speed of light. 2. It is a very important clue for makers of nuclear bombs. 3. Energy and mass are equivalent. 4. Light carries enormous energy. 300 Chapter 39, section 13, Conservation of Relativistic Momentum, Mass, and Energy Concept 35 28 39:13, highSchool, multiple choice, < 1 min, fixed. If a high-speed spaceship appears shrunken to half its normal length, how does its momentum compare with the classical formula p = m v? 1. 0.5 m v 2. 0.87 m v 3. m v 4. 2 m v 301 Chapter 39, section 17, General Relativity and Accelerating Reference Frames 302 the same color you send? Concept 36 12 39:17, highSchool, multiple choice, < 1 min, fixed. If we witness events taking place on the moon, where gravitation is weaker than on Earth, would we expect to see a gravitational red shift or a gravitational blue shift? 1. Red shift; events on the moon run slower than on Earth. 1. Yes; the frequency of light does not change, so the color she received is the same as the color you sent. 2. No; the frequency of light is increased, so the color is red shifted. 3. No; the frequency of light is decreased, so the color is blue shifted. 4. We need to know the exact frequency. 2. Blue shift; events on the moon run faster than on Earth. 3. It depends on the speed of event. 4. No shift; events run at the same speed on the moon and Earth. Concept 36 13 39:17, highSchool, multiple choice, < 1 min, fixed. Concept 36 19 39:17, highSchool, multiple choice, < 1 min, fixed. Is light emitted from the surface of a massive star red-shifted or blue-shifted by gravity? 1. Red shifted 2. Blue shifted Armed with highly sensitive detection equipment, you are in the front of a railroad car that is accelerating forward. Your friend at the rear of the car shines green light toward you. Do you find the light to be red-shifted (lowered in frequency), blue-shifted (increased in frequency), or neither? 1. red shift 2. blue shift 3. It depends on the speed. 4. no shift Concept 36 18 39:17, highSchool, multiple choice, < 1 min, fixed. Splitting hairs, if you shine a beam of colored light to a friend above in a high tower, will the color of light your friend receives be 3. No shift 4. It depends on the mass of star. Concept 36 20 39:17, highSchool, multiple choice, < 1 min, fixed. From our frame of reference on Earth, objects slow to a stop as they approach black holes in space because time is infinitely stretched by the strong gravity near the black hole. If astronauts accidentally falling into a black hole tried to signal back to Earth by flashing a light, what kind of “telescope” would we need to see the signals? 1. one sensitive to the X-rays 2. one sensitive to the ultra violet light 3. one sensitive to the visible lights Chapter 39, section 17, General Relativity and Accelerating Reference Frames 303 1. Yes. 4. one sensitive to radio waves 2. No. Concept 36 21 39:17, highSchool, multiple choice, < 1 min, fixed. Would an astronaut falling into a black hole see the surrounding universe red-shifted or blue-shifted? Concept 36 26 39:17, highSchool, multiple choice, < 1 min, fixed. Do binary stars (double-star systems that orbit about a common center of mass) radiate gravitational waves? Why or why not? 1. Red shifted 1. Yes; they are the accelerating masses. 2. Blue shifted 3. No shift 4. It depends on the gravity of the black hole. Concept 36 22 39:17, highSchool, multiple choice, < 1 min, fixed. How can we observe a black hole if neither matter nor radiation can escape from it? 1. We can observe the radiation from it. 2. We can use X-ray telescopes which are very sensitive to very short wavelengths. 2. Yes; they are more massive than one star. 3. No; their orbit is not circular. 4. No; radiating gravitational waves is one characteristic of a single star, not a doublestar system. Concept 36 28 39:17, highSchool, multiple choice, < 1 min, fixed. Comparing Einstein’s and Newton’s theories of gravitation, can the correspondence principle be applied? 1. Yes. 3. We can detect its emitted gravitational radiation. 4. We can observe the gravitational effect of the black hole on a visible star’s orbit located near it. Concept 36 25 39:17, highSchool, multiple choice, < 1 min, fixed. In the astronomical triangle, with sides defined by light paths, the sum of the interior angles is more than 180 degrees. Is there any astronomical triangle whose interior angles sum to less than 180 degrees? 2. No. Chapter 40, section 1, The Photon, the Quantum of Light 304 fixed. Concept 40 1 40:01, highSchool, multiple choice, < 1 min, fixed. What is correct about quantum physics? 1. Quantum physics is characterized by absolute predictability. 2. Quantum physics rules don’t apply for subatomic particles. What does it mean to say that something is quantized? 1. It could be regarded as macroscopic particles. 2. It doesn’t have any property of wave. 3. It only has particle properties. 4. It is composed of elementart units. 3. Quantum physics is primarily the physics know before 1900 that includes the study of motion according to Newton’s laws and the study of electromagnetism in accordance with the laws of Maxwell. Concept 40 30 40:01, highSchool, multiple choice, < 1 min, fixed. 4. Quantum physics rules are rules of propability, not certainly. If a particle is smaller than the wavelength of visible light, with which microscope could we discern it? Concept 40 19 40:01, highSchool, multiple choice, < 1 min, fixed. The camera that takes photograph of a woman’s face used ordinary lenses that are well known to refract waves. Yet the stepby-step formation of the images is evidence of photons. Which of the following is not right? 1. Light refracting through the lens system is understandable via the wave model of light. 2. The arrival of light spot by spot to form the image is understandable via the particle model of light. 1. the electron microscope 2. the optical microscope 3. both 4. neither Concept 40 31 40:01, highSchool, multiple choice, < 1 min, fixed. Would a beam of protons in a “proton microscope” exhibit greater or less diffraction than electrons of the same speed in an electron microscope? 1. greater 3. Single photons only have particle properties whereas light, composed of many photons, has wave properties. 2. less 3. the same 4. Light has both wave and particle properties. Concept 40 2 40:01, highSchool, multiple choice, < 1 min, 4. More information is needed. Concept 40 32 40:01, highSchool, multiple choice, < 1 min, Chapter 40, section 1, The Photon, the Quantum of Light fixed. Suppose nature were entirely different so that an infinite number of photons would be needed to make up even the tiniest amount of radiant energy, the wavelength of material particles were zero, light would have no particle properties, and matter would have no wave properties. This would be the classical world described by the mechanics of Newton and the electricity and magnetism of Maxwell. What would be the value of Planck’s constant for such a world with no quantum effects? 1. extraordinarily large 305 Consider E = h f , the formula of a proton’s energy where f in the formula is a wave frequency, which of the following is not right? 1. The formula links a particle property (the photon energy E ) to a wave property, the frequency f . 2. Since f is a wave frequency, the formula illustrates that the photon could be regarded as wave. 3. If h were zero, there would be no quantum phenomena. 4. The formula illstrates that the photon has both wave and particle properties. 2. positive 3. negative 4. zero Concept 40 33 40:01, highSchool, multiple choice, < 1 min, fixed. Suppose you lived in a hypothetical world where you’d be knocked down by a single photon, where matter would be so wavelike that it would be fuzzy and hard to grasp, and where the uncertainty principle would impinge on simple measurements of position and speed in a laboratory, making results irreproducible. In such a world, how would Planck’s constant compare to what it is in reality? Concept 40 41 40:01, highSchool, numeric, < 1 min, fixed. A typical wavelength of infrared radiation emitted by your body is 2.5 × 10−5 m. What is the energy per photon of such radiation? Concept 40 4 40:01, highSchool, multiple choice, < 1 min, fixed. The frequency of violet light is about twice that of red light. How does the energy of a violet photon compare with the energy of a red photon? 1. twice as energetic as red photons 1. extremely large 2. half as energetic as red photons 2. extremely small 3. the same as red photons 3. equal 4. It requires a case-by-case analysis. 4. More information is needed. Concept 40 3 40:01, highSchool, multiple choice, < 1 min, fixed. Concept 40 5 40:01, highSchool, multiple choice, < 1 min, fixed. Which of the following is not right? Chapter 40, section 1, The Photon, the Quantum of Light 1. The energy of a green photon is larger than that of a red one. 2. The energy of a violet photon is larger than that of a green one. 3. The wavelength of a red photon is larger than that of a violet one. 4. The energy of a white photon is larger than that of a violet one. Concept 40 6 40:01, highSchool, multiple choice, < 1 min, fixed. 306 photon jumps from B to A. Part 2 of 2 Find the wavelength λ3 emitted when the photon jumps from C to A. Hewitt CP9 32 E02 40:01, highSchool, multiple choice, > 1 min, fixed. Which color of light comes from a greater energy transition? 1. Red 2. Yellow If a beam of red light and a beam of blue light have exactly the same energy, which beam contains the greater number of photons? 1. the beam of red light 2. the beam of blue light 3. The beams have the same number of photons. 4. It requires a case-by-case analysis. Hewitt CP9 30 P01 40:01, highSchool, numeric, < 1 min, fixed. Part 1 of 2 In the diagram, the energy difference between states A and B is twice the energy difference between states B and C. In a transition (quantum jump) from C to B an electron emits a photon of wavelength 600 nm. C B A Find the wavelength λ2 emitted when the 3. Green 4. Blue Holt SF 23A 02 40:01, highSchool, numeric, < 1 min, wordingvariable. A vibrating mass-spring system has a frequency of 0.56 Hz. How much energy of this vibration is carried away in a one-quantum change? Holt SF 23A 03 40:01, highSchool, numeric, < 1 min, wordingvariable. A photon in a laboratory experiment has an energy of 5.0 eV. What is the frequency of this photon? Holt SF 23A 04 40:01, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 Radiation emitted from human skin reaches its peak at λ = 940 µm. a) What is the frequency of this radiation? Part 2 of 3 b) What type of electromagnetic waves are Chapter 40, section 1, The Photon, the Quantum of Light 307 these? 1. infrared waves A photon of a certain color of visible light has 2.9 × 10−19 J of energy. What color is the light? 2. microwaves 1. Blue 3. radio waves 2. Red 4. visible light 3. White 5. ultraviolet light 4. Yellow 6. x rays 5. None of these 7. gamma rays Part 3 of 3 c) How much energy is carried by one quantum of these electromagnetic waves? Holt SF 23Rev 14 40:01, highSchool, numeric, < 1 min, wordingvariable. A quantum of electromagnetic radiation has an energy of 2.0 keV. What is its frequency? Holt SF 23Rev 15 40:01, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 3 The energy of a photon increases as its wavelength decreases. a) What is the energy of a microwave photon with a wavelength of 5.00 cm? Part 2 of 3 b) What is the energy of a visible photon with a wavelength of 5.00×10−7 m? Part 3 of 3 c) What is the energy of an X-ray photon with a wavelength of 5.00 × 10−8 m? Holt SF 23Rev 45 40:01, highSchool, multiple choice, < 1 min, normal. Holt SF 23Rev 50 40:01, highSchool, numeric, < 1 min, wordingvariable. How many photons are emitted every 1.00 s by a 100.0 W sodium lamp if the wavelength of sodium light is 589.3 nm? Holt SF 23Rev 51 40:01, highSchool, numeric, < 1 min, wordingvariable. From the scattering of sunlight, Thomson found that the classical radius of the electron is 2.82 × 10−15 m. If sunlight with an intensity of 5.00 × 102 W/m2 falls on a disk with this radius, estimate the time required to accumulate 1.0 eV of energy. Assume that light is a classical wave and that the light striking the disk is completely absorbed. How does your estimate compare with the observation that photoelectrons are emitted within 10−9 s? Wavelength of a Photon 40:01, highSchool, numeric, < 1 min, normal. A quantum of electromagnetic radiation has an energy of 2 keV. What is its wavelength? The speed of light is c = 2.99792 × 108 m/s, and Planck’s constant is h = 6.62608 × 10−34 J s. Chapter 40, section 3, Blackbody Radiation and Planck’s Hypothesis Company distances of two stars 40:03, highSchool, multiple choice, > 1 min, fixed. Suppose two stars of the same apparent brightness are also believed to be the same size. The spectrum of one star peaks at λ1 whereas that of other peaks at λ2 . Use Wien’s law λ T = 2.9 × 10−3 mK and the Stefan-Boltzman law (L ∝ A T 4 , where A is the surface area of the star) to estimate the ratio D2 /D1 , where D1 and D2 are their respective distances from us. 308 1. No; the filament will have the same temperature as its environment. 2. No; the filament will be dark at room temperature. 3. Yes; the filament will be at a temperature that is greater than absolute zero. 4. Yes; the filament has a smaller heat capacity than its environment. Concept 30 37 40:03, highSchool, multiple choice, < 1 min, fixed. D2 1. = D1 λ1 λ2 2 D2 2. = D1 λ2 λ1 2 D2 = D1 λ1 λ2 3/2 1. Red D2 = 4. D1 D2 = 5. D1 D2 6. = D1 λ2 λ1 λ1 λ2 λ2 λ1 3/2 2. White D2 = 7. D1 λ1 λ2 1/2 3. If we continue heating a piece of initially room-temperature metal in a dark room, what will be its first visible color? 3. Violet 4. There will be no color at all. 1/2 D2 λ2 8. = D1 λ1 D2 9. =1 D1 D2 10. = (λ1 λ2 )1/3 D1 Concept 30 34 40:03, highSchool, multiple choice, < 1 min, fixed. We know that a lamp filament at 2500 K radiates white light. Does the lamp filament also radiate energy when it is at room temperature? Figuring Physics 13 40:03, highSchool, multiple choice, < 1 min, fixed. You’re a consultant to a manufacturer of space gear that wants to encase instruments in a covering that will have two properties: (1) absorb as little energy as possible on the side of the package facing the sun, and (2) emit as little energy as possible on the side facing away from the sun. You should recommend a covering with 1. the side facing the sun black and the other side shiny. 2. the side facing the sun shiny and the other side black. 3. both sides shiny. Chapter 40, section 3, Blackbody Radiation and Planck’s Hypothesis 4. both sides black. Holt SF 23A 01 40:03, highSchool, numeric, < 1 min, wordingvariable. Assume that the pendulum of a grandfather clock acts as one of Planck’s resonators. If it carries away an energy of 8.1 × 10−15 eV in a one quantum change, what is the frequency of the pendulum? 309 Chapter 40, section 4, Light Quantization and the Photoelectric Effect 310 fixed. Concept 30 21 40:04, highSchool, multiple choice, < 1 min, fixed. Your friend reasons that if ultraviolet light can activate the process of fluorescence, infrared light should also. Your friend looks to you for approval or disapproval of this idea. What is your position? 1. Your friend is correct; if the intensity of the infrared light is strong enough, fluorescence will be easily activated. 2. Your friend could be wrong; the energy of the ultraviolet photon is higher than the energy of infrared photon, so the fluorescence activated by the ultraviolet light may not necessarily be activated by the infrared light. 3. It depends; we need to know the intensity and the duration of the irradiation that will be used to activate the fluorescence. In the photoelectric effect, does brightness or frequency determine the kinetic energy of the ejected electrons? The number of the ejected electrons? 1. Brightness; brightness. 2. Brightness; frequency. 3. Frequency; brightness. 4. Frequency; frequency. Concept 40 11 40:04, highSchool, multiple choice, < 1 min, fixed. A very bright source of red light has much more energy than a dim source of blue light. What has no effect in ejecting electrons from a certain photosensitive surface? 1. Bright source of red light 4. None of these 2. Dim source of blue light Concept 30 22 40:04, highSchool, multiple choice, < 1 min, fixed. 3. Equally possible. 4. It requires a case-by-case analysis. When ultraviolet light falls on certain dyes, visible light is emitted. What will happen when infrared light falls on these dyes? Concept 40 12 40:04, highSchool, multiple choice, < 1 min, fixed. 