Lecture notes on Applied Physics

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SCHAUM’SEasy OUTLINES APPLIEDPHYSICSOther Books in Schaum’s Easy Outlines Series Include: Schaum’s Easy Outline: Calculus Schaum’s Easy Outline: College Algebra Schaum’s Easy Outline: College Mathematics Schaum’s Easy Outline: Discrete Mathematics Schaum’s Easy Outline: Differential Equations Schaum’s Easy Outline: Elementary Algebra Schaum’s Easy Outline: Geometry Schaum’s Easy Outline: Linear Algebra Schaum’s Easy Outline: Mathematical Handbook of Formulas and Tables Schaum’s Easy Outline: Precalculus Schaum’s Easy Outline: Probability and Statistics Schaum’s Easy Outline: Statistics Schaum’s Easy Outline: Trigonometry Schaum’s Easy Outline: Business Statistics Schaum’s Easy Outline: Principles of Accounting Schaum’s Easy Outline: Principles of Economics Schaum’s Easy Outline: Biology Schaum’s Easy Outline: Biochemistry Schaum’s Easy Outline: Molecular and Cell Biology Schaum’s Easy Outline: College Chemistry Schaum’s Easy Outline: Genetics Schaum’s Easy Outline: Human Anatomy and Physiology Schaum’s Easy Outline: Organic Chemistry Schaum’s Easy Outline: Physics Schaum’s Easy Outline: Programming with C++ Schaum’s Easy Outline: Programming with Java Schaum’s Easy Outline: Basic Electricity Schaum’s Easy Outline: Electromagnetics Schaum’s Easy Outline: Introduction to Psychology Schaum’s Easy Outline: French Schaum’s Easy Outline: German Schaum’s Easy Outline: Spanish Schaum’s Easy Outline: Writing and GrammarSCHAUM’SEasy OUTLINES APPLIEDPHYSICS Based on Schaum’s Outline of Theory and Problems of Applied Physics (Third Edition) by Arthur Beiser, Ph.D. Abridgement Editor George J. Hademenos, Ph.D. SCHAUM’S OUTLINE SERIES McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney TorontoCopyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be repro- duced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior writ- ten permission of the publisher. 0-07-142585-3 The material in this eBook also appears in the print version of this title: 0-07-139878-3. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occur- rence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. 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Contents Chapter 1 Vectors 1 Chapter 2 Motion 11 Chapter 3 Newton’s Laws of Motion 19 Chapter 4 Energy 28 Chapter 5 Momentum 33 Chapter 6 Circular Motion and Gravitation 37 Chapter 7 Rotational Motion 41 Chapter 8 Equilibrium 51 Chapter 9 Simple Harmonic Motion 58 Chapter 10 Waves and Sound 64 Chapter 11 Electricity 70 Chapter 12 Electric Current 75 Chapter 13 Direct-Current Circuits 80 Chapter 14 Capacitance 86 Chapter 15 Magnetism 93 Chapter 16 Electromagnetic Induction 102 Chapter 17 Light 108 Chapter 18 Spherical Mirrors 118 Chapter 19 Lenses 124 Chapter 20 Physical and Quantum Optics 131 Index 135 v Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.This page intentionally left blank.Chapter 1 Vectors In This Chapter: ✔ Scalar and Vector Quantities ✔ Vector Addition: Graphical Method ✔ Trigonometry ✔ Pythagorean Theorem ✔ Vector Addition: Trigonometric Method ✔ Resolving a Vector ✔ Vector Addition: Component Method Scalar and Vector Quantities A scalar quantity has only magnitude and is completely specified by a number and a unit. Examples are mass (a stone has a mass of 2 kg), vol- ume (a bottle has a volume of 1.5 liters), and frequency (house current has a frequency of 60 Hz). Scalar quantities of the same kind are added by using ordinary arithmetic. A vector quantity has both magnitude and di- rection. Examples are displacement (an airplane has flown 200 km to the southwest), velocity (a car is moving 60 km/h to the north), and force (a person 1 Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.2 APPLIED PHYSICS applies an upward force of 25 newtons to a package). Symbols of vector quantities are printed in boldface type (v = velocity, F = force). When vec- tor quantities of the same kind are added, their directions must be taken into account. Vector Addition: Graphical Method A vector is represented by an arrow whose length is proportional to a cer- tain vector quantity and whose direction indicates the direction of the quantity. To add vector B to vector A, draw B so that its tail is at the head of A. The vector sum A + B is the vector R that joins the tail of A and the head of B (Figure 1-1). Usually, R is called the resultant of A and B. The order in which A and B are added is not significant, so that A + B = B + A (Figures 1-1 and 1-2). Figure 1-1 Figure 1-2 Exactly the same procedure is followed when more than two vectors of the same kind are to be added. The vectors are strung together head to tail (being careful to preserve their correct lengths and directions), and