RELATIVITY
33
EXERCISES
Section 33.2 Matter, Motion, and Ether
13. INTERPRET In this problem we are asked to take wind speed into consideration to calculate the travel time of NTERPRET an airplane. DEVELOP Since the velocities are small compared to c, we
FROM QUARKS TO THE COSMOS
39
EXERCISES
Section 39.1 Particles and Forces
17. INTERPRETThis problem is about finding the lifetime of a virtual photon by applying the uncertainty principle. DEVELOPIn order to test the conservation of energy in a process inv
MOTION IN A STRAIGHT LINE
2
x t
EXERCISES
Section 2.1 Average Motion
13. INTERPRET We need to find average speed, given distance and time. DEVELOP Speed is distance divided by time. EVALUATE ASSESS 14.
v=
100 m 9.77 s
= 10.2 m/s
His time is about 10 secon
NUCLEAR PHYSICS
38
EXERCISES
Section 38.1 Elements, Isotopes, and Nuclear Structure
13. INTERPRET This problem is about writing the conventional symbols for the isotopes of radon. A DEVELOP The conventional symbol for a nucleus X is Z X, where A is the ma
MOLECULES AND SOLIDS
37
2 2
EXERCISES
Section 37.2 Molecular Energy Levels
16. The energies of rotational states (above the j = 0 state) are given by Equation 37.2, where for the HCl molecule, 2 /I = 2.63 meV (from Example 37.1). Thus, Erot = l (l + 1) 2/
ATOMIC PHYSICS
36
Note: For the problems in this chapter, useful numerical values of Plancks constant, in SI and atomic units, are: h = 6.626 10 34 J s = 4.136 10 15 eV s = 1240 eV nm/c, and h = h/2 = 1.055 1034 J s = 6.582 10 16 eV s = 197.3 MeV fm/c. Us
QUANTUM MECHANICS
35
2
EXERCISES
Section 35.2 The Schrdinger Equation
10. The one-dimensional wave function is related to the probability by Equation 35.2, dP = 2 ( x)dx. Since probability (a pure number) is dimensionless, the units of must be the square
PARTICLES AND WAVES
34
EXERCISES
Section 34.2 Blackbody Radiation
15. INTERPRET This is a problem about blackbody radiation. We want to explore the connection between temperature and the radiated power. DEVELOP From the Stefan-Boltzmann law (Equation 34.1
INTERFERENCE AND DIFFRACTION
32
EXERCISES
Section 32.2 Double-Slit Interference
10. The experimental arrangement and geometrical approximations valid for Equation 32.2a are satisfied for the situation and data given, so = ybright d /mL = (7.1 cm/2.2 m)(15
IMAGES AND OPTICAL INSTRUMENTS
31
EXERCISES
Section 31.1 Images with Mirrors
17. INTERPRET This problem is about image formation in a plane mirror. DEVELOP A small mirror (M ) on the floor intercepts rays coming from a customers shoes (O), which are trave
REFLECTION AND REFRACTION
30
EXERCISES
Section 30.1 Reflection
12. Since 1 = 1 for specular reflection, (Equation 30.1) a reflected ray is deviated by = 180 21 from the incident direction. If rotating the mirror changes 1 by 1 , then the reflected ray is
MAXWELLS EQUATIONS AND ELECTROMAGNETIC WAVES
29
EXERCISES
Section 29.2 Ambiguity in Ampres Law
13. INTERPRET In this problem we are asked to find the displacement current through a surface. DEVELOP As shown in Equation 29.1, Maxwells displacement current
ALTERNATING-CURRENT CIRCUITS
28
EXERCISES
Section 28.1 Alternating Current
14. 15. Use of Equations 28.1 and 28.2 allows us to write Vp = 2 Vrms = 2(230 V) = 325 V, and = 2 f = 2 (50 Hz) = 314 s 1. Then the voltage expressed in the form of Equation 28.3 i
ELECTROMAGNETIC INDUCTION
27
EXERCISES
Sections 27.2 Faradays Law and 27.3 Induction and Energy
15. INTERPRET In this problem we are asked to verify that the SI unit of the rate of change of magnetic flux is volt. DEVELOP We first note that the left-hand-
MAGNETISM: FORCE AND FIELD
26
EXERCISES
Section 26.2 Magnetic Force and Field
17. INTERPRET This problem is about the magnetic force exerted on a moving electron. DEVELOP The magnetic force on a charge q moving with velocity v is given by Equation 26.1: F