1. Visible light will be emitted with the same intensity. What is ejected when light strikes a metal surface? 2. There will be no visible light at all. 3. Ultraviolet light with very low intensity will be emitted. 1. Electrons 2. Photons 3. Neutrons 4. Infrared light with a shorter wavelength than the incident light will be emitted. Concept 40 10 40:04, highSchool, multiple choice, < 1 min, 4. Both electrons and photons Concept 40 13 40:04, highSchool, multiple choice, < 1 min, Chapter 40, section 4, Light Quantization and the Photoelectric Effect 311 fixed. 3. The charge remains the same. The photoelectric effect is used to open automatic doors when someone approaches. The door utilizes a beam of light that continuously shines on a photodetector. Why does the door open automatically when you block the beam by walking through it? 1. The generation of electrons in the photodetector ceases. 2. The generation of protons in the photodetector ceases. 3. The number of protons generated in the photodetector decreases. 4. The number of electrons generated in the photodetector increases. Concept 40 14 40:04, highSchool, multiple choice, < 1 min, fixed. If you shine an ultraviolet light on the metal ball of a negatively charged electroscope, what will happen? 1. The charge increases. 2. The charge decreases. 3. The charge remains the same. 4. It requires a case-by-case analysis. Concept 40 15 40:04, highSchool, multiple choice, < 1 min, fixed. If you shine an ultraviolet light on the metal ball of a positively charged electroscope, what will happen? 4. It depends on a case-by-case analysis. Concept 40 16 40:04, highSchool, multiple choice, > 1 min, fixed. What is not correct about the usage of photoelectric effect? 1. Electric eye: A beam of light is directed to a photosensitive surface that completes the path of an electric circuit. When the beam is interrupted, the circuit is broken. The entire photoelectric circuit may be used as a switch for another circuit. 2. Light meter: The variation of photoelectric current with variation in light intensity activates a galvanometer (or its equivalent), which is calibrated to show light intensity. 3. Sound track: An optical sound track on motion picture film is a strip of emulsion of variable density that transmits light of variable intensity onto a photosensitive surface, which in turn produces an electric current of the desired variations. This current is amplified and activates the loudspeaker. 4. Automatic door: The doors utilize a beam of light that continuously shines on a photodetector. When you block the beam by walking through it, the current in the photodetector increases. This change of current then activates the opening of the door. Concept 40 17 40:04, highSchool, multiple choice, < 1 min, fixed. Which aspect of the property of light does the photoelectric effect support? What about the interference experiment? 1. The charge increases. 2. The charge decreases. 1. Both support the corpuscular model of light. Chapter 40, section 4, Light Quantization and the Photoelectric Effect 312 Which color do you expect it to be? 2. Both support the wave model of light. 1. red 3. Corpuscular model; wave model 2. blue 4. Wave model; corpuscular model 3. green Concept 40 18 40:04, highSchool, multiple choice, < 1 min, fixed. Consider Einstein’s explanation of the photoelectric effect and Young’s explanation of the double-slit experiments. Which is/are correct? 1. Only Einstein’s 2. Only Young’s 3. Both are correct. 4. yellow Concept 40 8 40:04, highSchool, multiple choice, < 1 min, fixed. Silver bromide is a light-sensitive substance used in some types of photographic film. To cause exposure of film, it must be illuminated with light having sufficient energy to break apart the molecules. This film may be handled without danger of exposure in a darkroom illuminated with a certain light. Which light? 4. Both are wrong. 1. very bright red light Concept 40 20 40:04, highSchool, multiple choice, < 1 min, fixed. 2. very dim blue light 3. very bright blue light Which of the following is NOT evidence of the wave nature of light? 1. diffraction 2. polarization 3. interference 4. photoelectric effect 4. common blue light Concept 40 9 40:04, highSchool, multiple choice, < 1 min, fixed. Sunburn produces cell damage in the skin. Which of the following is the most capable of producing this damage? Concept 40 7 40:04, highSchool, multiple choice, < 1 min, fixed. 1. ultraviolet radiation One of the technical challenges facing the original developers of color television was the design of an image tube (camera) for a certain color of the image. It’s difficult to find a material that would respond to light of this color. 3. intense visible radiation 2. visible radiation 4. ultrared radiation Conceptual 22 Q13 40:04, highSchool, multiple choice, < 1 min, Chapter 40, section 4, Light Quantization and the Photoelectric Effect 313 fixed. Which light photon is more effective at inducing the photoelectric effect than visible light photons? 1. Ultraviolet light has more energy per photon than visible light. Therefore an ultraviolet photon is more likely able to give an electron enough energy to escape a metal surface. 2. Visible light has more energy per photon than ultraviolet light . Therefore a visible light photon is more likely able to give an electron enough energy to escape a metal surface. Hewitt CP9 31 P01 40:04, highSchool, numeric, > 1 min, fixed. A typical wavelength of infrared radiation emitted by your body is 2.5 × 10−5 m . Find the energy per photon of such radiation. The speed of light is 2.998 × 108 m/s. Holt SF 23B 01 40:04, highSchool, numeric, < 1 min, wordingvariable. Holt SF 23B 03 40:04, highSchool, numeric, < 1 min, wordingvariable. Light of frequency 1.00 × 1015 Hz illuminates a sodium surface. The ejected photoelectrons are found to have a maximum kinetic energy of 1.86 eV. Calculate the work function of sodium. Holt SF 23B 04 40:04, highSchool, multiple choice, < 1 min, wording-variable. Which of the following metals will exibit the photoelectric effect when light with a frequency of 7.0 × 1014 Hz frequency is shone on it? a. lithium, hft = 2.3eV b. silver, hft = 4.7eV c. cesium, hft = 2.14eV 1. Lithium and cesium 2. Lithium 3. Cesium 4. Lithium and silver In the photoelectric effect, it is found that incident photons with 5.00 eV of energy will produce electrons with a maximum kinetic energy of 3.00 eV. What is the threshold frequency of this material? Holt SF 23B 02 40:04, highSchool, numeric, > 1 min, fixed. 5. Silver 6. None of these Holt SF 23Rev 16 40:04, highSchool, numeric, < 1 min, wordingvariable. Part 1 of 2 Light of wavelength 350 nm falls on a potassium surface, and the photoelectrons have a maximum kinetic energy of 1.3 eV. a) What is the work function of potassium? Light of frequency 1.5 × 1015 Hz illuminates a piece of tin, and the tin emits photoelectrons with a maximum kinetic energy of 1.2 eV. What is the threshold frequency of the metal? Part 2 of 2 b) What is the threshold frequency for potassium? Holt SF 23Rev 17 40:04, highSchool, numeric, > 1 min, wordingvariable. Chapter 40, section 4, Light Quantization and the Photoelectric Effect Part 1 of 2 Light of wavelength 3.0 × 10−7 m shines on the metals lithium, iron, and mercury, which have work functions of 2.3 eV, 3.9 eV, and 4.5 eV, respectively. a) Which of these metals will exhibit the photoelectric effect? 1. Lithium 2. Iron 3. Mercury 4. Lithium and iron 5. Iron and mercury 6. None of these Part 2 of 2 b) For those metals that do exhibit the photoelectric effect, what is the maximum kinetic energy of the photoelectrons? 1. 5.2 eV and 2.4 eV 2. 1.84375 eV and 0.24375 eV 3. 10.1 eV 4. 7.4 eV, 5.0 eV and 2.1 eV 5. None of these Holt SF 23Rev 18 40:04, highSchool, numeric, < 1 min, wordingvariable. The threshold frequency of silver is 1.14 × 10 Hz. What is the work function of silver? 15 314 speeds ranging up to 460 km/s when light with a wavelength of λ = 625 nm is used. a) What is the work function of this surface? Part 2 of 2 b) What is the threshold frequency for this surface? Holt SF 23Rev 46 40:04, highSchool, numeric, < 1 min, wordingvariable. A light source of wavelength λ illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light 1 source of wavelength λ ejects photoelectrons 2 with a maximum kinetic energy of 4.00 eV. What is the work function of the metal? Holt SF 23Rev 47 40:04, highSchool, numeric, < 1 min, wordingvariable. Given: g = 9.81 m/s2 . A 0.50 kg mass falls from a height of 3.0 m. If all of the energy of this mass could be converted to visible light of wavelength 5.0 × 10−7 m, how many photons would be produced? Holt SF 23Rev 48 40:04, highSchool, numeric, > 1 min, wordingvariable. Red light (λ = 670.0 nm) produces photoelectrons from a certain material. Green light (λ = 520.0 nm) produces photoelectrons from the same material with 1.50 times the previous maximum kinetic energy. What is the material’s work function? Holt SF 23Rev 43 40:04, highSchool, numeric, < 1 min, normal. Holt SF 23Rev 52 40:04, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 Electrons are ejected from a surface with Ultraviolet light is incident normally on the surface of a substance that has a work func- Chapter 40, section 4, Light Quantization and the Photoelectric Effect tion of 3.44 eV. The incident light has an intensity of 0.055 W/m2 , and the electrons are photoelectrically emitted with a maximum speed of 5.2×105 m/s. Assuming that all of the photons are absorbed, how many electrons are emitted from a square centimeter of the surface every 1.0 s? Modern Physics 40:04, highSchool, multiple choice, < 1 min, fixed. Choose two topics below which were important in the development of quantum physics. a) photoelectric effect b) Bohr’s atomic model c) relativity d) Hall effect e) Maxwell equations 1. a and b 2. a and c 3. a and d 4. a and e 5. b and e 6. b and c 7. b and d 8. c and d 9. c and e 10. d and e 315 Chapter 40, section 5, The Compton Effect Concept 40 24 40:05, highSchool, multiple choice, < 1 min, fixed. When a photon hits an electron and gives it energy, what happens to the frequency of the photon after bouncing from the electron? 1. The frequency increases. 2. The frequency decreases. 3. The frequency remains the same. 4. It requires a case-by-case analysis. 316 Chapter 40, section 6, Particle-Wave Complementarity, Duality: Double Slits Concept 40 21 40:06, highSchool, multiple choice, < 1 min, fixed. Light has been argued as being a wave and then a particle, and back again. Which of the following is right? 1. Light’s true nature is as a particle. 2. Light’s true nature is as a wave. 3. Light’s true nature lies somewhere in between wave and particle models. 4. Light’s true nature is wave-particle duality. Concept 40 22 40:06, highSchool, multiple choice, < 1 min, fixed. What laboratory device utilizes the wave nature of electrons? 1. optical telescope 2. ammeter 3. electron microscope 4. thermometer Hewitt CP9 31 R11 40:06, highSchool, multiple choice, < 1 min, fixed. What evidence can you cite for the particle nature of light? 1. Photoelectric effect of light 2. Refraction phenomenon of light 3. Diffraction phenomenon of light 4. The many colors of light manifests the particle nature of light. 5. None of these 317 Chapter 40, section 7, Effect of Gravity on Light Concept 36 23 40:07, highSchool, multiple choice, < 1 min, fixed. Should it be possible in principle for a photon to circle a star? 1. Yes, if the star is massive enough to make light follow a circular path. 2. Yes, if the star rotates very fast to make light follow a circular path. 3. No; photons travel only in straight paths. 318 Chapter 41, section 1, The Atomic Nature of Matter 319 Concept 41 11 41:01, highSchool, multiple choice, < 1 min, fixed. Concept 41 28 41:01, highSchool, multiple choice, < 1 min, fixed. Is Brownian motion apparent for microscopic or macroscopic particles? Helium is an inert gas, meaning it doesn’t readily combine with other elements. Which of the following elements would you expect to also be an inert gas? 1. Brownian motion is apparent only for microscopic particles. 1. hydrogen 2. Brownian motion is apparent only for macroscopic particles. 3. Brownian motion is apparent both for microscopic and macroscopic particles. 2. carbon 3. nitrogen 4. oxygen 4. It depends on a case-by-case analysis. 5. neon Concept 41 12 41:01, highSchool, multiple choice, < 1 min, fixed. Are atoms visible with electron microscopes or optical microscopes? 1. only with electron microscopes 2. only with optical microscopes 3. with both electron and optical microscopes Concept 41 30 41:01, highSchool, multiple choice, < 1 min, fixed. Which of the following elements would you pedict to have properties most like those of silicon? 1. aluminum 2. phosphorus 3. germanium 4. with neither microscope 4. radium Concept 41 20 41:01, highSchool, multiple choice, < 1 min, fixed. A tree is composed mainly of carbon. Where does it get this carbon? 1. from sunshine 2. from soil 3. from water 4. from carbon dioxide in the air Concept 41 33 41:01, highSchool, multiple choice, < 1 min, fixed. The atoms that compose your body are mostly empty space, and structures such as the chair you’re sitting on are composed of atoms that are also mostly empty space. Why don’t you fall through the chair? 1. Macroscopic matter is too big to get through the microscopic empty space. Chapter 41, section 1, The Atomic Nature of Matter 2. The process of falling through the chair takes so long time that we can hardly observe it. 3. The protons are tightly bound. 320 2. liquid 3. equally strong 4. It requires a case-by-case analysis. 4. The electrical repulsion between atoms keeps us from falling through our chairs. Concept 41 45 41:01, highSchool, numeric, < 1 min, fixed. Concept 41 3 41:01, highSchool, multiple choice, < 1 min, fixed. Part 1 of 3 The diameter of an atom is about 1.0 × 10−10 meter. How many atoms make a line a millionth of a meter long? A cat strolls across your backyard. An hour later a dog with his nose to the ground follows the trail of the cat. Explain this occurrence from a molecular point of view. 1. The movement of the cat speed up the average speed of molecules of the air along its trail. The dog follows the trail by the variance of temperature. 2. The movement of the cat takes away some molecules and atoms of the grass along its trail, so the dog follows the trail by the density of the grass. 3. The cat leaves a trail of molecules and atoms on the grass. These in turn leave the grass and mix with the air, where they enter the dog’s nose, activating its sense of smell. 4. The cat leaves a trail of molecules and atoms on the grass, which changes the density of molecules of the grass. The dog follows the trail by the density of the grass. Part 2 of 3 How many atoms cover a square a millionth of a meter on a side? Part 3 of 3 How many atoms fill a cube a millionth of a meter on a side? Concept 41 6 41:01, highSchool, multiple choice, < 1 min, fixed. Which are older, the atoms in the body of an elderly person or those in the body of a baby? 1. an elderly person 2. a baby 3. of equal age 4. It requires a case-by-case analysis. Concept 41 35 41:01, highSchool, multiple choice, < 1 min, fixed. Concept 41 7 41:01, highSchool, multiple choice, < 1 min, fixed. If you have a solid and a liquid at room temperature, which has stronger interatomic forces? Where were the atoms that make up a newborn “manufactured”? 1. solid 1. in the mother’s body 2. explosions of ancient stars Chapter 41, section 1, The Atomic Nature of Matter 321 particles? 3. a chemical reaction 1. collisions among gas molecules 4. Unable to determine Concept 41 8 41:01, highSchool, multiple choice, < 1 min, fixed. A class of meteorites called chondrites contains a relative abundance of elements identical to the relative abundance observed in the sun (except for the volatile gases hydrogen and helium). What does this scientific finding suggest about the origin of the solar system? 1. The entire solar system probably had a common origin. 2. It took millions of years for most of the solar system to appear after the first particles appeared. 3. No conclusion can be drawn. 4. Attempting to correlate meteorite composition and the origin of the solar system is bad science. 