Physics for Engineers and Scientists Vol I- Ohanian and Markert PDF

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W. W. Norton & Company, Inc. • www.NortonEbooks.com PHYSICS FOR ENGINEERS AND SCIENTISTS THIRD EDITION Volume One Hans C. Ohanian, John T. Markert Physics for Engineers and Scientists Third Edition Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY O S C I L L AT I O N S , WAV E S , A N D F L U I...

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W. W. Norton & Company, Inc. • www.NortonEbooks.com

PHYSICS FOR ENGINEERS AND SCIENTISTS THIRD EDITION Volume One

Hans C. Ohanian, John T. Markert

Physics for Engineers and Scientists Third Edition

Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY O S C I L L AT I O N S , WAV E S , A N D F L U I D S T E M P E R AT U R E , H E AT, A N D T H E R M O D Y N A M I C S

W • W • NORTON & COMPANY

B

NEW YORK • LONDON

Physics for Engineers and Scientists Third Edition Volume1 (Chapters 1–21) MOTION, FORCE, AND ENERGY O S C I L L AT I O N S , WAV E S , A N D F L U I D S T E M P E R AT U R E , H E AT, A N D T H E R M O D Y N A M I C S

HANS C. OHANIAN, UNIVERSITY OF VERMONT

J O H N T. M A R K E R T, U N I V E R S I T Y O F T E X A S AT A U S T I N

W • W • NORTON & COMPANY

B

NEW YORK • LONDON

To Susan Ohanian, writer, who gently tried to teach me some of her craft.—H.C.O. To Frank D. Markert, a printer by trade; to Christiana Park, for her thirst for new knowledge; and to Erin, Ryan, Sean, and Gwen, for their wonder and clarity.—J.T.M.

Copyright © 2007 by W.W. Norton & Company, Inc. All rights reserved Printed in the United States of America Third Edition Composition: Techbooks Manufacturing: RR Donnelley & Sons Company Editor: Leo A. W. Wiegman Media Editor: April E. Lange Director of Manufacturing—College: Roy Tedoff Senior Project Editor: Christopher Granville Photo Researcher: Kelly Mitchell Editorial Assistant: Lisa Rand, Sarah L. Mann Copy Editor: Richard K. Mickey Book designer: Sandy Watanabe Layout artist: Paul Lacy Illustration Studio: JB Woolsey Arts, Inc. Cover Illustration: John Belcher, inter alia. Cover Design: Joan Greenfield Library of Congress Cataloging-in-Publication Data has been applied for. ISBN 978-0-393-11101-9 (ebook)

W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, N.Y. 10110 www.wwnorton.com W. W. Norton & Company Ltd., Castle House, 75/76 Wells Street, London W1T 3QT 1234567890 W. W. Norton & Company has been independent since its founding in 1923, when William Warder Norton and Mary D. Herter Norton first published lectures delivered at the People’s Institute, the adult education division of New York City’s Cooper Union. The Nortons soon expanded their program beyond the Institute, publishing books by celebrated academics from America and abroad. By mid-century, the two major pillars of Norton’s publishing program—trade books and college texts— were firmly established. In the 1950s, the Norton family transferred control of the company to its employees, and today—with a staff of four hundred and a comparable number of trade, college, and professional titles published each year—W. W. Norton & Company stands as the largest and oldest publishing house owned wholly by its employees.

Brief Contents Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; Chapters 37–41 appear in Volume 3.

