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VOLUME 11

An Invitation to Physics1

1 Introduction and Vectors5

1.1 Standards of Length，Mass，and Time5

1.2 Density and Atomic Mass9

1.3 Dimensional Analysis10

1.4 Conversion of Units11

1.5 Order-of-Magnitude Calculations12

1.6 Significant Figures13

1.7 Coordinate Systems15

1.8 Vectors and Scalars16

1.9 Some Properties of Vectors18

1.10 Components of a Vector and Unit Vectors20

1.11 Modeling， Alternative Representations，and Problem-Solving Strategy25

Summary30

Context 1 Mission to Mars38

2 Motion in One Dimension40

2.1 Average Velocity41

2.2 Instantaneous Velocity44

2.3 Analysis Models—The Particle Under Constant Velocity49

2.4 Acceleration51

2.5 Motion Diagrams54

2.6 The Particle Under Constant Acceleration56

2.7 Freely Falling Objects60

2.8 Context Connection—Liftoff Acceleration65

Summary66

3 Motion in Two Dimensions75

3.1 The Position， Velocity， and Acceleration Vectors75

3.2 Two-Dimensional Motion with Constant Acceleration78

3.3 Projectile Motion80

3.4 The Particle in Uniform Circular Motion87

3.5 Tangential and Radial Acceleration90

3.6 Relative Velocity91

3.7 Context Connection—Circular Orbits94

Summary96

4 The Laws of Motion106

4.1 The Concept of Force106

4.2 Newton’s First Law108

4.3 Inertial Mass110

4.4 Newton’s Second Law—The Particle tnder a Net Force111

4.5 The Gravitational Force and Weight114

4.6 Newton’s Third Law116

4.7 Applications of Newton’s Laws119

4.8 Context Connection—Controlling the Spacecraft in Empty Space127

Summary129

5 More Applications of Newton’s Laws139

5.1 Forces of Friction139

5.2 Newton’s Second Law Applied to a Particle in Uniform Circular Motion147

5.3 Nonuniform Circular Motion154

5.4 Motion in the Presence of Velocity-Dependent Resistive Forces156

5.5 Numerical Representations of Particle Dynamics159

5.6 The Fundamental Forces of Nature162

5.7 The Gravitational Field165

5.8 Context Connection—The Effect of Gravity on Our Spacecraft166

Summary167

6 Energy and Energy Transfer177

6.1 Systems and Environments178

6.2 Work Done by a Constant Force178

6.3 The Scalar Product of Two Vectors182

6.4 Work Done by a Varyng Force184

6.5 Kinetic Energy and the Work—Kinetic Energy Theorem188

6.6 The Nonisolated System191

6.7 Situations Involving Kinetic Fricton196

6.8 Power198

6.9 Context Connection —A Probe to the Sun200

Summary202

7 Potential Energy210

7.1 Potential Energy of a System210

7.2 The Isolated System212

7.3 Conservative and Nonconservative Forces217

7.4 Conservative Forces and Potential Energy223

7.5 The Nonisolated System in Steady State224

7.6 Potential Energy for Gravitational and Electric Forces226

7.7 Energy Diagrams and Stability of Equilibrium229

7.8 Context Connection—Escape Speed from the Sun231

Summary232

8 Momentum and Collisions243

8.1 Linear Momentum and Its Conservation243

8.2 Impulse and Momentum248

8.3 Collisions251

8.4 Two-Dimensional Collisions257

8.5 The Center of Mass260

8.6 Motion of a System of Particles264

8.7 Context Connection—Rocket Propulsion267

Summary269

9 Relativity279

9.1 The Principle of Newtonian Relativity280

9.2 The Michelson-Morley Experiment282

9.3 Einstein’s Principle of Relativity283

9.4 Consequences of Special Relativity284

9.5 The Lorentz Transformation Equations293

9.6 Relativistic Momentum and the Relativistic Form of Newton’s Laws296

9.7 Relativistic Energy297

9.8 Mass and Energy300

9.9 General Relativitv301

9.10 Context Connection—From Mars to the Stars304

Summary305

10 Rotational Motion312

10.1 Angular Speed and Angular Acceleration313

10.2 Rotational Kinematics—The Rigid Body Under Constant Angular Acceleration317

10.3 Relations Between Rotational andTranslational Quantities319

10.4 Rotational Kinetic Energy321

10.5 Torque and the Vector Product325

10.6 The Rigid Body in Equilibrium329

10.7 The Rigid Body Under a Net Torque332

10.8 Angular Momentum337

10.9 Conservation of Angular Momentum340