2. collisions of gas molecules with the dust particles 3. collisions among dust particles Conceptual 21 Q03 41:01, highSchool, multiple choice, < 1 min, fixed. Rutherford’s experiment involved firing nucleus-sized bullets at atoms of gold. He found that one atom in 1000 bounced backward. How could the experiment have turned out if the atoms were completely uniform in mass? 1. If the atoms were uniform in mass, the ‘bullets’ would all have done the same thing. 2. If the atoms were not uniform then mostly may have gone through, coming out on the other side with much lower speed. 3. Both of these 4. None of these Conceptual 09 Q2 41:01, highSchool, multiple choice, < 1 min, fixed. A carbon atom and an iron atom are moving in the same speed. Which atom has more kinetic energy? 1. The carbon atom 2. The iron atom 3. They have the same kinetic energy. Conceptual 09 Q8 41:01, highSchool, multiple choice, < 1 min, fixed. What causes the Brownian motion of dust Conceptual 21 Q04 41:01, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Advertisers often describe improvements in their products as a “quantum leap.” Is this an appropriate use of the term? I) A quantum leap is a jump with no stops in between. II) A quantum leap is an appropriate analog if the product make a significant improvement. III) A quantum leap is not an appropriate analog if the product make a significant improvement. 1. I only Chapter 41, section 1, The Atomic Nature of Matter 2. II only 3. III only 4. I and II only 5. I and III only Part 2 of 2 How big is a quantum leap? 1. very small 2. very big 3. smaller than an atom 4. Cannot be determined 322 Chapter 41, section 2, The Composition of Atoms 323 2. adding one proton to each gold nucleus Concept 41 10 41:02, highSchool, multiple choice, < 1 min, fixed. 3. equally valuable 4. It requires a case-by-case analysis. Can two different elements contain the same number of protons or neutrons? 1. the same number of protons but not the same number of neutrons 2. the same number of neutrons but not the same number of protons 3. the same number of both neutrons and protons Concept 41 23 41:02, highSchool, multiple choice, < 1 min, fixed. If two protons and two neutrons are removed from the nucleus of an oxygen atom, what nucleus remains? 1. original oxygen 2. an isotope of oxygen 4. neither the same number of neutrons nor of protons Concept 41 16 41:02, highSchool, multiple choice, < 1 min, fixed. The atomic masses of two isotopes of cobalt are 59 and 60. How many protons, neutrons and orbiting electrons are in each when the isotopes are electrically neutral? 3. nitrogen 4. carbon Concept 41 24 41:02, highSchool, multiple choice, < 1 min, fixed. What element results if you add a pair of protons to the nucleus of mercury? 1. original mercury 1. Co-59: 32, 27, 59; Co-60: 33, 27, 60. 2. an isotope of mercury 2. Co-59: 27, 59, 59; Co-60: 27, 60, 60. 3. thallium 3. Co-59: 27, 59, 27; Co-69: 27, 60, 27. 4. lead 4. Co-59: 27, 32, 27; Co-60: 27, 33, 27. 5. platinum Concept 41 22 41:02, highSchool, multiple choice, < 1 min, fixed. Which would be the more valued result: taking one proton from each nucleus in a sample of gold or adding one proton to each gold nucleus? 1. taking one proton from each gold nucleus Concept 41 25 41:02, highSchool, multiple choice, < 1 min, fixed. What element results if two protons and two neutrons are ejected from a radium nucleus? 1. original radium Chapter 41, section 2, The Composition of Atoms 324 2. an isotope of radium 3. polonium 4. radon 5. thorium 6. uranium Carbon, with a half-full outer shell of electrons, readily shares its electrons with other atoms and forms a vast number of molecules, many of which are the organic molecules that form the backbone of living matter. Looking at the periodic table, which element might play a role like carbon in life forms on some other planet? Concept 41 26 41:02, highSchool, multiple choice, < 1 min, fixed. 1. hydrogen You could swallow a capsule of germanium without ill effect, but if a proton were added to each of the germanium nuclei, why would you not want to swallow the capsule? 3. oxygen 2. carbon 4. silicon 5. aluminum 1. Protons (the hydrogen atoms) are toxic to human body. 2. Germanium atoms, when combined with hydrogen atoms, are toxic to human body. 3. Arsenic atoms are toxic to human body. 4. Adding a proton creates a heavy metal, which is toxic. Concept 41 32 41:02, highSchool, multiple choice, < 1 min, fixed. Which contributes more to an atom’s mass: electrons or protons? Which contributes more to an atom’s size? 1. protons; electrons Concept 41 29 41:02, highSchool, multiple choice, < 1 min, fixed. 2. protons; protons What element results if one of the neutrons in a nitrogen nucleus is converted by radioactive decay into a proton? 4. electrons; electrons 1. original nitrogen 2. an isotope of nitrogen 3. carbon 3. electrons; protons Conceptual 21 Q05 41:02, highSchool, multiple choice, < 1 min, fixed. What can be said about the Rutherford model of an atom based on Newton’s laws of motion, the laws of thermodynamics, and the nature of electromagnetic radiation? 4. oxygen Concept 41 31 41:02, highSchool, multiple choice, < 1 min, fixed. 1. The electrons are accelerating, so they would be giving off energy. 2. Continuous source of energy must be sup- Chapter 41, section 2, The Composition of Atoms 325 plied to the atom. 3. Rutherford model of the atom could not work 4. All of these 5. None of these Hewitt CP9 32 E03 41:02, highSchool, numeric, > 1 min, fixed. How does Rutherford’s model of the atom account for the back-scattering of alpha particles directed at the gold leaf? 1. A gold nucleus is positively charged and so is an alpha particle. 2. The nucleus is heavy and so is an alpha particle. 3. There is a dense concentration of positive charge and mass in the nucleus. 4. Negative charge of an electron is spread throughout the volume of the atom. Hewitt CP9 32 E04 41:02, highSchool, multiple choice, > 1 min, fixed. At the time of Rutherford’s gold leaf experiment, scientists knew that negatively charged electrons existed within the atom, but they did not know where the positive charge resided. What information about the positive charge was provided by Rutherford’s experiment? 1. The positive charge can freely move within the atom. 2. The positive charge must be concentrated in a small core (the atomic nucleus). 3. The positive charge is spread throughout the atom. 4. There is no positive charge associated with an atom. Chapter 41, section 3, Molecules Concept 11 01 41:03, highSchool, multiple choice, < 1 min, fixed. How many individual atoms are in a water molecule? 326 41:03, highSchool, multiple choice, < 1 min, fixed. If no molecules in a body could escape, would the body have any odor? 1. Yes; the odor is composed of waves radiated by the body. 1. three: one hydrogen and two oxygen 2. two: both hydrogen 2. Yes; odor has nothing to do with molecules. 3. three: one oxygen and two carbon 3. Yes, but the odor would be different. 4. three: one oxygen and two hydrogen 4. No 5. two: one oxygen and one hydrogen 6. It depends on the state of the water molecule. Concept 11 02 41:03, highSchool, multiple choice, < 1 min, fixed. When a container of gas is heated, what happens to the average speed of its molecules? Concept 41 15 41:03, highSchool, multiple choice, < 1 min, fixed. How many atoms are in a molecule of ethanol? 1. six 2. three 3. two 1. decreases 4. nine 2. increases 5. ten 3. No change 4. It cannot be determined without a direct measurement. Concept 11 41 41:03, highSchool, multiple choice, < 1 min, normal. During a certain thermodynamic process a sample of gas expands and cools, reducing its internal energy by 3000 J, while no heat is added or taken away. How much work is done during this process? Concept 11 4 Concept 41 19 41:03, highSchool, multiple choice, < 1 min, fixed. Gasoline contains only hydrogen and carbon atoms. Yet nitrogen oxide and nitrogen dioxide are produced when gasoline burns. What is the source of the nitrogen atoms? 1. created from the hydrogen atoms of gasoline by burning 2. created from the carbon atoms of gasoline by burning 3. created from the interaction of the carbon Chapter 41, section 3, Molecules 327 and hydrogen atoms of gasoline by burning 4. the air Concept 41 27 41:03, highSchool, multiple choice, < 1 min, fixed. What results when water is chemically decomposed? 1. vapor 2. mixture of water and vapor Concept 41 43 41:03, highSchool, numeric, < 1 min, normal. Gas A is composed of diatomic molecules of a pure element. Gas B is composed of monatomic molecules of another pure element. Gas A has 3 times the mass of an equal volume of gas B at the same temperature and pressure. How do the atomic masses of elements A and B compare? Concept 41 44 41:03, highSchool, numeric, < 1 min, fixed. 3. hydrogen and oxygen 4. It requires a case-by-case analysis. Concept 41 34 41:03, highSchool, multiple choice, < 1 min, fixed. 50 cubic centimeters of alcohol are mixed with 50 cubic centimeters of water. Why is the volume of the mixture is only 98 cubic centimeters? 1. Some alcohol evaporates. 2. The process of mixing releases heat. 3. Some water vaporizes. 4. The water and alcohol molecules fit into one another. Concept 41 41 41:03, highSchool, numeric, < 1 min, normal. How many grams of oxygen are in 18 g of water? Concept 41 42 41:03, highSchool, numeric, < 1 min, normal. How many grams of hydrogen are in 16 g of methane gas which has a chemical formula of CH4 ? A teaspoon of an organic oil dropped on the surface of a quiet pond spreads out to cover almost an acre. The oil film has a thickness equal to the size of a molecule. In the lab when you drop 0.001 milliliter of the organic oil on the still surface of water, you find that it spreads to cover an area of 1.0 square meter. If the layer is one molecule thick, what is the size of a single molecule? Concept 41 46 41:03, highSchool, numeric, < 1 min, fixed. There are approximately 1 × 1023 water molecules in a thimbleful of water and 1 × 1046 water molecules in the Earth’s oceans. Suppose that Columbus threw a thimbleful of water into the ocean and that these water molecules have by now mixed uniformly with all the water molecules in the oceans. If you dip a sample thimbleful of water from anywhere in the ocean, how many of the molecules from Columbus’s thimble are you likely to scoop up? Concept 41 47 41:03, highSchool, numeric, < 1 min, fixed. Part 1 of 2 There are approximately 1 × 1022 molecules in a single medium-sized breath of air and approximately 1 × 1044 molecules in the atmosphere of the whole world. Chapter 41, section 3, Molecules How many breaths of air are in the world’s atmosphere? 328 massive? 1. The C60 atom Part 2 of 2 If all the molecules from Julius Caesar’s last dying breath are now thoroughly mixed in the atmosphere, how many of these on the average do we inhale with each single breath? Concept 41 48 41:03, highSchool, numeric, < 1 min, fixed. Assume that the present world population of about 6 × 109 people is about 1/20 the number of people who ever lived on Earth. How does the number of people who ever lived compare to 1 × 1022 , the number of air molecules in a single breath? Concept 41 5 41:03, highSchool, multiple choice, < 1 min, fixed. The average speed of a perfume vapor molecule at room temperature may be about 300 m/s, but the speed at which the scent travels across the room is much less. Why? 1. Vapor molecules travel slower than air molecules. 2. Vapors move randomly. 3. There are many collisions with other molecules in the air. 4. Scent will actually travel across a room at almost 300 m/s. Conceptual 09 Q3 41:03, highSchool, numeric, > 1 min, fixed. Fullerenes are large molecules of carbon containing at least 60 carbon atoms. Discovered in 1985, fullerenes take a roughly spherical shape, with the carbon atoms arranged in such a way to make them look like soccer balls. Is a C60 molecule or a single gold atom more 2. The gold atom 3. A C60 atom is as massive as a gold atom. Chapter 41, section 4, The Bohr Atom Concept 30 06 41:04, highSchool, multiple choice, < 1 min, fixed. Why doesn’t a neon sign finally “run out” of excited atoms and produce dimmer and dimmer light? 1. There are numerous excited atoms in a neon sign; it takes a very long time for them to be exhausted. 2. Exhausted atoms will be re-excited by the energy source and emit light again. 3. The brightness of light is not determined by the number of excited atoms but by the energy difference between the excited atoms and the unexcited atoms. 329 2. six; level 4 to level 1 transition; level 4 to level 3 transition. 3. three; level 4 to level 1 transition; level 4 to level 3 transition. 4. three; level 2 to level 1 transition; level 4 to level 3 transition. Part 2 of 3 An electron de-excites from the fourth quantum level to the third and then directly to the ground state. Two photons are emitted. How does the sum of their frequencies compare to the frequency of the single photon that would be emitted by de-excitation from the fourth level directly to the ground state? 1. The sum is larger than the frequency of the single photon. 4. None of these Concept 30 43 41:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 3 Consider just four of the energy levels in a certain atom, as shown in the diagram below. n=4 n=3 1. The sum is equal to the frequency of the single photon. 1. The sum is smaller than the frequency of the single photon. 4. None of these Part 3 of 3 Suppose the four energy levels were somehow evenly spaced. How many spectral lines would result? n=2 1. six 2. four n=1 3. five How many spectral lines will result from all possible transitions among these levels? Which transition corresponds to the highestfrequency light emitted? Which transition corresponds to the lowest-frequency? 4. three Concept 41 4 41:04, highSchool, multiple choice, < 1 min, fixed. 1. three; level 4 to level 3 transition; level 2 to level 1 transition. If no molecules in a body could escape, would the body have any odor? Chapter 41, section 4, The Bohr Atom 1. Yes; odor has nothing with molecules that could escape from the body itself. 4. 2.90933 × 1016 Hz 2. Yes; bodies change the property of the molecules around them differently. We can detect the odor of a body when the changed molecules enter our noses. 330 6. 2.03653 × 1015 Hz 3. No; a body has odor only if some of its molecules enter a nose. 4. It requires a case-by-case analysis. Conceptual 21 Q06 41:04, highSchool, multiple choice, < 1 min, fixed. When you shine invisible ultraviolet light (black light) on certain objects, they glow with brilliant colors. Explain this behavior in terms of the Bohr atom. 1. UV light excites an electron in the atom to a higher energy level. 5. 7.27334 × 1015 Hz 7. 3.63667 × 1014 Hz 8. 3.63667 × 1016 Hz 9. 9.09167 × 1015 Hz 10. 2.54567 × 1015 Hz Hewitt CP9 32 E06 41:04, highSchool, multiple choice, < 1 min, fixed. Why does classical physics predict that atoms should collapse? 1. Classical physics was not based on experiments. 2. Classical physics predicts the future of the atomic world. 2. When electron moves down to a lower energy level it stops at several intermediate levels. 3. Classically an electron is attracted to a nucleus and eventually should fall on it. 3. A photon of visible light is emitted for each jump to the lower level. 4. Classically an electron accelerating around its orbit should emit radiation. 4. All of these 5. None of these Frequency of a Lyman line 41:04, highSchool, numeric, > 1 min, fixed. Determine the frequency of the second Lyman line, the transition from n = 3 to n = 1. 1. 2.90933 × 1015 Hz 2. 3.63667 × 1015 Hz 3. 2.90933 × 1014 Hz Hewitt CP9 32 E07 41:04, highSchool, multiple choice, < 1 min, fixed. If an electron in a hydrogen atom obeyed classical mechanics instead of quantum mechanics, what kind of spectrum would it emit? 1. line spectrum 2. partially line and partially continuous spectrum 3. continuous spectrum Chapter 41, section 4, The Bohr Atom 4. It wouldn’t emit any spectrum. Hewitt CP9 32 E10 41:04, highSchool, multiple choice, < 1 min, fixed. How can elements with low atomic numbers have so many spectral lines? 1. Electrons can be boosted to many energy levels, thus making many different transitions to ground level and levels between. 2. Elements with low atomic numbers have small masses. 3. Elements with low atomic numbers have many free electrons. 4. Elements with low atomic numbers usually don’t react chemically with other elements. 