PREFACE xiii

PART IV ELECTRICITY AND MAGNETISM

OWNER’S MANUAL xxv

22. ELECTRIC FORCE AND ELECTRIC CHARGE

PRELUDE: THE WORLD OF PHYSICS xxxv

23. THE ELECTRIC FIELD 24. GAUSS’ LAW

PART I MOTION, FORCE, AND ENERGY 1

25. ELECTROSTATIC POTENTIAL AND ENERGY

1. SPACE, TIME, AND MASS 2

26. CAPACITORS AND DIELECTRICS

2. MOTION ALONG A STRAIGHT LINE 28

27. CURRENTS AND OHM’S LAW

3. VECTORS 69

28. DIRECT CURRENT CIRCUITS

4. MOTION IN TWO AND THREE DIMENSIONS 94

29. MAGNETIC FORCE AND FIELD

5. NEWTON’S LAWS OF MOTION 130

30. CHARGES AND CURRENTS IN MAGNETIC FIELDS

6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173

31. ELECTROMAGNETIC INDUCTION

7. WORK AND ENERGY 204

32. ALTERNATING CURRENT CIRCUITS

8. CONSERVATION OF ENERGY 235 9. GRAVITATION 271

PART V WAVES AND OPTICS

10. SYSTEMS OF PARTICLES 305

33. ELECTROMAGNETIC WAVES

11. COLLISIONS 338

34. REFLECTION, REFRACTION, AND OPTICS

12. ROTATION OF A RIGID BODY 365

35. INTERFERENCE AND DIFFRACTION

13. DYNAMICS OF A RIGID BODY 394 14. STATICS AND ELASTICITY 429

PART II OSCILLATIONS, WAVES, AND FLUIDS 466

PART VI RELATIVITY, QUANTA, AND PARTICLES 36. THE THEORY OF SPECIAL RELATIVITY

15. OSCILLATIONS 468

37. QUANTA OF LIGHT

16. WAVES 507

38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS

17. SOUND 536 18. FLUID MECHANICS 565

PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600 19. THE IDEAL GAS 602

39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS 40. NUCLEI 41. ELEMENTARY PARTICLES AND COSMOLOGY APPENDICES A-1

20. HEAT 628 21. THERMODYNAMICS 661

v

Table of Contents Chapters 1–21 appear in Volume 1; Chapters 22–36 appear in Volume 2; and Chapters 37–41 appear in Volume 3.

PREFACE xiii

3.3

OWNER’S MANUAL xxv 3.4

PRELUDE: THE WORLD OF PHYSICS xxxv

PART I MOTION, FORCE, AND ENERGY 1 1. SPACE, TIME, AND MASS 2 1.1 1.2 1.3 1.4 1.5 1.6

Coordinates and Reference Frames 3 The Unit of Length 5 The Unit of Time 9 The Unit of Mass 11 Derived Units 13 Significant Figures; Consistency of Units and Conversion of Units 14

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 20

2. MOTION ALONG A STRAIGHT LINE 28 2.1 2.2 2.3 2.4 2.5 2.6 2.7*

Average Speed 29 Average Velocity for Motion along a Straight Line 32 Instantaneous Velocity 35 Acceleration 39 Motion with Constant Acceleration 42 The Acceleration of Free Fall 49 Integration of the Equations of Motion 54

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 57

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 87

4. MOTION IN TWO AND THREE DIMENSIONS 94 4.1 4.2 4.3 4.4 4.5 4.6

5. NEWTON’S LAWS OF MOTION 130 5.1 5.2 5.3 5.4 5.5 5.6

3.2

The Displacement Vector and Other Vectors 70 Vector Addition and Subtraction 72

Newton’s First Law 131 Newton’s Second Law 133 The Combination of Forces 138 Weight; Contact Force and Normal Force 141 Newton’s Third Law 144 Motion with a Constant Force 151

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 159

6. FURTHER APPLICATIONS OF NEWTON’S LAWS 173 6.1 6.3 6.4*

3.1

Components of Velocity and Acceleration 95 The Velocity and Acceleration Vectors 98 Motion with Constant Acceleration 102 The Motion of Projectiles 104 Uniform Circular Motion 112 The Relativity of Motion and the Addition of Velocities 115

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 118

6.2

3. VECTORS 69

The Position Vector; Components of a Vector 76 Vector Multiplication 81

Friction 174 Restoring Force of a Spring; Hooke’s Law 182 Force for Uniform Circular Motion 184 The Four Fundamental Forces 191