the resultant R is the vector drawn from the tail of the first vector to the head of the last. The order in which the vectors are added does not mat- ter (Figure 1-3).CHAPTER 1: Vectors 3 Figure 1-3 Solved Problem 1.1 A woman walks eastward for 5 km and then north- ward for 10 km. How far is she from her starting point? If she had walked directly to her destination, in what direction would she have headed? Solution. From Figure 1-4, the length of the resultant vector R corre- sponds to a distance of 11.2 km, and a protractor shows that its direction is 27 east of north. Figure 1-4 Trigonometry Although it is possible to determine the magnitude and direction of the resultant of two or more vectors of the same kind graphically with ruler or protractor, this procedure is not very exact. For accurate results, it is necessary to use trigonometry.4 APPLIED PHYSICS A right triangle is a triangle whose two sides are perpendicular. The hypotenuse of a right triangle is the side opposite the right angle, as in Figure 1-5; the hypotenuse is always the longest side. a sin q = c b cos q = c a tan q = b 22 2 ab+=c Figure 1-5 The three basic trigonometric functions—the sine, cosine, and tan- gent of an angle—are defined in terms of the right triangle of Figure 1-5 as follows: a opposite side sin q== c hypotenuse b adjacent side cos q== c hypotenuse a opposite side sin q tan q== = b adjacent side cosq The inverse of a trigonometric function is the angle whose function is given. Thus the inverse of sin q is the angle q. The names and abbre- viations of the inverse trigonometric functions are as follows: sin q = x −1 q== arcsinsin xx= angle whose sine is x cos q = y −1 q== arccos yy cos= angle whose cosine is y tanq = z −1 q== arctantan zz= angle whose tangent is zCHAPTER 1: Vectors 5 Remember In trigonometry, an expression such −1 as sin x does not signify 1/(sin x), even though in algebra, the expo- nent −1 signifies a reciprocal. Pythagorean Theorem The Pythagorean theorem states that the sum of the squares of the short sides of a right triangle is equal to the square of its hypotenuse. For the triangle of Figure 1-5, 2 2 2 a + b = c Hence, we can always express the length of any of the sides of a right tri- angle in terms of the lengths of the other sides: 22 2 2 22 ac=−b b=−c a c=a+b Another useful relationship is that the sum of the interior angles of any triangle is 180°. Since one of the angles in a right triangle is 90°, the sum of the other two must be 90°. Thus, in Figure 1-5, q +f = 90°. Of the six quantities that characterize a triangle—three sides and three angles—we must know the values of at least three, including one of the sides, in order to calculate the others. In a right triangle, one of the angles is always 90°, so all we need are the lengths of any two sides or the length of one side plus the value of one of the other angles to find the other sides and angles. Solved Problem 1.2 Find the values of the sine, cosine, and tangent of angleq in Figure 1-6.6 APPLIED PHYSICS Figure 1-6 Solution. opposite side 3 cm sin.q===06 hypotenuse 5 cm adjacent side 4 cm cos q===08 . hypotenuse 5 cm opposite side 3 cm tan.q===075 adjacent side 4 cm Vector Addition: Trigonometric Method It is easy to apply trigonometry to find the resultant R of two vectors A and B that are perpendicular to each other. The magnitude of the resul- tant is given by the Pythagorean theorem as: 22 RA=+B and the angle between R and A (Figure 1-7) may be found from B tan q = A by examining a table of tangents or by using a calculator to determine B −1 tan . ACHAPTER 1: Vectors 7 Figure 1-7 Resolving a Vector Just as two or more vectors can be added to yield a single resultant vec- tor, so it is possible to break up a single vector into two or more other vec- tors. If vectors A and B are together equivalent to vector C, then vector C is equivalent to the two vectors A and B (Figure 1-8). When a vector is replaced by two or more others, the process is called resolving the vec- tor, and the new vectors are known as the components of the initial vec- tor. Figure 1-8 The components into which a vector is resolved are nearly always chosen to be perpendicular to one another. Figure 1-9 shows a wagon be- ing pulled by a man with force F. Because the wagon moves horizontal- ly, the entire force is not effective in influencing its motion.8 APPLIED PHYSICS Figure 1-9 The force F may be resolved into two component vectors F and F , x y where F = horizontal component of F x F = vertical component of F y The magnitudes of these components are FF== cosqq F Fsin xy Evidently, the component F is responsible for the wagon’s motion, and x if we were interested in working out the details of this motion, we would need to consider only F . x In Figure 