331 Chapter 42, section 1, de Broglie Waves 332 fixed. Concept 40 25 42:01, highSchool, multiple choice, < 1 min, fixed. If a proton and an electron have identical speed, which has the longer wavelength? We don’t notice the wavelength of moving matter in our ordinary experience. Which of the following is right? 1. The wavelength is extraordinarily large. 1. the proton 2. The wavelength is extraordinarily small. 2. the electron 3. The wavelength could be either extraordinarily large or small. 3. They have the same wavelength. 4. The wavelength is ordinary. 4. More information is needed. Concept 40 26 42:01, highSchool, multiple choice, < 1 min, fixed. One electron travels twice as fast as another. Which has longer wavelength? Concept 40 29 42:01, highSchool, multiple choice, < 1 min, fixed. If a cannonball and a BB have the same speed, which has the longer wavelength? 1. The cannonball 1. The faster one 2. The BB 2. The slower one 3. The two have the same wavelength. 3. The two have the same wavelength. 4. More information is needed. 4. More information is needed. Concept 40 27 42:01, highSchool, multiple choice, < 1 min, fixed. What happens to the de Broglie wavelength of a proton as its velocity increases? 1. Increases 2. Decreases 3. Remains the same 4. More information is needed. Concept 40 28 42:01, highSchool, multiple choice, < 1 min, Concept 40 42 42:01, highSchool, numeric, < 1 min, normal. What is the de Broglie wavelength of an electron that strikes the back of the face of a 1 TV screen at the speed of light? 10 Concept 40 43 42:01, highSchool, numeric, < 1 min, fixed. You decide to roll a 0.1 kg ball across the floor so slowly that it will have a small momentum and a large de Broglie wavelength. If you roll it at 0.001 m/s, what will its wavelength be? Conceptual 22 Q09 42:01, highSchool, multiple choice, < 1 min, fixed. Chapter 42, section 1, de Broglie Waves A hydrogen atom and a uranium atom are moving at the same speed. Which one has the longer wavelength? 1. hydrogen 2. uranium 333 42:01, highSchool, numeric, < 1 min, wordingvariable. If the de Broglie wavelength of an electron is equal to 5.00 × 10−7 m, how fast is the electron moving? The mass of an electron is 9.10939 × −31 10 kg and Planck’s constant is 6.63×10−34 J/s. 3. same for both Conceptual 22 Q10 42:01, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 An electron and a proton are traveling at the same speed. Which one has more momentum? Holt SF 23C 03 42:01, highSchool, numeric, < 1 min, wordingvariable. How fast would one have to throw a 0.15 kg baseball if it were to have a wavelength equal to 5.00 × 10−7 m? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23C 04 42:01, highSchool, numeric, < 1 min, wordingvariable. 1. Electron 2. Proton Part 2 of 2 Which one has a longer wavelength? 1. Electron What is the de Broglie wavelength of a 1375 kg car traveling at 43 km/h? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23C 05 42:01, highSchool, numeric, < 1 min, wordingvariable. 2. Proton Hewitt CP9 31 P02 42:01, highSchool, numeric, > 1 min, fixed. What is the de Brogile wavelength of an electron that strikes the back of the face of a TV screen at 0.1 the speed of light? The speed of light is 2.998 × 108 m/s. Holt SF 23C 01 42:01, highSchool, numeric, < 1 min, wordingvariable. With what speed would a 50.0 g rock have to be thrown if it were to have a wavelength of 3.32 × 10−34 m? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23C 02 A bacterium moving across a petri dish at 3.5 µm/s has a de Broglie wavelength of 1.9 × 10−13 m. Planck’s constant is 6.63 × 10−34 J · s. What is the bacterium’s mass? Holt SF 23Rev 39 42:01, highSchool, numeric, < 1 min, normal. How fast must an electron move if it is to have a de Broglie wavelength of 5.2 × 10−11 m? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23Rev 40 42:01, highSchool, numeric, < 1 min, normal. Calculate the de Broglie wavelength of 0.15 kg baseball moving at 45 m/s? Chapter 42, section 1, de Broglie Waves Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23Rev 41 42:01, highSchool, numeric, < 1 min, wordingvariable. What is the speed of a proton with a de Broglie wavelength of 4.00 × 10−14 m? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23Rev 42 42:01, highSchool, numeric, < 1 min, normal. A mosquito moving at 12 m/s has a de Broglie wavelength of 5.5 × 10−30 m. Planck’s constant is 6.63 × 10−34 J · s. What is the mass of this mosquito? Holt SF 23Rev 44 42:01, highSchool, numeric, < 1 min, wordingvariable. What is the de Broglie wavelength of a proton traveling at 1.0 × 107 m/s? Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23Rev 49 42:01, highSchool, numeric, < 1 min, wordingvariable. Find the de Broglie wavelength of a ball with a mass of 0.200 kg just before it strikes the Earth after it has been dropped from a building 50.0 m tall. Planck’s constant is 6.63 × 10−34 J · s. Holt SF 23Rev 53 42:01, highSchool, numeric, > 1 min, fixed. Part 1 of 2 The wave nature of electrons makes an electron microscope, which uses electrons rather than light, possible. The resolving power of any microscope is approximately equal to the wavelength used. A resolution of approximately 1.0 × 10−11 m would be required in order to ”see” an atom. Planck’s constant is 6.63 × 10−34 J · s. a) If electrons were used, what minimum ki- 334 netic energy of the electrons (in eV) would be required to obtain this degree of resolution? Part 2 of 2 b) If photons were used, what minimum photon energy would be required? Chapter 42, section 5, The Heisenberg Uncertainty Principle Uncert in Posit for Giancoli 42:05, highSchool, numeric, < 1 min, normal. This problem is for PHY302L only, using Giancoli’s book. A 50 g ball moves at 30 m/s. If its speed is measured to an accuracy of 0.1%, what is the minimum uncertainty in its position? Uncert of Momentum for Giancoli 42:05, highSchool, numeric, < 1 min, normal. This problem is for PHY302L only, using Giancoli’s book. Assume we can localize a particle to an uncertainty of 0.5 nm. What will be the resulting minimum uncertainty in the particle’s momentum? 335 Chapter 43, section 14, Observables and Operators 1. No Conceptual 22 Q02 43:14, highSchool, multiple choice, < 1 min, wording-variable. Wave Function Your friend, John and Jean, are both driving from Chicago to Des Moines. You know that Jean is on the road, and you know when she left Chicago. On the other hand, you know that John is on the road, but you have no idea when he left. 2 1 Chicago Des Moines Which one is for John ? 1. 2 2. 1 Conceptual 22 Q06 43:14, highSchool, multiple choice, < 1 min, fixed. Chaotic systems are, for all practical purposes, unpredictable. How does this sort of unpredictability differ from that associated with quantum mechanics? 1. Classical chaotic systems are deterministic; quantum systems are not deterministic. 2. Quantum systems are deterministic; classical chaotic systems are not deterministic. Conceptual 22 Q07 43:14, highSchool, multiple choice, < 1 min, fixed. If you threw baseballs through a large twoslit apparatus, would you produce a diffraction pattern? 2. Yes 336 Chapter 45, section 2, Particle in a Three-Dimensional Box Angular Momentum 26 45:02, highSchool, numeric, < 1 min, fixed. What are the total angular momentum values that are obtained in the addition of l = 2 and s = 1/2 ? 5 1. , 2 7 2. , 2 5 3. , 2 3 4. , 2 3 2 5 2 31 , 22 1 2 Angular Momentum 26b 45:02, highSchool, numeric, < 1 min, fixed. What are the total angular momentum values that are obtained in the addition of l = 1 and s = 3/2 ? 7 1. , 2 7 2. , 2 5 3. , 2 3 4. , 2 5 , 2 5 2 3 , 2 1 2 3 2 1 2 Angular Momentum 26c 45:02, highSchool, multiple choice, < 1 min, fixed. What are the total angular momentum values that are obtained in the addition of l = 1/2 and s = 1/2 ? 5 1. , 2 3 2. , 2 1 3. , 2 3 2 1 2 0 4. 1, 0 337 Chapter 45, section 4, Space Quantization Angular Momentum 27 45:04, highSchool, numeric, < 1 min, fixed. What angular-momentum states result when angular momentum l1 = 3 is added to angular momentum l2 = 2? Check that the degeneracies 2l + 1 for these states add up to the total number of states (2 l1 + 1) (2 l2 + 1). Angular Momentum 31 45:04, highSchool, numeric, < 1 min, normal. The magnetic moment associated with the orbital motion of an atomic electron has magnitude 3.20933 × 10−23 C · m2 /sA m2 . What is the angular-momentum quantum number of the electron orbit? 338 Chapter 46, section 2, Atomic Spectra 339 of the planets. Conceptual 21 05 46:02, highSchool, multiple choice, < 1 min, fixed. If a one-electron atom can occupy any of four different energy levels, how many lines might appear in that atom’s spectrum? 1. six 2. By analyzing the spectrum of the atmosphere of the planets. 3. By analyzing the atoms that composed the planets. 4. By analyzing the molecules that compose the planets. 2. four 5. All of these 3. five 6. None of these 4. seven 5. None of these Conceptual 21 Q08 46:02, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Space probes often carry compact spectrometers among their scientific hardware. What kind of spectroscopy might scientists use to determine the surface composition of the cold, outer planets that orbit the Sun? Conceptual 21 Q09 46:02, highSchool, multiple choice, < 1 min, fixed. Suppose a particular atom has only two allowable electron orbits. How many different wavelength photons (spectral lines) would result from all electron transitions in this atom? 1. one 2. two 3. three 1. Each atom of molecule gives off a set of photons when it is excited. 2. Excited photons changes chemical property. 3. The photons emit light energy when they change the energy levels. 4. All of these 5. None of these Part 2 of 2 How might they use spectroscopy to determine the atmospheric composition of these planets? 1. By analyzing the spectrum of the surface 4. four 5. None of these Conceptual 21 Q15 46:02, highSchool, multiple choice, < 1 min, fixed. In his famous experiment, Rutherford fired alpha particles at a thin gold film. Most of the alpha particles went through the firm and a very few bounced back. Suppose instead that about one-half the alpha particles bounced back and one-half went through. How would this have changed his conclusion about the structure of the atom? 1. Atom is mostly empty space. Chapter 46, section 2, Atomic Spectra 340 2. The laser produce beam of light. 2. Nucleus is about 1/2 the size of the atom. 3. Both of these 3. The atom has no nucleus. 4. More information is needed. 4. The nucleus covers the entire atom. 5. None of these 5. None of these Conceptual 21 Q16 46:02, highSchool, multiple choice, < 1 min, fixed. In the process of fluorescence, an atom absorbs a photon of ultraviolet light and emits two or more photons of visible light. Is the reverse process possible? (That is, is it possible for an atom to absorb a photon of visible light and emit photons of ultraviolet light?) 1. Yes; ultraviolet photons have less energy than visible light. 2. No; ultraviolet photons have more energy than the visible light. 3. Yes; the energy is equal; 4. More information is needed. 5. None of these Conceptual 21 Q17 46:02, highSchool, multiple choice, < 1 min, fixed. A 100-watt bulb becomes warm and glows brightly enough to light a small room. On the other hand, a 100-watt laser can cut holes in steel and would not be effective at lighting a small room. What is true about the light coming from these two sources that accounts for these differences? 1. The light bulb illuminate a room. Hewitt CP9 32 R08 46:02, highSchool, multiple choice, < 1 min, fixed. What is true about the light emitted by an atom? 1. The emitted photon’s frequency is the classic frequency at which an electron vibrates. 2. An electron accelerating around its orbit continuously emits radiation. 3. The energy of the emitted photon is equal to the difference in energy between the two orbits. 4. None of these Chapter 46, section 5, The Spin-Orbit Interaction and Other Magnetic Effects Complex Atoms and Molecules 1 46:05, highSchool, multiple choice, < 1 min, fixed. Write the configuration for the ground state of the magnesium atom(Z = 12). If the closed shells always have Ltot = Stot = 0, what is the total angular momentum of magnesium? 1. 1s2 2s2 2p6 3s2 , Jtot = 1/2 2. 1s2 2s2 2p5 3s3 , Jtot = 1 3. 1s2 2s2 2p5 3s3 , Jtot = 1/2 4. 1s2 2s2 2p6 3s2 , Jtot = 0 Complex Atoms and Molecules 2 46:05, highSchool, multiple choice, < 1 min, fixed. Consider the ground state of the silicon atom (Z = 14). What is the electronic configuration for this state? 1. 1s2 2s2 2p6 3s2 3p2 2. 1s2 2s2 2p6 3s3 3p1 1 2 3 4. = 2, s = 2 3. = 1, s = Part 2 of 2 What are the possible values of the total angular momentum J ? Given the fact that there is a spin-orbit interaction, predict which of the J values has a lower energy. (Hint: Use what you learned about the spin-orbit coupling in hydrogen.) 3 3 5 1. , 2, , Jlowest = 2 2 2 5 3 5 2. , 2, , Jlowest = 2 2 2 5 3. 3, , 2, Jlowest = 2 2 31 4. 2, , , Jlowest = 24 22 Complex Atoms and Molecules 4 46:05, highSchool, multiple choice, < 1 min, fixed. The last (most energetic) electron in sodium is in a 3s state. What do you expect the order of the energies to be for the last electrons in the three possible states 3s, 3p, and 3d? 3. 1s2 2s2 2p6 3s1 3p3 1. 3d > 3p > 3s 4. 1s3 2s3 3p2 3s3 3p3 2. 3d > 3s > 3p Complex Atoms and Molecules 3 46:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 What are the orbital angular momentum and spin of the ground state of scandium (Z = 21)? 1 2 3 2. = 1, s = 2 1. = 2, s = 341 3. 3p > 3s > 3d 4. 3s > 3p > 3d 5. 3s = 3p = 3d Chapter 46, section 10, Exchange Symmetry and the Exclusion Principle Conceptual 24 Q14 46:10, highSchool, multiple choice, < 1 min, fixed. The Pauli exclusion priciple says that no two electrons can occupy the same energy state unless their spin point in opposite directions. In reference to this principle what happens if the atoms have an even number of electrons. 1. have small Curie constants; magnetic field of the spins cancel out 2. have large Curie constants; magnetic field of spins add up with each other 3. None of these 342 Chapter 46, section 13, The Periodic Table Conceptual 21 01 46:13, highSchool, multiple choice, < 1 min, wording-variable. How many protons does hydrogen (H) have? 1. 1 343 5. 36 Conceptual 21 04 46:13, highSchool, multiple choice, < 1 min, wording-variable. How many protons does +1 of sodium (Na) have? 2. 20 1. 11 3. 6 2. 35 4. 53 3. 82 5. 16 4. 26 Conceptual 21 02 46:13, highSchool, multiple choice, < 1 min, wording-variable. How many electrons does hydrogen (H) have? 1. 1 2. 6 5. 20 Conceptual 21 06 46:13, highSchool, multiple choice, < 1 min, fixed. If you were told that fluorine is an extremely reactive element (that is, it combines readily with other elements), what other element(s) would be extremely reactive? 3. 53 1. All elements in the same column 4. 20 2. All elements on the same row 5. 16 3. All elements after fluorine Conceptual 21 03 46:13, highSchool, multiple choice, < 1 min, wording-variable. How many electrons does +1 of sodium (Na) have? 4. All elements before fluorine 5. None of these Conceptual 21 07 46:13, highSchool, multiple choice, < 1 min, fixed. 1. 10 2. 18 If you were told that argon (Ar) is an exceptionally unreactive element, what other elements would also be extremely unreactive? 3. 23 1. All elements in the same column 4. 78 Chapter 46, section 13, The Periodic Table 2. All elements on the same row 344 46:13, highSchool, multiple choice, < 1 min, fixed. 3. All elements after argon 4. All elements before argon Why do two hydrogen (H) atoms combine with one oxygen (O) atom to form water (H2 O)? 5. None of these Conceptual 21 Q18 46:13, highSchool, multiple choice, < 1 min, fixed. Silicon (Si) and nitrogen (N) are adjacent to carbon (C) on the periodic table. Si and C have many similar chemical properties but C and N do not. What does NOT account for the difference? 1. Carbon and silicon are in the same column of the periodic table. 2. Carbon and silicon have same number of electrons in their outer shells. 3. Carbon and Nitrogen are in the same group 4. None of these 1. Two hydrogen donates its electron to oxygen. 2. Two hydrogen share its electrons with one oxygen. 3. None of these Conceptual 26 Q03 46:13, highSchool, multiple choice, < 1 min, fixed. An atom has six neutrons, six protons, and six electrons. Which element or ion is it? 1. Ca2+ 2. C 3. Li Conceptual 21 Q19 46:13, highSchool, multiple choice, < 1 min, fixed. 4. N Why is sodium chloride (NaCl) such a stable compound? 