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 192

vii

viii

CONTENTS

7. WORK AND ENERGY 204

12.2 12.3

7.1 7.2 7.3 7.4

Work 205 Work for a Variable Force 211 Kinetic Energy 214 Gravitational Potential Energy 218

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 224

12.4* 12.5

Rotation about a Fixed Axis 367 Motion with Constant Angular Acceleration 374 Motion with Time-Dependent Angular Acceleration 376 Kinetic Energy of Rotation; Moment of Inertia 378

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 384

8. CONSERVATION OF ENERGY 235 8.1 8.2 8.3 8.4* 8.5

Potential Energy of a Conservative Force 236 The Curve of Potential Energy 244 Other Forms of Energy 248 Mass and Energy 251 Power 253

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 259

9. GRAVITATION 271 9.1 9.2 9.3 9.4 9.5

Newton’s Law of Universal Gravitation 272 The Measurement of G 277 Circular Orbits 278 Elliptical Orbits; Kepler’s Laws 282 Energy in Orbital Motion 288

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 293

13. DYNAMICS OF A RIGID BODY 394 13.1 13.2 13.3 13.4*

Work, Energy, and Power in Rotational Motion; Torque 395 The Equation of Rotational Motion 399 Angular Momentum and its Conservation 406 Torque and Angular Momentum as Vectors 410

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 417

14. STATICS AND ELASTICITY 429 14.1 14.2 14.3 14.4

Statics of Rigid Bodies 430 Examples of Static Equilibrium 433 Levers and Pulleys 441 Elasticity of Materials 445

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 450

10. SYSTEMS OF PARTICLES 305 10.1 10.2 10.3 10.4

Momentum 306 Center of Mass 313 The Motion of the Center of Mass 323 Energy of a System of Particles 327

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 328

PART II OSCILLATIONS, WAVES, AND FLUIDS 466 15. OSCILLATIONS 468 15.1

11. COLLISIONS 338

15.2 15.3

11.1 11.2 11.3 11.4*

Impulsive Forces 339 Elastic Collisions in One Dimension 344 Inelastic Collisions in One Dimension 348 Collisions in Two and Three Dimensions 351

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 354

15.4 15.5*

Simple Harmonic Motion 469 The Simple Harmonic Oscillator 476 Kinetic Energy and Potential Energy 480 The Simple Pendulum 484 Damped Oscillations and Forced Oscillations 488

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 494

16. WAVES 507 12. ROTATION OF A RIGID BODY 365 16.1 12.1

Motion of a Rigid Body 366

16.2

Transverse and Longitudinal Wave Motion 508 Periodic Waves 509

CONTENTS

16.3 16.4

The Superposition of Waves 516 Standing Waves 520

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 524

21. THERMODYNAMICS 661 21.1 21.2 21.3

17. SOUND 536 17.1 17.2 17.3 17.4 17.5*

Sound Waves in Air 538 Intensity of Sound 540 The Speed of Sound; Standing Waves 543 The Doppler Effect 574 Diffraction 553

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 555

18. FLUID MECHANICS 565 18.1 18.2 18.3 18.4 18.5 18.6

Density and Flow Velocity 567 Incompressible Steady Flow; Streamlines 569 Pressure 573 Pressure in a Static Fluid 575 Archimedes’ Principle 580 Fluid Dynamics; Bernoulli’s Equation 582

21.4

The First Law of Thermodynamics 663 Heat Engines; The Carnot Engine 665 The Second Law of Thermodynamics 675 Entropy 677

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 681

PART IV ELECTRICITY AND MAGNETISM 22. ELECTRIC FORCE AND ELECTRIC CHARGE 22.1 22.2 22.3 22.4 22.5

The Electrostatic Force Coulomb’s Law The Superposition of Electrical Forces Charge Quantization and Charge Conservation Conductors and Insulators; Charging by Friction or by Induction

