P161Chapter_01 - Physics for Scientists and Engineers...

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Unformatted text preview: Physics for Scientists and Engineers Newton's Laws Concepts of Motion Chapter 1 Register Your Clicker https://www.clickers.umd.edu:8443/keypads.html Currently, the ELMS gradebook is treating uppercase "E" as a mathematical notation when combined in certain ways with numbers. Try converting the uppercase "E" to a lowercase "e" in the IDs that contain them. Make sure you enter an o or O in the clicker ID. Setting the Channel Number on Your Clicker For Phys 1412 use Channel 50 http://clickers.umd.edu/resources/docs/students/setting_channel.html What is this course? 25% 25% 25% 25% 1. 2. 3. 4. PHYS121 PHYS161 PHYS262 PHYS270 2 12 16 YS PH PH PH YS YS YS PH 27 0 1 1 26 Physics n Fundamental Science n n concerned with the basic principles of the Universe foundation of other physical sciences Classical Mechanics Relativity Thermodynamics Electromagnetism Optics Quantum Mechanics n Divided into five major areas n n n n n n Classical Physics n n Mechanics and electromagnetism are basic to all other branches of classical physics Classical physics developed before 1900 n Our study will start with Classical Mechanics n Also called Newtonian Mechanics Classical Physics, cont n Includes Mechanics n Major developments by Newton, and continuing through the latter part of the 19th century n n n Thermodynamics Optics Electromagnetism n All of these were not developed until the latter part of the 19th century Modern Physics n n n Began near the end of the 19th century Phenomena that could not be explained by classical physics Includes theories of relativity and quantum mechanics Classical Mechanics Today n n n n Still important in many disciplines Wide range of phenomena that can be explained with classical mechanics Many basic principles carry over into other phenomena Conservation Laws also apply directly to other areas Objective of Physics n n n To find the limited number of fundamental laws that govern natural phenomena To use these laws to develop theories that can predict the results of future experiments Express the laws in the language of mathematics Theory and Experiments n n Should complement each other When a discrepancy occurs, theory may be modified n Theory may apply to limited conditions n Example: Newtonian Mechanics is confined to objects n n 1)traveling slowly with respect to the speed of light and 2) larger than atoms n Try to develop a more general theory Model Building n n A model is often a simplified system of physical components Identify the components n Make predictions about the behavior of the system n n The predictions will be based on interactions among the components and/or Based on the interactions between the components and the environment Models of Matter n Greeks thought matter is made of atoms n n JJ Thomson (1897) discovered electrons Rutherford (1911) showed atoms had a central nucleus surrounded by electrons Models of Matter, cont n Nucleus has structure, containing protons and neutrons n n Number of protons gives atomic number Number of protons and neutrons gives mass number n Protons and neutrons are made up of quarks n Are quarks composed of other particles? Particle Model n n n n Will not consider the details of a large object like an automobile Consider the large object to be a point sized particle containing the mass of the large object. Describe the motion of the point particle If more detailed results are needed modify the effects on the point particle, e.g. compute air drag on an auto and use the drag force on the particle. Kinematics n n Describes motion while ignoring the agents(Forces) that caused the motion For now, will consider motion in one dimension n Along a straight line A particle is a point-like object, has mass but infinitesimal size n Will use the particle model n Position n Defined in terms of a frame of reference n One dimensional, so generally the x- or y-axis n The object's position is its location with respect to the frame of reference (Rear wheel) A =28 m B = 50 C = 36 D=0 E = -40 f = -55 Position-Time Graph n n The position-time graph shows the motion of the particle (car) The smooth curve is a guess as to what happened between the data points 1-D Displacement n Defined as the change in position during some time interval n Represented as Dx Dx = xf - xi SI units are meters (m) Dx can be positive or negative n Dx is different than distance, which is the length of a path followed by a particle - see graph 2-D