6. Mg2+ 5. Na+ 7. O2− 1. Sodium donates its electrons to chlorine. 8. None of these 2. Sodium donates the electron in it’s outer most shell to chlorine. 3. Sodium and chlorine share the electrons. Conceptual 26 Q04 46:13, highSchool, multiple choice, < 1 min, fixed. 4. Sodium and chlorine are volatile until they form the compound. An atom has 143 neutrons, 92 protons, and 91 electrons. What element is it? 5. None of these Conceptual 21 Q20 1. Pa 2. Th Chapter 46, section 13, The Periodic Table 3. Pu 345 Since most known isotopes are unstable, how could this state of affairs have arisen? 4. U 1. The unstable nuclei decayed long ago. 5. Cm 2. Very few atoms decay. 6. None of these Conceptual 26 Q05 46:13, highSchool, multiple choice, < 1 min, fixed. We know that the strong force acts very short distances. Suppose the range of the strong force were twice what it is now. (In other words, it would attract the same particles with the same force as now, even though they were twice as far away.) What will happen to the half-life of Uranium-238? 1. decrease 2. increase 3. Unstable nuclei exist for only a small period of time. Hewitt CP9 32 E05 46:13, highSchool, multiple choice, > 1 min, fixed. Uranium is 238 times more massive than hydrogen. Why, then, isn’t the diameter of the uranium atom 238 times that of the hydrogen atom? 1. Uranium has 92 times as much positive charge as hydrogen; this greater charge pulls the surrounding electrons into tighter orbits. 2. There are very strong forces between nuclei in the uranium atom. 3. no change Conceptual 26 Q06 46:13, highSchool, multiple choice, < 1 min, fixed. Why does radioactivity seem to be more common with heavier elements? 1. They have more number of electrons. 3. There are very few electrons in the uranium atom. 4. Most of the atom’s mass is localized in the nucleus and most of the volume is defined by electrons’ orbits. Hewitt CP9 32 E12 46:13, highSchool, multiple choice, < 1 min, fixed. 2. They have more number of protons. 3. They have less number of electrons. Why do atoms that have the same number of electron shells decrease in size with increasing atomic number? 4. They have less number of protons. Conceptual 26 Q07 46:13, highSchool, multiple choice, < 1 min, fixed. Almost all of the atoms with which we come into daily contact have stable nuclei. 1. The greater the atomic number, the fewer electrons the atom can have. 2. The electron shells are pulled in more tightly because of the larger number of protons in the nucleus. Chapter 46, section 13, The Periodic Table 3. Atoms decrease in size with increasing atomic number in order to release energy. 4. Elements with great atomic numbers usually don’t react chemically with other elements. 346 Chapter 46, section 17, Lasers and Holography Conceptual 21 Q07 46:17, highSchool, multiple choice, < 1 min, fixed. Different lasers have beams with different colors. Which of these is NOT true? 1. Different lasers use different materials. 2. Different materials have different energy levels for the electrons. 3. Different energy photons emitted by electron transition between levels. 4. Differnet lasers have different electromagnetic radiation for different materials. 5. None of these 347 Chapter 47, section 4, An Application of Fermi-Dirac Statistics: Many Particles 12 47:04, highSchool, numeric, < 1 min, fixed. Calculate the Fermi energy for potassium, for which the free-electron density is 1.4 × 1028 electrons/m3 . Many Particles 13 47:04, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Calculate the Fermi energy for Cu, for which A = 63.5, ρ = 8950 kg/m3 and approximately one electron per atom is free. Part 2 of 2 Repeat the calculation for lead, for which A = 207.2, ρ = 11400 kg/m3 . Assume in the case of lead that there are two free electrons per atom. 348 Chapter 48, section 1, Bonding Mechanisms Conceptual 09 Q4 48:01, highSchool, multiple choice, < 1 min, fixed. Consider techniques used to separate compounds and mixtures into components. Which statement is false? 1. In a compound, molecules must be broken apart to separate components. 2. In a mixture, components can be separated without destroying molecules. 3. Molecular structures are maintained when separating compounds or mixtures into components. Conceptual 26 Q02 48:01, highSchool, multiple choice, < 1 min, fixed. Reacting hydrogen and oxygen atoms together produces water H2 O. What would result from the fusion of two hydrogen nuclei with an oxygen nucleus? 1. Oxygen 2. Hydrogen 3. Neon 4. Sodium 5. Magnesium 6. None of these 349 Chapter 48, section 99, Associated problems in Chapter 48 350 2. metallic bonds Conceptual 23 01 48:99, highSchool, multiple choice, < 1 min, wording-variable. 3. covalent bonds 4. Either Part 1 of 2 Some elements readily form ionic or covalent bonds and some elements do not participate in chemical bonding at all. Which element has an atomic number of 6? Conceptual 23 Q03 48:99, highSchool, multiple choice, < 1 min, fixed. What type of chemical bonds is the most prevalent in biological molecules? 1. carbon 2. nitrogen 1. ionic bonds 3. hydrogen 2. metallic bonds Part 2 of 2 Is this element likely to participate in chemical bonding? Why? 1. Yes; it has an incomplete valance shell. 2. No; it has a full outer shell. Conceptual 23 Q01 48:99, highSchool, multiple choice, < 1 min, fixed. 3. covalent bonds 4. Either Conceptual 23 Q04 48:99, highSchool, multiple choice, < 1 min, fixed. Which of the following materials is your last choice to build a house? 1. ionic-bonded materials Which is a better choice to fill a balloonlike airship, hydrogen or helium? 1. Hydrogen; it is ligheter than helium. 2. metallic-bonded materials 3. covalent-bonded materials 2. Hydrogen; it is cheaper than helium. 4. materials held together by van der Waals forces 3. Helium; hydrogen is very reactive. Conceptual 23 Q05 48:99, highSchool, multiple choice, < 1 min, fixed. 4. Helium; it smells good. Conceptual 23 Q02 48:99, highSchool, multiple choice, < 1 min, fixed. What types strongest? of chemical bonds the What is the relationship between the properties of a newly formed chemical compound and the properties of the individual elements that compose it? 1. Their properties can be very different. 1. ionic bonds 2. Their properties are similar. Chapter 48, section 99, Associated problems in Chapter 48 351 1. MgCl 3. Their physical properties are similar. 2. MgCl2 4. Their chemical properties are similar. 3. Mg2 Cl Conceptual 23 Q06 48:99, highSchool, multiple choice, < 1 min, fixed. Diamonds and graphite are both made from carbon atoms. Why is graphite so much weaker? 1. Graphite is held together only by van der Waals forces. 2. Graphite is held together only by ionic bonds. 4. Mg2 Cl2 Conceptual 23 Q10 48:99, highSchool, multiple choice, < 1 min, fixed. What is the chemical formula for the covalent compound carbon chloride (carbon and chlorine)? 1. CCl 2. CCl2 3. Graphite is only covalently bonded in certain planes of atoms. Parallel planes are bonded together with weak van der Waals forces. 4. Diamonds are metallic-bonded while graphite is covalent-bonded. Conceptual 23 Q07 48:99, highSchool, multiple choice, < 1 min, fixed. What type of chemical bond does NaF (sodium fluoride) form? 3. CCl3 4. CCl4 Conceptual 23 Q11 48:99, highSchool, multiple choice, < 1 min, fixed. What is the chemical formula for the ionic compound magnesium oxide (magnesium and oxygen)? 1. MgO 1. ionic bond 2. MgO2 2. metallic bond 3. Mg2 O 3. covalent bond 4. MgO4 4. None of these Conceptual 23 Q08 48:99, highSchool, multiple choice, < 1 min, fixed. What is the chemical formula for the compound formed by magnesium and chlorine ? Conceptual 23 Q12 48:99, highSchool, multiple choice, < 1 min, fixed. Potassium iodide can be used as a thyroidblocking agent in the event of a radiation emergency. What is the chemical formula for the ionic compound potassium iodide (potassium and Chapter 48, section 99, Associated problems in Chapter 48 352 iodine)? 2. AlCl2 1. KI 3. AlCl3 2. KI2 4. Al2 Cl3 3. K2 I 5. Al2 Cl 4. KI4 Conceptual 23 Q13 48:99, highSchool, multiple choice, < 1 min, fixed. Part 2 of 2 Which element becomes the positive ion in this compound? 1. Al Part 1 of 2 Magnesium (Mg) and bromine (Br) form an ionic compound. What is its chemical formula? 1. MgBr 2. BrMg 3. MgBr2 2. Cl Conceptual 23 Q16 48:99, highSchool, multiple choice, < 1 min, fixed. Chlorine and argon appear in adjacent spots on the periodic table. Which one is more reactive, chlorine or argon? Why? 4. Mg2 Br 5. Br2 Mg 6. BrMg2 Part 2 of 2 Which element becomes the positive ion in this compound? 1. Mg 2. Br Conceptual 23 Q15 48:99, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Aluminum (Al) and chlorine (Cl) combine to form an ionic compound. What is its chemical formula? 1. AlCl 1. Argon is more reactive; it has more electrons. 2. Chlorine is more reactive; argon has a full outer shell. 3. Unable to determine Chapter 49, section 1, Bonding in Solids Conceptual 26 Q01 49:01, highSchool, multiple choice, < 1 min, fixed. Mixing copper and zinc atoms forms the alloy brass. What would form if you fused the nucleus of a copper atom with the nucleus of a zinc atom? 1. Praseodymium 2. Zinc 3. Copper 4. Neodymium 5. Cerium 6. None of these Hewitt CP9 12 E02 49:01, highSchool, multiple choice, < 1 min, fixed. What supports the claim that crystals are composed of atoms that are arranged in specific patterns? 1. good conductivity 2. transparency 3. symmetric diffraction patterns 4. hardness 353 Chapter 49, section 9, Semiconductor Devices Conceptual 25 01 49:09, highSchool, numeric, < 1 min, normal. Part 1 of 2 There is an effort in the world today to convert television into so-called high definition TV(HDTV). In HDTV, the picture is split up into many as 1100 by 1100 (as opposed to 550 by 550) pixels. What is the information content of an HDTV picture? Give the answer in megabits. Part 2 of 2 What is the information content that must be transmitted each second in an HDTV broadcast? Give the answer in gigabits per second. Conceptual 25 04 49:09, highSchool, numeric, < 1 min, fixed. How many seconds do you have to listen to a CD to receive as much information as is contained in an average book? Assume an average book contains about 4 × 106 bits of information and a CD processes information at a rate of 705000 bit/second. Conceptual 25 05 49:09, highSchool, numeric, < 1 min, normal. Part 1 of 3 The Encyclopedia Britannica contains about 1800 words per page. There are 28 volumes and each volume has about 1000 pages. What is the information content of the words in a set of the encyclopedia in bits? Give the answer in gigabits. Part 2 of 3 What is the information content of the words in a set of the encyclopedia in bytes? Give the answer in megabytes. Part 3 of 3 If a data storage capacity of 1 × 1012 bits per square inch is reached, how many sets (not 354 volume) of the encyclopedia could fit on an ordinary CD? Conceptual 25 07 49:09, highSchool, numeric, < 1 min, normal. How much information is contained in a 300 page book? Assume 500 words on each page and 36 bit of information in each word. Conceptual 25 08 49:09, highSchool, numeric, > 1 min, normal. Part 1 of 2 Rosa writes a 20-page paper for her extracredit history grade. Each page has an average of 26 lines, with 12 words words per line. How many bits of information has Rosa generated in her paper? Part 2 of 2 Can she store her paper on a normal mode 3.5-inch floppy disk? Conceptual 25 09 49:09, highSchool, numeric, > 1 min, fixed. Part 1 of 2 The Cyrillic alphabet (used to write Russian and some other Eastern European languages) was devised in the ninth century and had 43 letters, whereas the alphabet used for modern Russian has 30. How many bits would it take to specify a single letter in modern alphabets? Part 2 of 2 How many bits would it take to specify a single letter in Cyrillic alphabets? Conceptual 25 10 49:09, highSchool, numeric, > 1 min, fixed. The version of modern written Japanese called ”kanji” has 1945 different characters. How many bits would it take to specify kanji character? Chapter 49, section 9, Semiconductor Devices Conceptual 25 Q01 49:09, highSchool, multiple choice, < 1 min, fixed. 3. terahertz radiation If water in a pipe is analogous to electricity in a wire, what is analogous to a diode and to a transistor? 355 5. radiowaves 1. nothing; faucet 2. pipes; nothing 4. microwave Conceptual 25 Q09 49:09, highSchool, multiple choice, < 1 min, fixed. Which method most likely requires more digital storage capacity? 3. faucet; pipes 4. T-connection; elbow 5. elbow ; faucet 1. storing the words of a song using a wordprocessing program 2. storing an actual recording of the song on a CD 6. Non of these. 3. storing using punch cards Conceptual 25 Q06 49:09, highSchool, multiple choice, < 1 min, fixed. Would a diode result from taking two ntype semiconductor and placing them together? 1. No. An electrical field will not be created in an n-n junction. 2. Yes. An electrical field will be created in an n-n junction. 3. No. There will not be enough holes to create electric field but some amount of electric field will be present. Conceptual 25 Q08 49:09, highSchool, multiple choice, < 1 min, fixed. Which would be more effective at making a photovoltaic cell work? 1. infrared light 2. ultraviolet light Conceptual 25 Q10 49:09, highSchool, numeric, < 1 min, fixed. Part 1 of 2 You have five pennies and five nickels in a hat. You draw them out randomly and flip each coin. How many bits of information are required to record the sequence of coins drawn from the hat (e.g., penny, nickel, penny, ....)? Part 2 of 2 How many bits are required to record the sequence of heads/tails? Chapter 49, section 10, Doped Semiconductors 356 ductor Conceptual 25 Q02 49:10, highSchool, multiple choice, < 1 min, wording-variable. What would a silicon semiconductor doped with boron be? 1. p-type 2. i-type 3. n-type Conceptual 25 Q04 49:10, highSchool, multiple choice, < 1 min, fixed. In order to make an n-type semiconductor, silicon can be doped with a small amount of phosphorus. Why is arsenic also a good element to use as a dopant? 1. Arsenic has many allotropic forms. 2. Arsenic has the same number of outer shell electrons does of phosphorus. 3. Arsenic has similar atomic mass to phosphorus. 4. Arsenic has a similar atomic radius to phosphorus. Conceptual 25 Q05 49:10, highSchool, multiple choice, < 1 min, fixed. Which of the following has the highest electrical conductivity? 1. two phosphorus doped silicon semiconductor 2. three phosphorus doped silicon semiconductor 3. one phosphorus doped silicon semicon- 4. silicon semiconductor without any doping Chapter 51, section 1, Discovering the Nucleus Holt SF 25Rev 38 51:01, highSchool, numeric, > 1 min, fixed. Consider the hydrogen atom to be a sphere with a radius equal to the Bohr radius, 0.53 × 10−10 m, and calculate the approximate value of the ratio of atomic density to nuclear density. Holt SF 25Rev 39 51:01, highSchool, numeric, > 1 min, fixed. Certain stars are thought to collapse at the end of their lives, combining their protons and electrons to form a neutron star. Such a star could be thought of as a giant atomic nucleus. If a star with a mass equal to that of the sun (1.99 × 1030 kg) were to collapse into neutrons, what would be the radius of the star? 357 Chapter 51, section 2, Some Nuclear Properties Binding energy 51:02, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Calculate the total binding energy for 28 Si. 14 The mass of 28 Si is 27.9769 u, the mass of 14 the proton is 1.00782 u and the mass of the neutron is 1.00866 u. 1. 236.539 MeV 2. 246.539 MeV 358 Calcuate the Q-value for the He burning reaction 4 2 He + 4 He → 8 Be + γ . 2 4 Take the mass of 4 He is 4.0026 u and of 8 Be is 8.0053 u, 1 uc2 = 931.5 MeV. Express your final answer in MeV. Part 2 of 2 Calcuate the Q-value for the He burning reaction 4 2 He + 8 Be → 12 C + γ . 4 6 Take the mass of 12 C is 12 u. Express your final answer in MeV. 3. 256.539 MeV 4. 266.539 MeV Holt SF 25A 01 51:02, highSchool, numeric, > 1 min, fixed. 5. 226.539 MeV 6. 216.539 MeV 7. None of these Part 2 of 2 What is the binding energy of the last protonelectron pair in 28 Si? The mass of 27 Al is 13 14 26.9815 u. 1. 11.5841 MeV Part 1 of 2 Calculate the total binding energy of 20 Ne. 10 Part 2 of 2 Calculate the total binding energy of 40 Ca. 20 Holt SF 25A 02 51:02, highSchool, numeric, > 1 min, fixed. Determine the difference in the binding energy of 3 H and 3 He. 2 1 2. 