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 587

23. THE ELECTRIC FIELD

PART III TEMPERATURE, HEAT, AND THERMODYNAMICS 600

23.1 23.2 23.3

19. THE IDEAL GAS 602 19.1 19.2 19.3 19.4

The Ideal-Gas Law 603 The Temperature Scale 609 Kinetic Pressure 613 The Internal Energy of an Ideal Gas 616

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 619

23.4 23.5

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

24. GAUSS’ LAW 24.1 24.2

20. HEAT 628 20.1 20.2 20.3 20.4 20.5 20.6*

Heat as a Form of Energy Transfer 629 Thermal Expansion of Solids and Liquids 633 Thermal Conduction 638 Changes of State 642 The Specific Heat of a Gas 644 Adiabatic Expansion of a Gas 647

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS 650

The Electric Field of Point Charges The Electric Field of Continuous Charge Distributions Lines of Electric Field Motion in a Uniform Electric Field Electric Dipole in an Electric Field

24.3 24.4 24.5

Electric Flux Gauss’ Law Applications of Gauss’ Law Superposition of Electric Fields Conductors and Electric Fields

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

25. ELECTROSTATIC POTENTIAL AND ENERGY 25.1 25.2

The Electrostatic Potential Calculation of the Potential from the Field

ix

x

CONTENTS

25.3 25.4 25.5

Potential in Conductors Calculation of the Field from the Potential Energy of Systems of Charges

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

26. CAPACITORS AND DIELECTRICS 26.1 26.2 26.3 26.4

Capacitance Capacitors in Combination Dielectrics Energy in Capacitors

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

27. CURRENTS AND OHM’S LAW 27.1 27.2 27.3 27.4

Electric Current Resistance and Ohm’s Law The Resistivity of Materials Resistances in Combination

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

28. DIRECT CURRENTS CIRCUITS 28.1 28.2 28.3 28.4 28.5 28.6* 28.7* 28.8*

Electromotive Force Sources of Electromotive Force Single-Loop Circuits Multi-Loop Circuits Energy in Circuits; Joule Heat Electrical Measurements The RC Circuit The Hazards of Electric Currents

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

29. MAGNETIC FORCE AND FIELD 29.1 29.2 29.3 29.4 29.5

The Magnetic Force The Magnetic Field Ampére’s Law Solenoids and Magnets The Biot-Savart Law

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

30. CHARGES AND CURRENTS IN MAGNETIC FIELDS 30.1 30.2 30.3 30.4 30.5*

Circular Motion in a Uniform Magnetic Field Force on a Wire Torque on a Loop Magnetism in Materials The Hall Effect

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

31. ELECTROMAGNETIC INDUCTION 31.1 31.2 31.3 31.4 31.5 31.6*

Motional EMF Faraday’s Law Some Examples; Lenz’ Law Inductance Magnetic Energy The RL Circuit

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

32. ALTERNATING CURRENT CIRCUITS*

Resistor Circuit 32.2 Capacitor Circuit 32.3 Inductor Circuit 32.4 * Freely Oscillating LC and RLC Circuits 32.5 * Series Circuits with Alternating EMF 32.6 Transformers 32.1

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

PART V WAVES AND OPTICS 33. ELECTROMAGNETIC WAVES 33.1 33.2* 33.3 33.4 33.5 33.6*

Induction of Magnetic Fields; Maxwell’s Equations The Electromagnetic Wave Pulse Plane Waves; Polarization The Generation of Electromagnetic Waves Energy of a Wave The Wave Equation

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

CONTENTS

34. REFLECTION, REFRACTION, AND OPTICS 34.1 34.2 34.3 34.4 34.5 34.6*

Huygens’ Construction Reflection Refraction Spherical Mirrors Thin Lenses Optical Instruments

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

38. SPECTRAL LINES, BOHR’S THEORY, AND QUANTUM MECHANICS 38.1 38.2 38.3 38.4 38.5

Spectral Lines Spectral Series of Hydrogen The Nuclear Atom Bohr’s Theory Quantum Mechanics; The Schrödinger Equation

