MATHEMATICAL FORMULAS* Quadratic Formula Derivatives and Integrals (cid:3) Ifax2(cid:4)bx(cid:4)c(cid:3)0,thenx(cid:3) (cid:5)b(cid:6) 1b2(cid:5)4ac d sin x(cid:3)cosx sinxdx(cid:3)(cid:5)cosx 2a dx (cid:3) d Binomial Theorem cos x(cid:3)(cid:5)sinx cosxdx(cid:3)sinx dx (1(cid:4)x)n(cid:3)1(cid:4) nx (cid:4) n(n(cid:5)1)x2 (cid:4) ... (x2(cid:9)1) (cid:3) 1! 2! d ex(cid:3)ex exdx(cid:3)ex dx (cid:3) Products of Vectors dx (cid:3)ln(x(cid:4) 2x2(cid:4)a2) Letube the smaller of the two angles betweena:andb:. (cid:3) 2x2(cid:4)a2 Then xdx 1 (cid:3)(cid:5) a:(cid:2)b:(cid:3) b:(cid:2)a:(cid:3) ab (cid:4) ab (cid:4) ab (cid:3) abcosu (x2(cid:4)a2)3/2 (x2(cid:4)a2)1/2 x x y y z z (cid:3) (cid:2) (cid:2) dx (cid:3) x ˆi ˆj kˆ (x2(cid:4)a2)3/2 a2(x2(cid:4)a2)1/2 :a (cid:8):b (cid:3)(cid:5):b (cid:8) :a (cid:3) a a a x y z Cramer’s Rule b b b x y z (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) Two simultaneous equations in unknowns xandy, a a a a a a (cid:3)ˆi y z (cid:5)ˆj x z (cid:4)kˆ x y ax(cid:4)b y(cid:3)c and ax(cid:4)b y(cid:3)c, b b b b b b 1 1 1 2 2 2 y z x z x y have the solutions (cid:3)(ab (cid:5)b a)iˆ (cid:4)(ab (cid:5)ba)ˆj (cid:4)(ab (cid:5)ba)kˆ y z y z z x z x x y x y (cid:2) (cid:2) c b 1 1 |:a (cid:8):b|(cid:3)ab sin u x(cid:3) (cid:2)c2 b2(cid:2) (cid:3) c1b2(cid:5)c2b1 a b ab (cid:5)ab 1 1 1 2 2 1 a b 2 2 Trigonometric Identities and (cid:2) (cid:2) sina(cid:6)sinb(cid:3)2 sin 1(a(cid:6)b) cos 1(a(cid:7)b) a c 2 2 1 1 y(cid:3) (cid:2)a2 c2(cid:2) (cid:3) a1c2(cid:5)a2c1 . cosa(cid:4)cosb(cid:3)2 cos 1(a(cid:4)b) cos 1(a(cid:5)b) a b ab (cid:5)ab 2 2 1 1 1 2 2 1 a b 2 2 *See Appendix E for a more complete list. SI PREFIXES* Factor Prefix Symbol Factor Prefix Symbol 1024 yotta Y 10–1 deci d 1021 zetta Z 10–2 centi c 1018 exa E 10–3 milli m 1015 peta P 10–6 micro m 1012 tera T 10–9 nano n 109 giga G 10–12 pico p 106 mega M 10–15 femto f 103 kilo k 10–18 atto a 102 hecto h 10–21 zepto z 101 deka da 10–24 yocto y *In all cases,the first syllable is accented,as in ná-no-mé-ter. E X T E N D E D FUNDAMENTALS OF PHYSICS T E N T H E D I T I O N This page intentionally left blank E X T E N D E D Halliday & Resnick FUNDAMENTALS OF PHYSICS T E N T H E D I T I O N J EAR L WALK E R CLEVELAND STATE UNIVERSITY EXECUTIVE EDITOR Stuart Johnson SENIOR PRODUCT DESIGNER Geraldine Osnato CONTENT EDITOR Alyson Rentrop ASSOCIATE MARKETING DIRECTOR Christine Kushner TEXT and COVER DESIGNER Madelyn Lesure PAGE MAKE-UP Lee Goldstein PHOTO EDITOR Jennifer Atkins COPYEDITOR Helen Walden PROOFREADER Lilian Brady SENIOR PRODUCTION EDITOR Elizabeth Swain COVER IMAGE © 2007 CERN This book was set in 10/12 Times Ten by cMPreparé,CSR Francesca Monaco,and was printed and bound by Quad Graphics.The cover was printed by Quad Graphics. This book is printed on acid free paper. Copyright © 2014,2011,2008,2005 John Wiley & Sons,Inc.All rights reserved. 