10 MeV 3. 0.115841 MeV 4. 21.5841 MeV Holt SF 25A 03 51:02, highSchool, numeric, > 1 min, fixed. Calculate the binding energy of the last neutron in the 43 Ca nucleus. (Hint: Compare 20 the mass of 43 Ca with the mass of 42 Ca plus 20 20 the mass of a neutron.) 5. 31 MeV 6. 1.15841 MeV Holt SF 25A 04 51:02, highSchool, numeric, > 1 min, fixed. 7. 115.841 MeV 8. None of these He burning reaction 51:02, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Find the binding energy per nucleon of 238 U 92 in MeV. Holt SF 25A 05 51:02, highSchool, numeric, > 1 min, fixed. Chapter 51, section 2, Some Nuclear Properties Two isotopes having the same mass number are known as isobars. Calculate the difference in binding energy per nucleon for the isobars 23 Na and 23 Mg. 11 12 Holt SF 25Rev 07 51:02, highSchool, numeric, > 1 min, fixed. Calculate the total binding energy of 12 C. 6 Holt SF 25Rev 08 51:02, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Calculate the total binding energy of tritium (3 H). 1 Part 2 of 2 Calculate the total binding energy of helium-3 (3 He). 2 Holt SF 25Rev 09 51:02, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Calculate the average binding energy per nucleon of 24 Mg. 12 Part 2 of 2 Calculate the average binding energy per nucleon of 85 Rb. 37 Holt SF 25Rev 43 51:02, highSchool, numeric, > 1 min, fixed. A pair of nuclei for which Z1 = N2 and Z2 = N1 are called mirror isobars (the atomic and neutron numbers are interchangeable). Binding energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charge independence means that the proton-proton, protonneutron, and neutron-neutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei, 15 O (15.003065 u) 8 and 15 N (15.000108 u). 7 Holt SF 25Rev 44 359 51:02, highSchool, numeric, > 1 min, fixed. Find the threshold kinetic energy that the incident neutron must have to produce the following reaction: 1 4 0 n + 2 He → 2H + 3H 1 1 Chapter 51, section 3, Binding Energy and Nuclear Forces Hewitt CP9 32 E31 51:03, highSchool, numeric, > 1 min, normal. Part 1 of 2 The higher the energy level occupied by an electron in the hydrogen atom, the larger the atom. The size of the atom is proportional to n2 , where n = 1 labels the lowest, or ground state, n = 2 is the second state, n = 3 is the third state, and so on. If the atom’s diameter is 1 × 10−10 m in its lowest energy state, what is its diameter in state number 25? Part 2 of 2 How many unexcited atoms could fit within this one giant atom? 360 Chapter 51, section 4, Nuclear Models Hewitt CP9 33 E01 51:04, highSchool, multiple choice, < 1 min, fixed. X rays are most similar to which of the following? 361 4. No; hydrogen cannot be broken apart. Hewitt CP9 33 E042 51:04, highSchool, multiple choice, < 1 min, fixed. Why are gamma rays not deflected? 1. Alpha rays 1. They have no electric charge. 2. Beta rays 2. They have a short lifetime. 3. Gamma rays 3. They have strong penetration ability. Hewitt CP9 33 E02 51:04, highSchool, multiple choice, < 1 min, fixed. Why is a sample of radioactive material always a little warmer than its surroundings? 1. The radioactive material has better heat conduction than other materials. 2. The radiating alpha or beta particles impart internal energy to the atoms of the sample. 4. They don’t react chemically with other materials. 5. They carry great energy. Hewitt CP9 33 E04 51:04, highSchool, multiple choice, < 1 min, fixed. Why are alpha and beta rays deflected in opposite directions in a magnetic field? 1. They have different masses. 3. The radioactive material always has a rapid chemical reaction inside. 4. Heat is easier to get into radioactive materials than other materials. Hewitt CP9 33 E03 51:04, highSchool, multiple choice, < 1 min, fixed. Some people say that all things are possible. Is it possible for a hydrogen nucleus to emit an alpha particle? 2. They have different lifetimes. 3. They have different penetration abilities. 4. They are oppositely charged. 5. They have different chemical characteristics. Hewitt CP9 33 E06 51:04, highSchool, multiple choice, < 1 min, fixed. 1. Yes 2. No; hydrogen cannot participate in nuclear reactions. 3. No; an alpha particle has four nucleons – two protons and two neutrons. How do the paths of alpha, beta, or gamma rays compare in an electric field? 1. Alpha and beta particles are pushed in the same direction by an electric field; gamma rays are unaffected. Chapter 51, section 4, Nuclear Models a uranium mine? 2. Gamma and beta rays are pushed oppositely by an electric field; alpha rays are unaffected. 1. alpha 2. beta 3. Alpha and gamma rays are pushed oppositely by an electric field; beta rays are unaffected. 4. Alpha and beta particles are pushed oppositely by an electric field; gamma rays are unaffected. 5. Alpha, beta and gamma rays are pushed in the same direction. Hewitt CP9 33 E07 51:04, highSchool, multiple choice, < 1 min, fixed. Which type of radiation produces the greatest change in mass number when emitted by an atomic nucleus? 1. alpha 2. beta 3. gamma Hewitt CP9 33 E08 51:04, highSchool, multiple choice, < 1 min, fixed. Which type of radiation produces the least change in mass number? 1. alpha 2. beta 3. gamma Hewitt CP9 33 E09 51:04, highSchool, multiple choice, < 1 min, fixed. Which type of radiation predominates within an enclosed elevator descending into 3. gamma 362 Chapter 51, section 5, Radioactivity 363 Conceptual 26 Q10 51:05, highSchool, multiple choice, < 1 min, fixed. A radioactive isotope is found to decay to one-sixteenth its original amount in 12 years. What is the half-life of this isotope? Suppose you are a scientist from the future who has discovered the ruins of the Empire State Building. How would you go about estimating the date when it was built? Conceptual 26 Q13 51:05, highSchool, numeric, < 1 min, fixed. 1. Try to find artifacts made of organic material. 2. Try to find old belongings to consult with a historian. Conceptual 26 Q11 51:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Carbon-14 decays by beta decay with a half life of 5700 years. What does a carbon-14 nucleus become when it undergoes beta decay? 1. Nitrogen-14 A radioactive isotope is found to decay to one-eighth its original amount in 30 years. What is the half-life of this isotope? Conceptual 26 Q14 51:05, highSchool, multiple choice, < 1 min, fixed. Part 1 of 2 Is it possible for a radioactive nucleus to decay two times and end up as the same element that it started as? 1. Yes; if it were two gamma decays. 2. Yes; if it were alpha and gamma decays. 3. Yes; if it were beta and gamma decays. 4. No; its impossible to end up as the same element. 2. Uranium-234 3. Radium-226 Part 2 of 2 What if the nucleus were restricted to alpha and beta decays only? 4. Lead-206 5. Polonium-218 1. Yes; if it were two alpha decays. 2. Yes; if it were two beta decays. 6. Bismuth-214 3. Yes; if it were beta and alpha decays. Part 2 of 2 If an ancient campfire were analyzed, and it was found to have only about one-eighth the carbon-14 that is normally found in living things, how long ago was that campfire extinguished? Conceptual 26 Q12 51:05, highSchool, multiple choice, < 1 min, fixed. 4. No; its impossible. Holt SF 25B 01 51:05, highSchool, multiple choice, > 1 min, fixed. Complete this radioactive-decay formula: →? +−0e + ν 1 12 5B Chapter 51, section 5, Radioactivity 1. 12 C 6 2. 12 Be 4 3. 11 O 8 364 Holt SF 25B 04 51:05, highSchool, multiple choice, > 1 min, fixed. Complete this radioactive-decay formula: →221 Fr +? 87 4. 10 F 9 225 89 Ac 5. 10 B 5 1. 4 He 2 6. None of these 2. 2 2 H 1 Holt SF 25B 02 51:05, highSchool, multiple choice, > 1 min, fixed. Complete this radioactive-decay formula: →?+4 He 2 212 83 Bi 1. 208 Tl 81 2. 208 81 Hg 3. 216 85 At 4. 216 Po 85 5. 208 At 85 6. 216 81 Tl 3. The reaction is impossible. 4. None of these Holt SF 25B 06 51:05, highSchool, multiple choice, > 1 min, fixed. The isotope 56 27 Co. 56 26 Fe decays into the isotope By what process will this decay occur? 1. β − 2. β + 3. α 4. γ 7. None of these 5. None of these Holt SF 25B 03 51:05, highSchool, multiple choice, > 1 min, fixed. Complete this radioactive-decay formula: ? →14 N +−0 e + ν 7 1 1. 14 C 6 2. 12 C 6 3. 14 O 8 4. 15 B 6 5. None of these Holt SF 25C 01 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The half-life of 214 Po is 164 84 µs. A polonium214 sample contains 2.0 × 106 nuclei. a) What is the decay constant for the decay? Part 2 of 2 b) How many polonium nuclei, in curies, will decay per second? Holt SF 25C 02 Chapter 51, section 5, Radioactivity 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The half-life of 214 Bi is 19.7 min. A 83 9 bismuth-214 sample contains 2.0 × 10 nuclei. a) What is the decay constant for the decay? Part 2 of 2 b) How many bismuth nuclei, in curies, will decay per second? Holt SF 25C 03 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The half-life of 131 I is 8.07 days. 53 a) Calculate the decay constant for this isotope. Part 2 of 2 b) What is the activity in Ci for a sample that contains 2.5 × 1010 iodine-131 nuclei? Holt SF 25C 04 51:05, highSchool, numeric, > 1 min, normal. Suppose that you start with 1.23 g of a pure radioactive substance and determine 4 h later that only 0.076875 g of the substance is left undecayed. What is the half-life of this substance? Holt SF 25C 05 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 222 Radon-222 ( 86 Rn) is a radioactive gas with a half-life of 3.82 days. A gas sample contains 4.0 × 108 radon atoms initially. a) Determine how many radon atoms will remain after 12 days. Part 2 of 2 b) Determine how many radon nuclei will have decayed by this time. 365 Holt SF 25Rev 23 51:05, highSchool, multiple choice, > 1 min, fixed. Determine the missing product of the following reaction: 7 4 1 3 Li+2 He →? +0 n 1. 10 B 5 2. 11 B 5 3. 10 Be 5 4. 11 C 5 5. 3 H 1 Holt SF 25Rev 24 51:05, highSchool, multiple choice, > 1 min, fixed. A nuclear reaction of significant historical note occurred in 1932, when a beryllium target was bombarded with alpha particles. Analysis of the experiment indicated that the following reaction occurred: 4 9 12 2 He+4 Be → 6 C+X What is X in this reaction? 1. 1 n 0 2. 0 n 1 3. 0 e 1 4. 1 e 0 5. γ 6. None of these Holt SF 25Rev 25 51:05, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Complete the following nuclear reaction: Chapter 51, section 5, Radioactivity ?+14 N →1 H+17 O 7 1 8 1. 4 He 2 2. 2 H 1 3. 2 He 2 4. 22 H 1 366 variable. The amount of carbon-14 (14 C) in a wooden 6 artifact is measured to be 6.25 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5730 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact. 5. None of these Part 2 of 2 Complete the following nuclear reaction: 7 1 4 3 Li+1 H →2 He+? 1. 4 He 2 2. 8 Be 4 3. 3 He 2 4. 22 H 1 5. None of these Holt SF 25Rev 26 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 A radioactive sample contains 1.67 × 1011 atoms of 108 Ag ( half-life= 2.42 min) at some 47 instant. Calculate the decay constant. Part 2 of 2 b) Calculate the activity of the sample in mCi. Holt SF 25Rev 27 51:05, highSchool, numeric, > 1 min, fixed. How long will it take a sample of polonium210 with a half-life of 140 days to decay to one-sixteenth its original strength? Holt SF 25Rev 28 51:05, highSchool, numeric, > 1 min, wording- Holt SF 25Rev 29 51:05, highSchool, numeric, > 1 min, wordingvariable. A sample of organic material is found to contain 18 g of carbon. Based on samples of pottery found at the site, investigators believe the material is about 23000 years old. Estimate what percentage of the material’s carbon-14 has decayed. Holt SF 25Rev 54 51:05, highSchool, numeric, > 1 min, wordingvariable. A piece of charcoal known to be approximately 25000 years old contains 7.96 × 1010 C-14 atoms. Determine the number of decays per minute expected from this sample. Holt SF 25Rev 55 51:05, highSchool, numeric, > 1 min, wordingvariable. Part 1 of 2 The half-life of radium-228 is 5.76 years. At some instant a sample contains 2.0 × 109 nuclei. a) Calculate the decay constant. Part 2 of 2 b) Calculate the activity of the sample in Ci. Holt SF 25Rev 56 51:05, highSchool, numeric, > 1 min, wordingvariable. Chapter 51, section 5, Radioactivity A sample of a radioactive isotope is measured to have an activity of 240.0 mCi. If the sample has a half-life of 14 days, how many nuclei of the isotope are there at this time? Holt SF 25Rev 57 51:05, highSchool, numeric, > 1 min, wordingvariable. At some instant of time the activity of a sample of radioactive material is 5.0 µCi. If the sample contains 1.0 × 109 radioactive nuclei, what is the half-life of the material? Holt SF 25Rev 58 51:05, highSchool, numeric, > 1 min, fixed. Smoke detectors use the isotope 241 Am in their operation. The half-life of Am is 432 years. If the smoke detector is improperly discarded in a landfill, estimate how long it will take for its activity to reduce to a relatively safe level of 0.1 percent of its original activity? (Hint: The estimation process you should use notes that the activity reduces to 50% in one half-life, to 25% in two half-lives, and so on.) 367 Chapter 51, section 6, Decay Processes Holt SF 25Rev 41 51:06, highSchool, numeric, > 1 min, fixed. Find the energy released in the alpha decay of 238 U. Use the masses in the following table: 92 Nucleus Mass 238 92 U 238.050 784 u 234 90 Th 234.043 593 u 4 2 He 4.002 602 u 368 Chapter 51, section 8, Beta Decay Holt SF 25B 05 51:08, highSchool, multiple choice, > 1 min, fixed. Nickel-63 decays by β − emission to copper63. Write the complete decay formula for this process. 1. 63 Ni →63 Cu +−0e + ν 28 29 1 2. 63 Ni →63 Cu +0e + ν 28 29 1 3. 63 Ni →63 Cu + γ 28 28 0 4. 63 Ni →63 Cu +4 He +−1e 28 29 2 5. None of these Holt SF 25Rev 40 51:08, highSchool, numeric, > 1 min, fixed. Tritium, 3 H, decays to 3 He by beta emis2 1 sion. Determine the energy released in the process. 369 Chapter 51, section 12, Radioactive Dating Hewitt CP9 33 q07 51:12, highSchool, multiple choice, < 1 min, fixed. Carbon dating allows us to 1. understand the motion of the Moon around the Earth. 2. explain global warming. 3. discover the age of dead bodies. 4. keep an accurate daily calendar. 370 Chapter 52, section 1, Nuclear Reactions 371 obtained? Atomic Nucleus 25 52:01, highSchool, numeric, > 1 min, fixed. Mirror nuclei are pairs of nuclei in which the numbers of protons and neutrons are exchanged. 11 B(boron; Z = 5) and 11 C(carbon; Z = 6) are examples. Show that if the nn nuclear force differed from the pp nuclear force, the masses of the mirror nuclei would have a non-zero contribution from this effect. Such a term is explicitly ruled out in the semiempirical mass formula. Compare a calculation of the mass difference from the semiempirical mass formula with the measured mass difference of 1.98 MeV/c2 . Atomic Nucleus 29 52:01, highSchool, numeric, < 1 min, fixed. 1. nuclear reactor 2. gaseous diffusion 3. ultra centrifuge 4. mines Hewitt CP9 33 q02 52:01, highSchool, multiple choice, < 1 min, fixed. How is Pu239 for atomic weapons currently obtained? 1. nuclear reactor 2. gaseous diffusion What is the minimum energy that can be released in the reaction n +235 U →93 Rb +141 Cs + 2 n? (The mass of 93 Rb is 92.9217 u, the mass of 141 Cs is 140.919 u, the mass of 235 U is 235.044 u and the mass of n is 1.00866 u.) Atomic Nucleus 31 52:01, highSchool, numeric, > 1 min, fixed. In his experiment to identify the neutron, Chadwick used the reaction α +11 B → n +14 N. He measured the kinetic energies of the particles involved, which were 5.26 MeV for the α-particle, 3.26 MeV for the neutron, and 0.57 MeV for the nitrogen nucleus; the boron nucleus was at rest. The mass of 11 B is 11.0093 u, the mass of 14 N is 14.0031 u and the mass of α-particle is 4.0026 u. Using these data, find the mass of the neutron. Hewitt CP9 33 q01 52:01, highSchool, multiple choice, < 1 min, fixed. How is U235 for atomic weapons currently 3. ultra centrifuge 4. mines Hewitt CP9 33 q03 52:01, highSchool, multiple choice, < 1 min, fixed. What explains why chain reactions do not take place in pure natural uranium? 1. The main component of natural uranium U235 does not lead to chain reactions. 2. The main component of natural uranium U238 doesn’t fission. 3. There is usually not enough uranium localized in one place to overcome critical mass. 4. Natural uranium is not pure. Hewitt CP9 33 q04 52:01, highSchool, multiple choice, < 1 min, fixed. What did Rutherford discover? Chapter 52, section 1, Nuclear Reactions 372 of U238 in uranium ore. 1. radioactive decay 2. Gold is heavier than lead. 3. Electrons do not scatter alpha particles. 