10.10 Precessional Motion of Gyroscopes343

10.11 Rolling of Rigid Bodies344

10.12 Context Connection—Gyroscopes in Space347

Summary349

11 Gravity， Planetary Orbits， and the Hydrogen Atom363

11.1 Newton’s Law of Universal Gravitation Revisited364

11.2 Structural Models369

11.3 Kepler’s Laws370

11.4 Energy Considerations in Planetary and Satellite Motion375

11.5 Atomic Spectra and the Bohr Theory of Hydrogen381

11.6 Context Connertion—Changing from a Circular to an Elliptical Orbit387

Summary389

Context 1 Conclusion A Successful Mission Plan397

Context 2 Earthquakes402

12 Oscillatoty Motion404

12.1 Motion of a Particle Attached to a Spring405

12.2 Mathematical Representation of Simple Harmonic Motion406

12.3 Energy Considerations in Simple Harmonic Motion413

12.4 The Simple Pendulum417

12.5 The Physical Pendulum419

12.6 Damped Oscillations421

12.7 Forced Oscillations422

12.8 Context Connection—Resonance in Structures423

Summary425

13 Mechanical Waves434

13.1 Propagation of a Disturbance435

13.2 The Wave Model439

13.3 The Traveling Wave441

13.4 The Speed of Transverse Waves on Strings445

13.5 Ref lection and Transmission of Waves448

13.6 Rate of Energy Transfer by Sinusoidal Waves on Strings450

13.7 Sound Waves452

13.8 The Doppler Effect454

13.9 Context Connection—Seismic Waves459

Summary462

14 Superposition and Standing Waves470

14.1 The Principle of Superposition471

14.2 Interference of Waves473

14.3 Standing Waves476

14.4 Standing Waves in Strings479

14.5 Standing Waves in Air Columns483

14.6 Beats： Interference in Time486

14.7 Nonsinusoidal Wave Patterns488

14.8 Context Connection—Building on Antinodes492

Summary494

Context 2 Conclusion Minimizing the Risk503

Context 3 Search for the Titanic506

15 Fluid Mechanics508

15.1 Pressure509

15.2 Variation of Pressure with Depth511

15.3 Pressure Measurements515

15.4 Buoyant Forces and Arch imedes’s Pnnciple516

15.5 Fluid Dynamics521

15.6 Streamlines and the Continuity Equation for Fluids522

15.7 Bernoulli’s Principle524

15.8 Other Applications of Fluid Dynamics527

15.9 Context Connection—A Near Miss Even Before Leaving Southampton528

Summary530

Context 3 Conclusion Finding and Visiting the Titanic541

VOLUME 2546

Context 4 Global Warming546

16 Temperature and the Kinetic Theory of Gases548

16.1 Temperature and the Zeroth Law of Thermodvnamics549

16.2 Thermometers and Temperature Scales550

16.3 Thermal Expansion of Solids and Liquids555

16.4 Macroscopic Description of an Ideal Gas562

16.5 The Kinetic Theory of Cases564

16.6 Distribution of Molecular Speeds570

16.7 Context Connection—The Atmospheric Lapse Rate572

Summary574

17 Energy in Thermal Processes：The First Law of Thermodynamics582

17.1 Heat and Internal Energy583

17.2 Specific Heat585

17.3 Latent Heat and Phase Changes588

17.4 Work in Thermodynamic Processes592

17.5 The First Law of Thermodynamics595

17.6 Some Applications of the First Law of Thermodynamics597

17.7 Molar Specific Heats of Ideal Gases601

17.8 Adiabatic Processes for an Ideal Gas603

17.9 Molar Specific Heats and the Equipartition of Energy605

17.10 Energy Transfer Mechanisms in Thermal Processes608

17.11 Context Connection—Energy Balance for the Earth614

Summary616

18 Heat Engines，Entropy， and the Second Law of Thermodynamics628

18.1 Heat Engines and，the Second Law of Thermodynamics629

18.2 Reversible and Irreversible Processes632

18.3 The Carnot Engine632

18.4 Heat Pumps and Refrigerators635

18.5 An Alternative Statement of the Second Law637

18.6 Entropy638

18.7 Entropy and the Second Law of Thermodynamics643

18.8 Entropy Changes in Irreversiblc Proccsscs646

18.9 Context Connection—The Atmosphere as a Heat Engine648

Summary650

Context 4 Conclusion Predicting the Correct Surface Temperature659

Context 5 Lightning664

19 Electric Forces and Electric Fields666

19.1 Historical Oveniew667

19.2 Properties of Electric Charges667

19.3 Insulators and Conductors669

19.4 Coulomb’s Law671

19.5 Electric Fields674