Displacement n A particle travels from A to B along the path shown by the dotted red line n This is the distance traveled and is a scalar n The displacement is the solid line from A to B n n The displacement is independent of the path taken between the two points Displacement is a vector Vectors and Scalars n Vector quantities need both magnitude (size or numerical value) and direction to completely describe them n Will use + and signs to indicate vector directions n Scalar quantities are completely described by magnitude only Adding Vectors 2-D Displacement of Sam r0 = initial position vector r1 = final position vector Dr = displacement vector r r r r1 = r0 + Dr Speed Speed is a scalar quantity, i.e. it does not have a direction. distance traveled average speed = time interval spent traveling 18. m average speed = = 0.60m / s 30. s Velocity r r Dr v avg = Dt Because v is a vector it has both a magnitude, i.e. the speed, and a direction, i.e. the direction of r Dr Velocity Vectors Relating Position to Velocity r r r Dr = r2 - r1 r r Dr v= Dt r v r r2 = r1 + vDt Acceleration r r Dv a= Dt Velocity can change in three ways both giving an acceleration: 1) The magnitude can change, i.e. speed changes or 2) the direction of the velocity vector changes or 3) both speed and direction change Uniform Circular Motion Acceleration in UCM r r Dv a= Dt r r r Dv = v f - v i r r r v f = v i + aDt Throwing a Ball Acceleration due to Gravity r r Dv a= Dt r r r Dv = v f - v i r r r v f = v i + aDt A particle undergoes acceleration while moving from point 1 to point 2. Which of the choices shows the velocity vector as the object moves away from point 2? A particle undergoes acceleration while moving from point 1 to point 2. Which of the choices shows the velocity vector as the object moves away from point 2? Quantities Used n In mechanics, three basic quantities are used n n n Length Mass Time These are other quantities can be expressed in terms of basic quantities n Will also use derived quantities n Systems of Measurements n US System of measurement n everyday units n n n Length is measured in feet Time is measured in seconds Mass is measured in slugs n often uses weight, in pounds, instead of mass as a fundamental quantity Standards of Quantities n SI Systme International n n agreed to in 1960 by an international committee main system used in this text Length n Units n SI meter, m n n Previously defined in terms of a standard meter bar. Now defined by the distance traveled by light in a vacuum during a given period of time. Mass n Units n SI kilogram, kg n n Based on a specific cylinder kept at the International Bureau of Standards See Table 1.2 for masses of various objects Standard Kilogram Time n Units n seconds, s n Defined in terms of the oscillation of radiation from a cesium atom Prefixes n n n Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation Prefixes, cont. n n n The prefixes can be used with any base units They are multipliers of the base unit Examples: n n 2 mm = 2X10-3 m 3 g = 3X10-3 kg Derived Quantities n Contain combinations of the fundamental quantities of length, mass and time Density n n Density is an example of a derived quantity It is defined as mass per unit volume n Units are kg/m3 n n n water r 1,000 kg/m3 air r 1.2 kg/m3 lead r 11,300 kg/m3 Densities Average Density of the Earth? n The radius is Re = 6.37 x 106 m, hence the volume is V = p (6.37 10 ) = 1.08 10 m 4 3 r= 6 3 21 3 The mass is 5.98 x 1024 kg (from orbit observations) therefore the density is : M e 5.98 10 24 kg 3 3 r= = = 5.54 10 kg /m 21 3 Ve 1.08 10 m Average Density of the Earth n n The density of granite on the earth's surface is 2.75 x 103 kg/m3. What does this tell us about the interior of the earth? Atomic Mass n n The atomic mass is the total number of protons and neutrons in the element Often measured in atomic mass units, u (or amu), the mass of a proton. Note electron masses are negligable compared with 1 amu n 1 u = 1.6605387 x 10-27 kg Basic Quantities and Their Dimension n n Here by dimension we mean how a quantity depends on L,M & T it denotes the physical nature of a quantity not its size Dimensions are denoted with square brackets n n n Length [L] Mass [M] Time [T] Dimensional Analysis n n Technique to check the correctness of an equation or to assist in deriving an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities n add, subtract, multiply, divide n Both sides of equation must have the same dimensions Dimensional Analysis, cont. n n Cannot give numerical factors: this is its limitation