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QC21.3.H35 2014 530—dc23 2012035307 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 B R I E F C O N T E N T S V O L U M E 1 V O L U M E 2 1 Measurement 21 Coulomb’s Law 2 Motion Along a Straight Line 22 Electric Fields 3 Vectors 23 Gauss’ Law 4 Motion in Two and Three Dimensions 24 Electric Potential 5 Force and Motion—I 25 Capacitance 6 Force and Motion—II 26 Current and Resistance 7 Kinetic Energy and Work 27 Circuits 8 Potential Energy and Conservation of Energy 28 Magnetic Fields 9 Center of Mass and Linear Momentum 29 Magnetic Fields Due to Currents 10 Rotation 30 Induction and Inductance 11 Rolling, Torque, and Angular Momentum 31 Electromagnetic Oscillations and Alternating Current 12 Equilibrium and Elasticity 32 Maxwell’s Equations; Magnetism of Matter 13 Gravitation 33 Electromagnetic Waves 14 Fluids 34 Images 15 Oscillations 35 Interference 16 Waves—I 36 Diffraction 17 Waves—II 37 Relativity 18 Temperature, Heat, and the First Law of Thermodynamics 38 Photons and Matter Waves 19 The Kinetic Theory of Gases 39 More About Matter Waves 20 Entropy and the Second Law of Thermodynamics 40 All About Atoms 41 Conduction of Electricity in Solids 42 Nuclear Physics 43 Energy from the Nucleus 44 Quarks, Leptons, and the Big Bang Appendices / Answers to Checkpoints and Odd-Numbered Questions and Problems / Index v C O N T E N T S 1Measurement 1 Adding Vectors by Components 46 1-1 MEASURING THINGS, INCLUDING LENGTHS 1 Vectors and the Laws of Physics 47 What Is Physics? 1 3-3 MULTIPLYING VECTORS 50 Measuring Things 1 Multiplying Vectors 50 The International System of Units 2 Changing Units 3 REVIEW & SUMMARY 55 QUESTIONS 56 PROBLEMS 57 Length 3 Significant Figures and Decimal Places 4 4 Motion in Two and Three Dimensions 62 1-2 TIME 5 4-1 POSITION AND DISPLACEMENT 62 Time 5 What Is Physics? 62 Position and Displacement 63 1-3 MASS 6 Mass 6 4-2 AVERAGE VELOCITY AND INSTANTANEOUS VELOCITY 64 REVIEW & SUMMARY 8 PROBLEMS 8 Average Velocity and Instantaneous Velocity 65 2 Motion Along a Straight Line 13 4-3 AVERAGE ACCELERATION AND INSTANTANEOUS ACCELERATION 67 2-1 POSITION, DISPLACEMENT, AND AVERAGE VELOCITY 13 Average Acceleration and Instantaneous Acceleration 68 What Is Physics? 13 4-4 PROJECTILE MOTION 70 Motion 14 Projectile Motion 70 Position and Displacement 14 Average Velocity and Average Speed 15 4-5 UNIFORM CIRCULAR MOTION 76 Uniform Circular Motion 76 2-2 INSTANTANEOUS VELOCITY AND SPEED 18 Instantaneous Velocity and Speed 18 4-6 RELATIVE MOTION IN ONE DIMENSION 78 Relative Motion in One Dimension 78 2-3 ACCELERATION 20 Acceleration 20 4-7 RELATIVE MOTION IN TWO DIMENSIONS 80 Relative Motion in Two Dimensions 80 2-4 CONSTANT ACCELERATION 23 REVIEW & SUMMARY 81 QUESTIONS 82 PROBLEMS 84 Constant Acceleration: A Special Case 23 Another Look at Constant Acceleration 26 5 Force and Motion—I 94 2-5 FREE-FALL ACCELERATION 27 Free-Fall Acceleration 27 5-1 NEWTON’S FIRST AND SECOND LAWS 94 What Is Physics? 