ELECTRIC CIRCUITS
25
EXERCISES
Section 25.1 Circuits, Symbols, and Electromotive Force
14. A literal reading of the circuit specifications results in connections like those in sketch (a). Because the connecting wires are assumed to have no resistance (a r
ELECTRIC CURRENT
24
EXERCISES
Section 24.1 Electric Current
14. The current is the amount of charge passing a given point in the wire, per unit time, so in one second, 19 q = I t = (1.5 A)(1s) = 1.5 C. The number of electrons in this amount of charge is 1
ELECTROSTATIC ENERGY AND CAPACITORS
23
EXERCISES
Section 23.1 Electrostatic Energy
14. Number the charges qi = 50 C, i = 1, 2, 3, 4, as they are spaced along the line at a = 2 cm intervals. There are six pairs, so W = pairs kqi q j /rij = k (q1q2 /a + q1q
ELECTRIC POTENTIAL
22
EXERCISES
Section 22.1 Electric Potential Difference
16. The potential difference and the work per unit charge, done by an external agent, are equal in magnitude, so
W = qV = (50 C)(12 V) = 600 J. (Note: Since only magnitudes are nee
GAUSSS LAW
21
EXERCISES
Section 21.1 Electric Field Lines
18. The number of lines of force emanating from (or terminating on) the positive (or negative) charges is the same (14 in Fig. 21.31), so the middle charge is 3 C and the outer ones are +3 C. The n
ELECTRIC CHARGE, FORCE, AND FIELD
20
EXERCISES
Section 20.1 Electric Charge
14. Nearly all of the mass of an atom is in its nucleus, and about one half of the nuclear mass of the light elements in living matter (H, O, N, and C) is protons. Thus, the numbe
THE SECOND LAW OF THERMODYNAMICS
19
EXERCISES
Sections 19.2 and 19.3 The Second Law of Thermodynamics and Its Applications
14. The efficiency of a reversible engine, operating between two absolute temperatures, Th > Tc, is given by Equation 19.3. (a) e =
HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS
18
EXERCISES
Section 18.1 The First Law of Thermodynamics
15. INTERPRET We identify the system as the water in the insulated container. The problem is about work done to raise the temperature of a system. Th
THE THERMAL BEHAVIOR OF MATTER
17
EXERCISES
Section 17.1 Gases
18. The molar volume of an ideal gas at STP for the surface of Mars can be calculated as in Example 17.1. However, expressing the ideal gas law for 1 mole of gas at the surfaces of Mars and Ea
TEMPERATURE AND HEAT
16
TF =
EXERCISES
Section 16.1 Heat, Temperature, and Thermodynamic Equilibrium
14. We assume that the U.S. meteorologist predicts the same temperature, but expresses it on the Fahrenheit scale (Equation 16.2): TF = 9 (15) + 32 = 5 F.
FLUID MOTION
15
V2 V1 mtot m1 + m2 1V1 + 2V2 = 1 = = + 2 Vtot V1 + V2 V1 + V2 V1 + V2 V1 + V2
EXERCISES
Section 15.1 Density and Pressure
16. The mass of molasses, which occupies a volume equal to the capacity of the jar, is m = V = (1600 kg /m 3 ) (0.7
WAVE MOTION
14
v=
EXERCISES
Section 14.1 Waves and Their Properties
16. Wave crests (adjacent wavefronts) take a time of one period to pass a fixed point, traveling at the wave speed (or phase velocity) for a distance of one wavelength. Thus T = /v = 18 m
OSCILLATORY MOTION
13
1 1 = = 2.27 10 3 s f 440 Hz
EXERCISES
Section 13.1 Describing Oscillatory Motion
16. 17. T = 1/f = 1/440 Hz = 2.27 ms (Equation 13.1). INTERPRET The question here is about the oscillatory behavior of the violin string. Given the fre
STATIC EQUILIBRIUM
12
2
EXERCISES
Section 12.1 Conditions for Equilibrium 14.
(a) Fi = (2i + 2 2i 3 + ) N = 0. j jj (b) ( i )0 = [2i (2i + 2 j ) + ( i ) (2i 3 j ) + ( 7i + j ) j ] N m = (4 + 3 7)k N m = 0.
INTERPRET We have been told that the choice of p
ROTATIONAL VECTORS AND ANGULAR MOMENTUM
11
EXERCISES
Section 11.1 Angular Velocity and Acceleration Vectors
12. If we assume that the wheels are rolling without slipping (see Section 10.5), the magnitude of the angular velocity is = v cm /r = (70 m/ 3.6 s