Dimensions of some common quantities are given below Symbols n n The symbol used in an equation is not necessarily the symbol used for its dimension Some quantities have one symbol used consistently n For example, time is t virtually everywhere n Some quantities have many symbols used, depending upon the specific situation n For example, lengths may be x, y, z, r, d, h, etc. Dimensional Analysis n n Given the equation: x = 1/2 at 2 Check dimensions on each side to see if it might be correct: n The T2's cancel, leaving L for the dimensions of each side n n The equation is dimensionally correct There are no dimensions for the constant 1/2 Conversion of Units n n n When units are not consistent, you may need to convert to appropriate ones, e.g. ft to m Units can be treated like algebraic quantities that can cancel each other out See the inside of the front cover for an extensive list of conversion factors Conversion n n n Always include units for every quantity, when you do a calculation you can carry the units through the entire calculation Multiply original value by a ratio equal to one, e.g. 12in/1ft = 1 Example 15.0 in = ? cm Conversion Table (Front Cover) 1 in = 2.54 cm Reasonableness of Results n n When solving a problem, you need to check your answer to see if it seems reasonable, e.g. a car going 106 m/s is not reasonable Make an order of magnitude "guess" to estimate what the answer should be. Order of Magnitude n A way to approximate a solution to a problem based on a number of simple assumptions Order of magnitude is the power of 10 that applies, e.g. order of magnitude of 20 is 10, 300 is 102, 700 = 103 etc. n How Many Ping Pong Balls can fit in an average room? n n n Take an average room size as 20ft x 15ft x 8ft. Vroom 103 ft3 The radius of a ping pong ball is about half an inch. Vball (.1ft)3=10-3 ft3 The ballpark estimate for the number N of balls that could fit in a room is: N Vball Vroom N 106 Significant Figures n n A significant figure is one that is reliably known Zeros may or may not be significant n n Those used to position the decimal point are not significant To remove ambiguity, use scientific notation n In a measurement, the significant figures include the first estimated digit Significant Figures, examples n 0.0075 m has 2 significant figures n n The leading zeros are placeholders only Can write in scientific notation to show more clearly: 7.5 x 10-3 m for 2 significant figures The decimal point gives information about the reliability of the measurement Use 1.5 x 103 m for 2 significant figures Use 1.50 x 103 m for 3 significant figures Use 1.500 x 103 m for 4 significant figures n 10.0 m has 3 significant figures n n 1500 m is ambiguous n n n Operations with Significant Figures Multiplying or Dividing n n When multiplying or dividing, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures. Example: 25.57 m x 2.45 m = 62.6 m2 n The 2.45 m limits your result to 3 significant figures Operations with Significant Figures Adding or Subtracting n n When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum. Example: 135 cm + 3.25 cm = 138 cm n The 135 cm limits your answer to the units decimal value Operations With Significant Figures Summary n n n The rule for addition and subtraction are different than the rule for multiplication and division For adding and subtracting, the number of decimal places is the important consideration For multiplying and dividing, the number of significant figures is the important consideration Rounding Off Numbers n n n n Last retained digit is increased by 1 if the last digit dropped is 5 or above, e.g. 1.36 -> 1.4 Last retained digit remains as it is if the last digit dropped is less than 5 , e.g. 1.34 ->1.3 If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number, 1.35 -> 1.4, Saving rounding until the final result will help eliminate accumulation of errors Measurement Uncertainity n When measurements are made there is always an uncertainty n n Example: a rectangular plate is measured to have dimensions n L = 5.5 .1 m and n W = 6.4 .1 m This can be expressed as percentages n L = 5.5 1.8% [1.8 =100 (.1/5.5)] n W = 6.4 1.6% Propagation of Uncertainty n When measured quantities are multiplied or divided the total uncertainty is the sum of the individual percentage uncertainties n Area = L x W=(5.5m 1.8%)(6.4m1.6%) = 35m23.4% Propagation of Uncertainty n When measured quantities are added or subtracted the absolute uncertainties are added n W - L = (6.4m0.1m) - (5.5m0.1m) = 0.9m 0.2m ...
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