94 2-6 GRAPHICAL INTEGRATION IN MOTION ANALYSIS 29 Newtonian Mechanics 95 Graphical Integration in Motion Analysis 29 Newton’s First Law 95 REVIEW & SUMMARY 30 QUESTIONS 31 PROBLEMS 32 Force 96 Mass 97 3 Vectors 40 Newton’s Second Law 98 3-1 VECTORS AND THEIR COMPONENTS 40 5-2 SOME PARTICULAR FORCES 102 What Is Physics? 40 Vectors and Scalars 40 Some Particular Forces 102 Adding Vectors Geometrically 41 5-3 APPLYING NEWTON’S LAWS 106 Components of Vectors 42 Newton’s Third Law 106 3-2 UNIT VECTORS, ADDING VECTORS BY COMPONENTS 46 Applying Newton’s Laws 108 Unit Vectors 46 REVIEW & SUMMARY 114 QUESTIONS 114 PROBLEMS 116 vi CONTENTS vii 6 Force and Motion—II 124 8-4 WORK DONE ON A SYSTEM BY AN EXTERNAL FORCE 191 6-1 FRICTION 124 Work Done on a System by an External Force 192 What Is Physics? 124 8-5 CONSERVATION OF ENERGY 195 Friction 124 Conservation of Energy 195 Properties of Friction 127 REVIEW & SUMMARY199 QUESTIONS 200 PROBLEMS 202 6-2 THE DRAG FORCE AND TERMINAL SPEED 130 The Drag Force and Terminal Speed 130 9 Center of Mass and Linear Momentum 214 6-3 UNIFORM CIRCULAR MOTION 133 9-1 CENTER OF MASS 214 Uniform Circular Motion 133 What Is Physics? 214 REVIEW & SUMMARY138 QUESTIONS 139 PROBLEMS 140 The Center of Mass 215 9-2 NEWTON’S SECOND LAW FOR A SYSTEM OF PARTICLES 220 7 Kinetic Energy and Work 149 Newton’s Second Law for a System of Particles 220 7-1 KINETIC ENERGY 149 9-3 LINEAR MOMENTUM 224 What Is Physics? 149 Linear Momentum 224 What Is Energy? 149 The Linear Momentum of a System of Particles 225 Kinetic Energy 150 9-4 COLLISION AND IMPULSE 226 7-2 WORK AND KINETIC ENERGY 151 Collision and Impulse 226 Work 151 9-5 CONSERVATION OF LINEAR MOMENTUM 230 Work and Kinetic Energy 152 Conservation of Linear Momentum 230 7-3 WORK DONE BY THE GRAVITATIONAL FORCE 155 9-6 MOMENTUM AND KINETIC ENERGY IN COLLISIONS 233 Work Done by the Gravitational Force 156 Momentum and Kinetic Energy in Collisions 233 7-4 WORK DONE BY A SPRING FORCE 159 Inelastic Collisions in One Dimension 234 Work Done by a Spring Force 159 9-7 ELASTIC COLLISIONS IN ONE DIMENSION 237 7-5 WORK DONE BY A GENERAL VARIABLE FORCE 162 Elastic Collisions in One Dimension 237 Work Done by a General Variable Force 162 9-8 COLLISIONS IN TWO DIMENSIONS 240 7-6POWER 166 Collisions in Two Dimensions 240 Power 166 9-9 SYSTEMS WITH VARYING MASS: A ROCKET 241 REVIEW & SUMMARY168 QUESTIONS 169 PROBLEMS 170 Systems with Varying Mass: A Rocket 241 REVIEW & SUMMARY243 QUESTIONS 245 PROBLEMS 246 8 Potential Energy and Conservation of Energy 177 8-1 POTENTIAL ENERGY 177 10 Rotation 257 What Is Physics? 177 10-1 ROTATIONAL VARIABLES 257 Work and Potential Energy 178 What Is Physics? 258 Path Independence of Conservative Forces 179 Rotational Variables 259 Determining Potential Energy Values 181 Are Angular Quantities Vectors? 