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

35. INTERFERENCE AND DIFFRACTION 35.1 35.2* 35.3 35.4 35.5 35.6

Thin Films The Michelson Interferometer Interference from Two Slits Interference from Multiple Slits Diffraction by a Single Slit Diffraction by a Circular Aperture; Rayleigh’s Criterion

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

39. QUANTUM STRUCTURE OF ATOMS, MOLECULES, AND SOLIDS 39.1 39.2 39.3* 39.4 39.5

Principal, Orbital, and Magnetic Quantum Numbers; Spin The Exclusion Principle and the Structure of Atoms Energy Levels in Molecules Energy Bands in Solids Semiconductor Devices

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

PART VI RELATIVITY, QUANTA, AND PARTICLES

40. NUCLEI 40.1

36. THE THEORY OF SPECIAL RELATIVITY 36.1 36.2 36.3 36.4 36.5 36.6 36.7*

The Speed of Light; the Ether Einstein’s Principle of Relativity Time Dilation Length Contraction The Lorentz Transformations and the Combination of Velocities Relativistic Momentum and Energy Mass and Energy

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

40.2 40.3 40.4 40.5 40.6* 40.7

37.1 37.2 37.3 37.4 37.5 37.6

Blackbody Radiation Energy Quanta Photons and the Photoelectric Effect The Compton Effect X Rays Wave vs. Particle

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

Isotopes The Strong Force and the Nuclear Binding Energy Radioactivity The Law of Radioactive Decay Fission Nuclear Bombs and Nuclear Reactors Fusion

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

41. ELEMENTARY PARTICLES AND COSMOLOGY 41.1

37. QUANTA OF LIGHT

xi

41.2 41.3 41.4 41.5 41.6

The Tools of High-Energy Physics The Multitude of Particles Interactions and Conservation Laws Fields and Quanta Quarks Cosmology

SUMMARY / QUESTIONS / PROBLEMS / REVIEW PROBLEMS / ANSWERS TO CHECKUPS

xii

CONTENTS

APPENDICES APPENDIX 1: GREEK ALPHABET A-1

APPENDIX 2: MATHEMATICS REVIEW A-1

APPENDIX 6: THE INTERNATIONAL SYSTEM OF UNITS (SI) A-21 A6.1 A6.2

A2.1 A2.2 A2.3 A2.4 A2.5 A2.6 A2.7

Symbols A-1 Powers and Roots A-1 Arithmetic in Scientific Notation A-2 Algebra A-3 Equations with Two Unknowns A-5 The Quadratic Formula A-5 Logarithms and the Exponential Function A-5

APPENDIX 3: GEOMETRY AND TRIGONOMETRY REVIEW A-7 A3.1 A3.2 A3.3 A3.4 A3.5

Perimeters, Areas, and Volumes A-7 Angles A-7 The Trigonometric Functions A-8 The Trigonometric Identities A-9 The Laws of Cosines and Sines A-10

APPENDIX 4: CALCULUS REVIEW A-10 A4.1 A4.2 A4.3 A4.4 A4.5 A4.6

Derivatives A-10 Important Rules for Differentiation A-11 Integrals A-12 Important Rules for Integration A-15 The Taylor Series A-18 Some Approximations A-18

APPENDIX 5: PROPAGATING UNCERTAINTIES A-19

A6.3

Base Units A-21 Derived Units A-23 Prefixes A-23

APPENDIX 7: BEST VALUES OF FUNDAMENTAL CONSTANTS A-23

APPENDIX 8: CONVERSION FACTORS A-26

APPENDIX 9: THE PERIODIC TABLE AND CHEMICAL ELEMENTS A-31

APPENDIX 10: FORMULA SHEETS A-33

Chapters 1–21 A-33 Chapters 22–41 A-34 APPENDIX 11: ANSWERS TO ODD-NUMBERED PROBLEMS AND REVIEW PRO...