4. The nucleus is much smaller than the atom. Hewitt CP9 33 q05 52:01, highSchool, multiple choice, < 1 min, fixed. Which of the following was explained by the Bohr atom? 1. the fact that most of the mass of an atom is in the nucleus 2. the photoelectric effect 2. Uranium ore doesn’t contain particles active enough to induce a chain reaction. 3. Uranium in ore is mixed with other substances that impede the reaction and has no moderator to slow down the neutrons. 4. There is no uranium deposit in the world large enough for a chain reaction. Hewitt CP9 34 E02 52:01, highSchool, multiple choice, < 1 min, fixed. Some heavy nuclei, containing even more protons than the uranium nucleus, undergo “spontaneous fission”, splitting apart without absorbing a neutron. Why is spontaneous fission observed only in the heaviest nuclei? 3. atomic spectra 4. nuclear fission Hewitt CP9 33 q06 52:01, highSchool, multiple choice, < 1 min, fixed. To achieve a chain reaction, what is most important? 1. high density 1. Gravitational forces are small for light nuclei. 2. In a heavy atom, the outmost electrons are very far from the center of the atom. 3. A light nucleus does not have enough energy for fission. 4. The electric attraction between protons is weaker than the repulsive nuclear force in the heaviest nuclei. 2. high temperature 3. neutron multiplication less than 1 Hewitt CP9 34 E03 52:01, highSchool, multiple choice, < 1 min, fixed. 4. neutron multiplication greater than 1 Hewitt CP9 34 E01 52:01, highSchool, multiple choice, < 1 min, fixed. Why doesn’t uranium ore spontaneously undergo a chain reaction? 1. There is not a high enough concentration Why is nuclear fission not likely to be used directly for powering automobiles? 1. A fission reactor has a critical mass. Its minimum size is too large to power a small vehicle. 2. The power generated by nuclear fission is enormous and cannot be reduced to meet the Chapter 52, section 1, Nuclear Reactions 373 needs of one automobile. tional force. 3. External nuclear radioactivity can harm the driver. 4. Larger materials have a greater electric force. 4. We haven’t found a good way to control nuclear fission. Hewitt CP9 34 E06 52:01, highSchool, multiple choice, < 1 min, fixed. 5. Nuclear reactions are harmful for the environment. Hewitt CP9 34 E04 52:01, highSchool, multiple choice, < 1 min, fixed. Which shape is likely to need less material for a critical mass? 1. a cube 2. a cone Why does a neutron make a better nuclear probe than a proton or an electron? 1. A neutron is more stable than a proton or an electron. 3. a sphere 4. a hexahedron 5. a cylinder 2. A neutron takes more power when it moves. 3. A neutron has greater mass than both a proton and an electron. 4. A neutron does not react chemically with other neuclei. 5. A neutron has no electric charge and is therefore not repelled by an atomic nucleus. Hewitt CP9 34 E07 52:01, highSchool, multiple choice, < 1 min, fixed. Does the average distance that a neutron travels through fissionable material before escaping increase or decrease when two pieces of fissionable material are assembled into one piece? Does this assembly increase or decrease the probability of an explosion? 1. Both decrease. Hewitt CP9 34 E05 52:01, highSchool, multiple choice, < 1 min, fixed. 2. increases; decreases 3. decreases; increases Why will the escape of neutrons be proportionally less in a large piece of fissionable material than in a smaller piece? 4. Both increase. 1. Larger materials have a greater nuclear force. Hewitt CP9 34 E09 52:01, highSchool, multiple choice, < 1 min, fixed. 2. Larger materials have proportionally less surface area per volume. Why does plutonium not occur in appreciable amounts in natural ore deposits? 3. Larger materials have a greater gravita- 1. Plutonium has a relatively short half Chapter 52, section 1, Nuclear Reactions life. 2. Plutonium has a relatively long half life. 374 4. to restrict radioactive contamination to the reactor itself and to prevent interaction of the contaminants with the outside environment 3. Plutonium has a relatively heavy mass. 4. Plutonium easily reacts chemically with other materials. 5. Plutonium is a gas. Hewitt CP9 34 E10 52:01, highSchool, multiple choice, < 1 min, fixed. Hewitt CP9 34 E13 52:01, highSchool, multiple choice, < 1 min, fixed. Why is carbon better than lead as a moderator in nuclear reactors? 1. Carbon can be manipulated easier than lead. Why, after a uranium fuel rod reaches the end of its fuel cycle (typically 3 years) does most of its energy come from the fissioning of plutonium? 2. A lead nucleus is more massive than a carbon nucleus. 1. Plutonium builds up over time because it is produced by proton absorption in U238 . 4. Lead is too dangerous for human health. 2. Plutonium builds up over time because it is produced by electron absorption in U238 . 3. Plutonium builds up over time because it is produced by alpha particle absorption in U238 . 4. Plutonium builds up over time because it is produced by neutron absorption in U238 . Hewitt CP9 34 E12 52:01, highSchool, multiple choice, < 1 min, fixed. The water that passes through a reactor core does not pass into the turbine; instead, heat is transferred to a separate water cycle that is entirely outside the reactor. Why is this done? 3. Carbon has more isotopes than lead. Hewitt CP9 34 E14 52:01, highSchool, multiple choice, < 1 min, fixed. Is the mass of an atomic nucleus greater or less than the sum of the masses of the nucleons composing it? Why don’t the nucleon masses add up to the total nuclear mass? 1. Less; work must be done to separate a nucleus into its component nucleons. 2. More; other energies are contained in a nucleus that the nucleon components don’t have. 3. Less; some electrons disappear when the nucleon components form a nucleus. 4. More; a nucleus is larger than the sum of the nucleon components. 1. to create more power 2. to avoid accidental explosions Holt SF 25Rev 50 52:01, highSchool, multiple choice, > 1 min, fixed. 3. to obtain more coolant When 18 O is struck by a proton, 18 F and Chapter 52, section 1, Nuclear Reactions another particle are produced. What is the other particle? 1. 1 n 0 2. 21 n 0 3. 0 e− 1 4. 4 He 2 5. 1 H 1 6. 2 H 1 7. None of these Holt SF 25Rev 51 52:01, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Complete the following nuclear reactions: a) 27 Al+4 He →?+30 P 15 2 13 1. 1 n 0 2. 1 H 1 3. 4 He 2 4. 2 Be 4 5. 10 Be 4 Part 2 of 2 b) 1 n+? → 4 He+7 Li 0 2 3 1. 10 B 5 2. 10 Be 4 3. 2 H 1 4. 12 C 6 5. 11 B 5 375 Chapter 52, section 3, Interactions Involving Neutrons Atomic Nucleus 05 52:03, highSchool, numeric, > 1 min, fixed. In this problem you will use the semiempirical mass formula to conclude that the nucleus is, to a good approximation, incompressible. Start by noting that the volume term in the formula dominates for, say, A greater than 100. We can call the resulting energy Evol = −bvol A. Express Evol as a function of radius. By how much is the energy altered for a change in volume that results from an overall change in the radius ∆R? In addition to providing an analytic answer, evaluate your result numerically by finding the energy change for a 0.01 change in the radius. Your numbers should be on the order of 50 MeV per nucleon– such a large number that you can conclude that the nucleus is incompressible. Holt SF 25Rev 46 52:03, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Natural gold has only one stable isotope, 197 79 Au. If gold is bombarded with slow neutrons, β − particles are emitted. a) Which of the following is the correct reaction equation? 0 1. 1 n +197Au →198 Pt ++1e + ν 0 79 78 2. 197 +−0e + ν →196 Pt + 1 n Au 79 1 78 0 3. 1 n +197Au →197 Au +−0e + ν 0 79 79 1 4. 1 n +197Au →198 Hg +−0e + ν 1 80 79 0 5. 1 n +198Hg →197 Au +−0e + ν 0 80 79 1 6. 4 He +197Au →201 Pb +−0e + ν 1 82 79 2 7. None of these Part 2 of 2 b) Calculate the maximum energy of the emitted beta particles. 376 Chapter 52, section 4, Nuclear Fission Atomic Nucleus 02 52:04, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Given that it may take as much as 10 MeV to remove a nucleon from a nucleus, estimate the difference between the mass of a nucleus and the sum of the masses of the nucleons that compose it. Part 2 of 2 How big is the corresponding effect in atoms if we regard the atomic constituents as the nucleus as a whole plus the electrons? Atomic Nucleus 04 52:04, highSchool, numeric, > 1 min, fixed. 13 377 Holt SF 25Rev 47 52:04, highSchool, multiple choice, > 1 min, fixed. Part 1 of 2 Consider the two ways 235 U can undergo fission when bombarded with a neutron. In each case, neutrons are also released. Find the number of neutrons released when 140 Xe and 94 Sr are released as fission fragments. 1. 2 2. 1 3. 3 4. 4 13 Consider the nuclei N(Z = 7) and C (Z = 6). The difference in mass between them is measured to be 1.19 MeV/c2 . Which terms in the semiempirical mass formula contribute to that difference? Use your answer in conjunction with the expression for the coulomb energy in the semiempirical mass formula, (3/5) Z 2 e2 /(4 π 0 R0 A1/3 ), to calculate R0 . 5. None of these Part 2 of 2 Find the number of neutrons released when 132 Sn and 101 Mo are released as fission fragments. 1. 3 Concept 34 E15 52:04, highSchool, multiple choice, < 1 min, fixed. 2. 1 The energy release of nuclear fission is tied to the fact that the heaviest nuclei have about 0.1% more mass per nucleon than nuclei near the middle of the periodic table of elements. What would be the effect on energy release if the 0.1% figure were 1.0% instead? 4. 4 1. the same as before 2. one tenth of the original energy release 3. ten times the original energy release 4. a hundred times the original energy release 3. 2 5. None of these Holt SF 25Rev 48 52:04, highSchool, multiple choice, > 1 min, fixed. When a 6 Li nucleus is struck by a proton, 3 an alpha particle and a product nucleus are released. What is the product nucleus? 1. 3 He 2 2. 4 He 2 Chapter 52, section 4, Nuclear Fission 3. 3 2 Li 4. 1 H 1 5. 3 H 1 6. None of these Holt SF 25Rev 52 52:04, highSchool, multiple choice, > 1 min, fixed. A fission reaction that occurs when uranium-235 absorbs a neutron leads to the formation of barium-141 and krypton-92. a) What is the missing product in this reaction? ergy to keep a 100.0 W light bulb burning for 1.0 h. Holt SF 25Rev 61 52:04, highSchool, numeric, > 1 min, wordingvariable. How many atoms of 235 U must undergo fission to operate a 1.0 × 103 MW power plant for one day if the conversion efficiency is 30.0 percent? Assume 208 MeV released per fission event. Holt SF 25Rev 62 52:04, highSchool, numeric, > 1 min, wordingvariable. An all-electric home uses about 2.0 × 10 kW · h of electrical energy per month. How many 235 U atoms would be required to provide this house with its energy needs for one year? Assume 100.0 percent conversion efficiency and 208 MeV released per fission. 3 1. 31 n 0 2. 21 n 0 3. 4 He 2 4. 3 He 2 5. 3 H 1 Holt SF 25Rev 59 52:04, highSchool, numeric, > 1 min, fixed. It has been estimated that Earth has 9.1 × 1011 kg of natural uranium that can be economically mined. Of this total, 0.70 percent is 235 U. If all the world’s energy needs (7.0 × 12 10 J/s) were supplied by 235 U fission, how long would this supply last? Assume that 208 MeV of energy is released per fission event and the mass of 235 U is about 3.9 × 10−25 kg. Holt SF 25Rev 60 52:04, highSchool, numeric, > 1 min, wordingvariable. If the average energy released in a fission event is 208 MeV, find the total number of fission events required to provide enough en- 378 Chapter 52, section 6, Nuclear Reactors 379 Concept 34 E21 52:06, highSchool, multiple choice, < 1 min, fixed. 4. Splitting light nuclei yields energy; the total mass of the products is less than the total mass of the fusing nuclei. Heavy nuclei can be made to fuse; for instance, by firing one gold nucleus at another one. Does such a process yield energy or cost energy? Why? Conceptual 26 Q08 52:06, highSchool, multiple choice, > 1 min, wording-variable. 1. Fusing heavy nuclei yields energy; the total mass of the products is greater than the total mass of the fusing nuclei. 2. Fusing heavy nuclei costs energy; the total mass of the products is greater than the total mass of the fusing nuclei. Which of the following is the disadvantage of nuclear power? 1. high expense of nuclear generating plant 2. can generate enormous amount of energy from a very small amount of material 3. cannot generate enough energy 3. Fusing heavy nuclei costs energy; the total mass of the products is less than the total mass of the fusing nuclei. Conceptual 26 Q09 52:06, highSchool, multiple choice, < 1 min, fixed. 4. Fusing heavy nuclei yields energy; the total mass of the products is less than the total mass of the fusing nuclei. Can nuclear radiation escape from nuclear plants? Concept 34 E22 52:06, highSchool, multiple choice, < 1 min, fixed. Light nuclei can be split. For instance a deuteron (proton-neutron combination) can be caused to split into a single proton and single neutron. Does such a process yield energy or cost energy? Why? 1. Splitting light nuclei costs energy; the total mass of the products is greater than the total mass of the fusing nuclei. 2. Splitting light nuclei costs energy; the total mass of the products is less than the total mass of the fusing nuclei. 3. Splitting light nuclei yields energy; the total mass of the products is greater than the total mass of the fusing nuclei. 1. Yes; the surrounding of the plant is hazardous. 2. Yes; nothing as such can block it completely. 3. No; but small amounts of gamma radiation will escape. 4. No; no radiation will escape. Hewitt CP9 33 q10 52:06, highSchool, multiple choice, < 1 min, fixed. What is needed for controlled thermonuclear reactions to work? 1. high temperature 2. long time 3. high density Chapter 52, section 6, Nuclear Reactors 4. All of these 5. None of these 380 Chapter 52, section 8, Nuclear Fusion Concept 34 E16 52:08, highSchool, multiple choice, < 1 min, fixed. In what ways are fission and fusion reactions similar? 1. Both involve the transformation of one or more elements into other elements. 2. Both have critical masses. 3. Both require high temperatures. 381 4. fusion; fusion; neither Concept 34 E27 52:08, highSchool, multiple choice, > 1 min, fixed. Which produces more energy: fissioning a single uranium nucleus or fusing a pair of deuterium nuclei? fissioning a gram of uranium or fusing a gram of deuterium? 1. fissioning a single uranium nucleus; fusing deuterium 4. Both need both heavy and light nuclei. Concept 34 E17 52:08, highSchool, multiple choice, < 1 min, xed. Chemical burning is similar to nuclear fusion in many aspects. Which statement is not correct? 1. Both require minimum ignition temperature to start. 2. fusing a pair of duterium nuclei; fusing deuterium 3. fissioning a single uranium nucleus; fissioning uranium 4. fusing a pair of duterium nuclei; fissioning uranium Holt SF 25Rev 49 52:08, highSchool, multiple choice, > 1 min, fixed. 2. Both have critical masses. 3. Any amount of thermonuclear fuel or of combustible fuel can be stored. 4. In both the reaction is spread by heat from one region to neighboring regions. Suppose 10 B is struck by an alpha particle, 5 releasing a proton and a product nucleus in the reaction. What is the product nucleus? 1. 13 C 6 Concept 34 E23 52:08, highSchool, multiple choice, < 1 min, fixed. 2. 5 He 2 Which process (fission or fusion) would release energy from gold, from carbon, and from iron? 4. 15 O 8 1. fission; fusion; neither 2. fission; fission; fusion 3. fusion; fission; neither 3. 12 C 6 5. 13 B 5 6. None of these Holt SF 25Rev 53 52:08, highSchool, multiple choice, > 1 min, fixed. Chapter 52, section 8, Nuclear Fusion Part 1 of 2 When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels, such as helium. At temperatures above 1.0 × 108 K, helium fusion can occur. a) Two alpha particles fuse to produce a nucleus A and a gamma ray. What is nucleus A? 1. 8 Be 4 2. 42 H 1 3. 6 Be 4 4. 8 B 5 5. None of these Part 2 of 2 b) Nucleus A absorbs an alpha particle to produce a nucleus, B, and a gamma ray. What is nucleus B? 1. 12 C 6 2. 4 He 2 3. 12 B 6 4. 62 H 1 5. None of these 382 Chapter 52, section 14, Radiation Detectors Atomic Nucleus 16 52:14, highSchool, numeric, < 1 min, normal. 