1-9, the force F lies in a vertical plane, and the two com- ponents F and F are enough to describe it. In general, however, three x y mutually perpendicular components are required to completely describe the magnitude and direction of a vector quantity. It is customary to call the directions of these components the x, y, and z axes, as in Figure 1-10. The component of some vector A in these directions are accordingly de- noted A , A , and A . If a component falls on the negative part of an axis, x y z its magnitude is considered negative. Thus, if A were downward in Fig- z ure 1-10 instead of upward and its length were equivalent to, say, 12 N, we would write A =−12 N. (The newton (N) is the SI unit of force; it is z equal to 0.225 lb.)CHAPTER 1: Vectors 9 Figure 1-10 Solved Problem 1.3 The man in Figure 1-9 exerts a force of 100 N on the wagon at an angle of q = 30° above the horizontal. Find the horizon- tal and vertical components of this force. Solution. The magnitudes of F and F are, respectively, x y FF== cosq() 100 N() cos 30° = 86.6 N x FF== q.() 100 N() 30° = 50 0 N y We note that F + F = 136.6 N although F itself has the magnitude F = x y 100 N. What is wrong? The answer is that nothing is wrong; because F x and F are just the magnitudes of the vectors F and F , it is meaningless y x y to add them. However, we can certainly add the vectors F and F to find x y the magnitude of their resultant F. Because F and F are perpendicular, x y 22 2 2 FF=+F=() 86.. 6 N +() 50 0 N = 100 N xy as we expect. sinsin10 APPLIED PHYSICS Vector Addition: Component Method When vectors to be added are not perpendicular, the method of addition by components described below can be used. There do exist trigonometric procedures for dealing with oblique triangles (the law of sines and the law of cosines), but these are not necessary since the component method is entirely general in its application. To add two or more vectors A, B, C, … by the component method, follow this procedure: 1. Resolve the initial vectors into components in the x, y, and z di- rections. 2. Add the components in the x direction to give R , add the com- x ponents in the y direction to give R , and add the components in y the z direction to give R . That is, the magnitudes of R , R , and z x y R are given by, respectively, z RA=+B+C+L xx x x RA=+B+C+L yy y y RA=+B+C+L zz z z 3. Calculate the magnitude and direction of the resultant R from its components R , R , and R by using the Pythagorean theorem: x y z 222 R=+ RRR+ xy z If the vectors being added all lie in the same plane, only two components need to be considered.Chapter 2 Motion In This Chapter: ✔ Velocity ✔ Acceleration ✔ Distance, Velocity, and Acceleration ✔ Acceleration of Gravity ✔ Falling Bodies ✔ Projectile Motion Velocity The velocity of a body is a vector quantity that describes both how fast it is moving and the direction in which it is headed. In the case of a body traveling in a straight line, its velocity is sim- ply the rate at which it covers distance. The average velocity ¯ v of such a body when it covers the distance s in the time t is s v = t distance Average velocity = time The average velocity of a body during the time t does not complete- ly describe its motion, however, because during the time t, it may some- 11 Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.12 APPLIED PHYSICS times have gone faster than ¯ v and sometimes slower. The velocity of a body at any given moment is called its instantaneous velocity and is giv- en by ∆ s v = inst ∆ t Here,Ds is the distance the body has gone in the very short time interval Dt at the specified moment. (D is the capital Greek letter delta.) Instanta- neous velocity is what a car’s speedometer indicates. When the instantaneous velocity of a body does not change, it is moving at constant velocity. For the case of constant velocity, the basic formula is sv = t Distance = (constant velocity)(time) Solved Problem 2.1 The velocity of sound in air at sea level is about 343 m/s. If a person hears a clap of thunder 3.00 s after seeing a lightning flash, how far away was the lightning? Solution. The velocity of light is so great compared with the velocity of sound that the time needed for the light of the flash to reach the person can be neglected. Hence s = vt = (343 m/s)(3.00 s) = 1029 m = 1.03 km Acceleration A body whose velocity is changing is accelerated. A body is accelerated when its velocity is increasing, de- creasing, or changing its direction. The acceleration of a body is the rate at which its velocity is changing. If a body moving in a straight line has a velocity of v at the start of a certain time interval 0 t and of v at the end, its acceleration is

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