264 8-2 CONSERVATION OF MECHANICAL ENERGY 184 10-2 ROTATION WITH CONSTANT ANGULAR ACCELERATION 266 Conservation of Mechanical Energy 184 Rotation with Constant Angular Acceleration 266 8-3 READING A POTENTIAL ENERGY CURVE 187 10-3 RELATING THE LINEAR AND ANGULAR VARIABLES 268 Reading a Potential Energy Curve 187 Relating the Linear and Angular Variables 268 viii CONTENTS 10-4 KINETIC ENERGY OF ROTATION 271 Equilibrium 327 Kinetic Energy of Rotation 271 The Requirements of Equilibrium 329 The Center of Gravity 330 10-5 CALCULATING THE ROTATIONAL INERTIA 273 Calculating the Rotational Inertia 273 12-2 SOME EXAMPLES OF STATIC EQUILIBRIUM 332 Some Examples of Static Equilibrium 332 10-6 TORQUE 277 Torque 278 12-3 ELASTICITY 338 Indeterminate Structures 338 10-7 NEWTON’S SECOND LAW FOR ROTATION 279 Elasticity 339 Newton’s Second Law for Rotation 279 REVIEW & SUMMARY 343 QUESTIONS 343 PROBLEMS 345 10-8 WORK AND ROTATIONAL KINETIC ENERGY 282 Work and Rotational Kinetic Energy 282 13 Gravitation 354 REVIEW & SUMMARY 285 QUESTIONS 286 PROBLEMS 287 13-1 NEWTON’S LAW OF GRAVITATION 354 What Is Physics? 354 11 Rolling, Torque, and Angular Momentum 295 Newton’s Law of Gravitation 355 11-1 ROLLING AS TRANSLATION AND ROTATION COMBINED 295 13-2 GRAVITATION AND THE PRINCIPLE OF SUPERPOSITION 357 What Is Physics? 295 Rolling as Translation and Rotation Combined 295 Gravitation and the Principle of Superposition 357 11-2 FORCES AND KINETIC ENERGY OF ROLLING 298 13-3 GRAVITATION NEAR EARTH’S SURFACE 359 The Kinetic Energy of Rolling 298 Gravitation Near Earth’s Surface 360 The Forces of Rolling 299 13-4 GRAVITATION INSIDE EARTH 362 11-3 THE YO-YO 301 Gravitation Inside Earth 363 The Yo-Yo 302 13-5 GRAVITATIONAL POTENTIAL ENERGY 364 11-4 TORQUE REVISITED 302 Gravitational Potential Energy 364 Torque Revisited 303 13-6 PLANETS AND SATELLITES: KEPLER’S LAWS 368 11-5 ANGULAR MOMENTUM 305 Planets and Satellites: Kepler’s Laws 369 Angular Momentum 305 13-7 SATELLITES: ORBITS AND ENERGY 371 11-6 NEWTON’S SECOND LAW IN ANGULAR FORM 307 Satellites: Orbits and Energy 371 Newton’s Second Law in Angular Form 307 13-8 EINSTEIN AND GRAVITATION 374 11-7 ANGULAR MOMENTUM OF A RIGID BODY 310 Einstein and Gravitation 374 The Angular Momentum of a System of Particles 310 REVIEW & SUMMARY 376 QUESTIONS 377 PROBLEMS 378 The Angular Momentum of a Rigid Body Rotating About a Fixed Axis 311 11-8 CONSERVATION OF ANGULAR MOMENTUM 312 14 Fluids 386 Conservation of Angular Momentum 312 14-1 FLUIDS, DENSITY, AND PRESSURE 386 What Is Physics? 386 11-9 PRECESSION OF A GYROSCOPE 317 What Is a Fluid? 386 Precession of a Gyroscope 317 Density and Pressure 387 REVIEW & SUMMARY 318 QUESTIONS 319 PROBLEMS 320 14-2 FLUIDS AT REST 388 12 Equilibrium and Elasticity 327 Fluids at Rest 389 12-1 EQUILIBRIUM 327 14-3 MEASURING PRESSURE 392 What Is Physics? 327 Measuring Pressure 392