14 C decays with a lifetime of 8270 yr. What is the 14 C activity, defined to be the number of decays per unit time in a sample of the material, expected in a timber structure that is 1200 yr years old? Give your results as a ratio of the activity of a sample of the timber to that of the same-sized sample of modern wood. 383 Chapter 53, section 1, Elementary Particles Conceptual 27 07 53:01, highSchool, numeric, > 1 min, wordingvariable. One naturally occuring reaction in a radioactive decay process is nitrogen-12 (atomic number 7) decaying into carbon-12 (atomic number 6) plus an unknown particle. What is the charge of this unknown particle? Conceptual 27 08 53:01, highSchool, numeric, > 1 min, fixed. Some astronomers have theorized that galaxies (matter) and antigalaxies (antimatter) have existed. Each galaxy contains about 1011 masses of the Sun (the mass of the Sun is 1.9 × 1030 kg). Calculate the total energy released if a matter-antimatter galaxy pair annihilated. Conceptual 27 09 53:01, highSchool, numeric, > 1 min, fixed. Temperature can be related to energy by 1 the equation E = k T, where the tempera2 ture T is in Kelvin and k = 1.38 × 10−23 J/K. What is the difference in the temperatures generated between an electron-positron annihilation and a proton-neutron annihilation? 384 Chapter 53, section 2, The Fundamental Forces in Nature Conceptual 27 01 53:02, highSchool, multiple choice, > 1 min, wording-variable. Part 1 of 2 Arrange the four fundamental forces according to strength from strongest to weakest. 1. gravity; strong nuclear force; weak nuclear force; electromagnetic force 2. strong nuclear force; weak nuclear force; electromagnetic force; gravity 3. electromagnetic force; strong nuclear force; weak nuclear force; gravity 4. strong nuclear force; weak nuclear force; gravity; electromagnetic force Part 2 of 2 What is the range of gravity? 1. long range 2. very short range 3. short range 4. None of these Steady state model 53:02, highSchool, numeric, > 1 min, normal. Estimate the rate at which hydrogen atoms would have to be created, according to the steady-state model, to maintain the present density of the unverse of about 5 × 10−27 kg/m3 , Assume the radius of the universe is 1 × 1011 ly, mass of the hydrozen atom is 1.67 × 10−27 kg and the universe is expanding with Hubble constant 80 km/s/Mpc. Express the answer in atoms/km3 /yr. Threshold temp for particle prod 53:02, highSchool, numeric, > 1 min, fixed. 385 Part 1 of 3 Determine the thereshold temperature for producing various particles below. Additional exercises: (NOT to be submitted to homework service.) Based on the “temperature/time” plot for the history of the universe after the big bang, estimate the time when each of the threshold productions occurs. See if your answer agrees with the explanation to within a factor of 10, after the homework is due. a) kaons (M ≈ 500 MeV/c 2 ). Part 2 of 3 b) Υ (M ≈ 9500 MeV/c 2 ). Part 3 of 3 c) muons (M ≈ 100 MeV/c 2 ). Chapter 53, section 5, Particles and Antiparticles Conceptual 27 02 53:05, highSchool, numeric, < 1 min, wordingvariable. What is the electric charge of an antiproton? Conceptual 27 06 53:05, highSchool, numeric, < 1 min, fixed. A proton and an antiproton, both at rest with respect to one another, mutually annihilate into two gamma rays. How much energy is produced in this annihilation?(Hint: How are mass and energy related to one another?) 386 4. small radius; larger centripetal acceleration Conceptual 27 Q03 53:05, highSchool, multiple choice, > 1 min, fixed. When an electron and a positron annihilate, they form a pair of photons. Suppose a friend told you that sometimes, instead of two photons, the positron and electron annihilate into a proton and a neutron. What would then be true? 1. it is possible; charge is not conserved 2. it is impossible; charge is not conserved Conceptual 27 Q01 53:05, highSchool, multiple choice, < 1 min, fixed. 3. it is possible; charge is conserved 4. it is impossible; charge is conserved Which particle-antiparticle interaction releases more energy? 1. electron-positron annihilation 2. proton-antiproton annihilation 3. both have the same energy Conceptual 27 Q02 53:05, highSchool, multiple choice, < 1 min, fixed. Some particle accelerators accelerate particles around in circular paths up to speeds very close to the speed of light. Which radius will be advantageous and why? 1. large radius; larger centripetal acceleration 2. large radius; smaller centripetal acceleration 3. small radius; smaller centripetal acceleration 5. None of these Holt SF 25Rev 45 53:05, highSchool, numeric, > 1 min, wordingvariable. A photon with an energy of 2.09 GeV creates a proton-antiproton pair in which the proton has a kinetic energy of 95 MeV. What is the kinetic energy of the antiproton? Chapter 53, section 7, Classification of Particles Conceptual 24 05 53:07, highSchool, numeric, < 1 min, fixed. Mesons are made from a quark and an antiquark. A particle called pimeson is made from an up quark and an antidown quark. What is the charge of this particle? Conceptual 27 03 53:07, highSchool, numeric, > 1 min, fixed. A hadron called the sigma particle is made from two down quarks and one strange quark. What is the charge of the sigma particle? Conceptual 27 04 53:07, highSchool, multiple choice, < 1 min, fixed. Are any leptons made of quarks? 1. No; leptons are distinct from quarks. 2. Yes; leptons are point particles. 3. Yes; leptons have fractional electric charge. 4. No; charge. leptons have fractional electric 5. None of these 387 Chapter 53, section 15, The Eightfold Way Apparent brightness of Jupiter 53:15, highSchool, numeric, > 1 min, normal. What is the apparent brightness of the Sun as seen on Jupiter? Jupiter is 5.2 times farther from the Sun than the Earth. Assume apparent brightness of the sun seen at Earth is 1300 W/m2 . Luminosity of the Sun 53:15, highSchool, numeric, > 1 min, normal. Part 1 of 2 The instensity that the rate energy reaches the Earth from the Sun (the “solar constant”) is about 1300 W/m2 . a) What is the apparent brightness of the Sun? Part 2 of 2 b) What is the absolute luminosity of the Sun? Assume the distance between the earth and the Sun is 1.5 × 1011 m. 388 Chapter 53, section 16, Quarks Conceptual 27 Q04 53:16, highSchool, numeric, < 1 min, wordingvariable. How many quarks are there in a helium-4 nucleus? Conceptual 27 Q05 53:16, highSchool, multiple choice, < 1 min, fixed. A neutron is made of three quarks. Is it possible that two up quarks and a down quark could make a neutron? 1. No; a neutron has no electric charge. 2. Yes; a neutron has an electric charge of +1. 3. No; a neutron has electric charge of +1. 4. Yes; a neutron has no electric charge. 5. None of these Holt SF 25Rev 42 53:16, highSchool, numeric, > 1 min, fixed. Part 1 of 2 Disregard binding energies and estimate the mass of the u quark from the masses of the proton and neutron. Part 2 of 2 Disregard binding energies and estimate the mass of the d quark from the masses of the proton and neutron. 389 Chapter 54, section 5, The Cosmic Connection Conceptual 29 01 54:05, highSchool, numeric, < 1 min, normal. Part 1 of 2 In February 1987, a supernova was seen to explode in the Large Magellanic Cloud, a small galaxylike structure near the Milky way galaxy. The supernova was about 170000 light-years from Earth. How far away was this explosion? Part 2 of 2 If it were somehow possible for you to drive your car along some steller highway in the sky to the location of this explosion, how long would it take you to get there, assuming you drove at 100 km/h? Conceptual 29 02 54:05, highSchool, numeric, < 1 min, fixed. Using the Sun as a standard candle, calculate the distance from the Sun to Venus if the energy detected per square meter on Venus is 2.89 kW/m2 . The energy emitted by the Sun is 4.24 × 1023 kW. Conceptual 29 03 54:05, highSchool, numeric, < 1 min, fixed. Suppose that you observe a Cepheid variable to have a period of about 100 days and, hence, a luminosity of 6.4 × 1028 W. Suppose also that the amount of light you get from that star corresponds to an energy flow of about 2 × 10−14 W/m2 at the location of your telescope. How far is that star from Earth? Conceptual 29 04 54:05, highSchool, numeric, < 1 min, normal. 390 km , s · Mpc what is the approximate velocity of a galaxy 10 Mpc away? Assume a Hubble constant of 70 Conceptual 29 06 54:05, highSchool, numeric, < 1 min, normal. If a galaxy is 700 Mpc away, how fast is it receding from us? Conceptual 29 07 54:05, highSchool, numeric, < 1 min, fixed. Part 1 of 2 An observer on one of the raisins in our bread-dough analogy measures distances and velocities of neighboring raisins as follows Distance Velocity 0.5 cm 1.02 cm/h 0.9 cm 2 cm/h 1.4 cm 2.9 cm/h 2.1 cm 4.05 cm/h 3 cm 5.9 cm/h 3.4 cm 7.1 cm/h Plot the data on a graph and estimate the Hubble constant for the raisins. 1. 2 /h 2. 3 /h 3. 4 /h 4. 5 /h 5. 6 /h 6. 7 /h Part 2 of 2 Estimate the time that elapsed since the dough started rising. How many kilometers are in 2 parsec? Conceptual 29 05 54:05, highSchool, numeric, < 1 min, normal. Conceptual 29 09 54:05, highSchool, numeric, < 1 min, fixed. Part 1 of 2 Some theories say that during the inflama- Chapter 54, section 5, The Cosmic Connection tory period, the scale of the universe increased by a factor of 1050 . Suppose your height were to increase by a factor of 1050 . How tall would an average person of 1.5 meters tall be? Part 2 of 2 The observable universe is roughly 30 billion light years across. What fraction of the universe would your height be? 391 Conceptual 29 Q02 54:05, highSchool, multiple choice, < 1 min, fixed. If the universe is closed, what will a future Hubble see when he looks through a telescope during the period of contraction? 1. blueshift 2. redshift Conceptual 29 10 54:05, highSchool, numeric, < 1 min, fixed. Suppose a proton (diameter about 10−13 cm) were to inflate by a factor of 1050 . How big would it be? Conceptual 29 11 54:05, highSchool, numeric, < 1 min, normal. 4. None of these Conceptual 29 Q03 54:05, highSchool, multiple choice, < 1 min, fixed. Suppose that scientists were able to travel to a different universe. The figure shows a distance-versus-velocity graph for galaxies measured in two universes. Conceptual 29 Q01 54:05, highSchool, multiple choice, < 1 min, fixed. y Why does the Earth seem to be at the center of the Hubble expansion? Velocity How fast is a galaxy 5 billion light-years from Earth moving away from us? 3. All of these 1. Galaxies in every direction are moving away from the Earth according to the same Hubble constant. Our universe New universe Distance x Which universe is older? 2. Galaxies in every direction are moving toward the Earth according to the same Hubble constant. 1. Our universe 3. Galaxies in every direction are moving away from the Earth according to different Hubble constants. 3. Both are of the same age 4. Galaxies in every direction are moving toward the Earth according to different Hubble constants. 5. None of these 2. New universe Conceptual 29 Q04 54:05, highSchool, multiple choice, < 1 min, fixed. If a life form on a planet in a distant galaxy measured the Hubble constant from its loca- Chapter 54, section 5, The Cosmic Connection tion, how would it compare to the value measured from Earth? (Assume the same unit of measuremeant is used.) 392 54:05, highSchool, numeric, < 1 min, fixed. Conceptual 29 Q07 54:05, highSchool, multiple choice, < 1 min, fixed. Our galaxy moves relative to the blackbody background radiation with a speed of roughly 300 km/s. By how much is the frequency of this radiation shifted due to the movement in the direction towards the radiation at the peak frequency of the radiation? In the direction away from the radiation at this same peak frequency? It is possible to subtract the effect of the motion because its effect can be found for any direction. If the universe were expanding more rapidly that it presently is, the Hubble constant will Cosmology 08 54:05, highSchool, numeric, < 1 min, normal. 1. same 2. higher 3. lower We define the ratio 1. increase. Y= 2. decrease. 3. remain the same. Conceptual 29 Q08 54:05, highSchool, multiple choice, < 1 min, fixed. If all that you knew was the energy per square meter that the Sun radiated on the surface of the Earth, could you determine the distance from the Sun to Earth? MHe . MH + MHe This quantity is measured to be about 0.25. Neglect the binding energy of the nuclei involved as well as the difference between neutron and proton masses in order to express Y in terms of the proton mass and the numbers of helium and hydrogen nuclei in the universe; you should find that the proton mass cancels from the expression. Solve the equation you come up with in order to find the ratio of the number of helium nuclei to the number of hydrogen nuclei. 1. Yes; this is all information you need. 2. No; more information is necessary. Conceptual 29 Q09 54:05, highSchool, multiple choice, < 1 min, fixed. Galaxies moving towards us are called 1. redshifted 2. blueshifted 2. None of these Cosmology 07 Cosmology 14 54:05, highSchool, numeric, < 1 min, normal. We define Ω = ρ/ρc and Ω(t) = Ω(t0 ) Ω(t0 ) + (1 − Ω(t0 )) (R/R0 ) If Ω(t0 ) = 0.2 (t0 is now), what was Ω(tx ), where tx is the time the matter dominated epoch started, about 105 yr? Use the result that the radius of the universe has increased by a factor of 2000 since then. Galaxy distance from receding speed Chapter 54, section 5, The Cosmic Connection 54:05, highSchool, numeric, > 1 min, normal. Estimate the distance of a galaxy in units of light years which is moving at a speed 0.1 c away from us. Assume H = 80 × 103 m/s/Mpc. Galaxy speed 02 54:05, highSchool, numeric, > 1 min, normal. Estimate the distance of a galaxy in units of light years which is moving at a speed 0.1 c away from us. Assume H = 80 × 103 m/s/Mpc. Galaxy speed 54:05, highSchool, numeric, > 1 min, normal. Part 1 of 2 Based on the relativistic Doppler shift formula: 1+ v λ c , = λ 1− v c estimate the speed of a galaxy, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm. Part 2 of 2 Estimate the distance of this galaxy from us. Assume H = 80 × 103 m/s/Mpc. Galaxy speed from red shift 54:05, highSchool, numeric, > 1 min, normal. Based on the Doppler shift formula: λ = λ 1+ 1− v c v c , estimate the speed of a galaxy, if the wavelength of the hydrogen line, which is 434 nm on earth, is now shifted to 610 nm as it is emitted from the galaxy. How far away 54:05, highSchool, numeric, > 1 min, normal. A star exhibits a parallax of 0.28 seconds of arc. 393 Assume 1 parsec(pc) = 3.26 ly, where parsecs are parallax angles in seconds of arcs. How far away is it? Schwarzschild radius of a star 54:05, highSchool, numeric, > 1 min, normal. Determine the Schwarzschild radius of a star comparable to our Sun with a mass 1.99 × 1030 kg. Assume G = 6.67 × 10−11 in SI units. Chapter 54, section 6, Cosmic Background Radiation Conceptual 29 Q05 54:06, highSchool, multiple choice, < 1 min, fixed. Suppose that a new experiment showed that the wavelength of the cosmic background radiation were slightly shorter than its previosly measured value. How would that change our estimate of the average temperature of the universe? 1. The average temperature will be higher 2. The average temperature will be lower 3. The average temperature will remain the same Conceptual 29 Q06 54:06, highSchool, multiple choice, < 1 min, fixed. Why cannot nuclei or atoms form during enormously high temperatures? 1. The energy of collisions between particles is much greater than the binding energy of atoms or nuclei. 2. The energy of collisions between particles is much less than the binding energy of atoms or nuclei. 3. The energy of collisions between particles is equal to the binding energy of atoms or nuclei. 4. None of these 394 Chapter 54, section 8, The Big Bang Cosmology 06 54:08, highSchool, numeric, > 1 min, normal. How much time will have elapsed since the big bang when the temperature of the background blackbody radiation is dominated by radiation with wavelengths around 1 m? 395 ...
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This note was uploaded on 02/26/2012 for the course PHYSICS 302K taught by Professor Irenepolycarpou during the Spring '09 term at University of Texas at Austin.

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Chap_23_64+regular+physics - 8 August 2007 Homework Service...

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