19.6 Electtic Field Lines681

19.7 Motion of Charged Particles in a Uniform Electric Field683

19.8 Electric Flux686

19.9 Gauss’s Law689

19.10 Application of Gauss’s Law to Symmetric Charge Distributions691

19.11 Conductors in Electrostatic Equilibrium695

19.12 Context Connection—The Atmospheric Electric Field697

Summary699

20 Electric Potential and Capacitance709

20.1 Potential Difference and Electric Potential710

20.2 Potential Differences in a Uniform Electric Field712

20.3 Electric Potential and Electric Potential Energy Due to Point Charges715

20.4 Obtaining Electric Field from Electric Potential718

20.5 Electric Potential Due to Continuous Charge Distributions720

20.6 Electric Potential of a Charged Conductor723

20.7 Capacitance725

20.8 Combinations of Capacitors730

20.9 Energy Stored in a Charged Capacitor734

20.10 Capacitors with Dielectrics737

20.11 Context Connection—The Atmosphere as a Capacitor743

Summary744

21 Current and Direct Current Circuits756

21.1 Electric Current757

21.2 Resistance and Ohm’s Law760

21.3 Superconductors766

21.4 A Structural Model for Electrical Conduction768

21.5 Electric Energy and Power771

21.6 Sources of emf774

21.7 Resistors in Series and in Parallel776

21.8 Kirchhoff’s Rules and Simple DC Circuits782

21.9 RCCircuits786

21.10 Context Connection—The Atmosphere as a Conductor791

Summary792

Context 5 Conclusion Modeling the Atmosphere to Determine the Number of Lightning Strikes803

Context 6 Magnetic Levitation Vehicles806

22 Magnetic Forces and Magnetic Fields808

22.1 Historical Overview809

22.2 The Magnetic Field810

22.3 Motion of a Charged Particle in a Magnetic Field815

22.4 Applications of the Motion of Charged Particles in a Magnetic Field818

22.5 Magnetic Force on a Current-Carrying Conductor821

22.6 Torque on a Current Loop in a Uniform Magnetic Field824

22.7 The Biot-Savart Law826

22.8 The Magnetic Force Between Two Parallel Conductors830

22.9 Ampere’s Law831

22.10 The Magnetic Field of a Solenoid835

22.11 Magnetism in Matter836

22.12 Context Connection—The Attractive Model for Magnetic Levitation838

Summary840

23 Faraday’s Law and Inductance852

23.1 Faraday’s Law of Induction852

23.2 Motional emf859

23.3 Lenz’s Law863

23.4 Induced emfs and Electric Fields867

23.5 Self-Inductance869

23.6 RL Circuits872

23.7 Energy Stored in a Magnetic Field876

23.8 Context Connection—The Repulsive Model for Magnetic Levitation879

Summary881

Context 6 Conclusion Propelling and Braking the Vehicle893

Context 7 Lasers896

24 Electromagnetic Waves898

24.1 Displacement Current and the Generalized Ampere’s Law899

24.2 Maxwell’s Equations900

24.3 Electromagnetic Waves901

24.4 Hertz’s Discoveries906

24.5 Energy Carried by Electromagnetic Waves910

24.6 Momentum and Radiation Pressure912

24.7 The Spectrum of Electromagnetic Waves916

24.8 Polarization919

24.9 Context Connection—The Special Properties of Laser Light921

Summary924

25 Reflection and Refraction of Light932

25.1 The Nature of Light933

25.2 The Ray Model in Geometric Optics934

25.3 The Wave Under Reflection935

25.4 The Wave Under Refraction938

25.5 Dispersion and Prisms944

25.6 Huygens’s Principle947

25.7 Total Internal Reflection949

25.8 Context Connection—Optical Fibers952

Summary956

26 Image Formation by Mirrors and Lenses965

26.1 Images Formed by Flat Mirrors966

26.2 Images Formed by Spherical Minors969

26.3 Images Formed by Refraction977

26.4 Thin Lenses981

26.5 Lens Aberrations990

26.6 Context Connection—Medical Fiberscopcs991

Summary993

27 Wave Optics1002

27.1 Conditions for Interference1003

27.2 Young’s Double-Slit Experiment1003

27.8 Light Waves in Interference1005

27.4 Change of Phase Due to Reflection1009

27.5 Interference in Thin Films1010

27.6 Diffraction Patterns1014

27.7 Resolution of Single-Slit and Circular Apertures1018

27.8 The Diffraction Grating1022

27.9 Diffraction of X-Rays by Crystals1026

27.10 Context Connection—Holography1027

Summary1029

Context 7 Conclusion Using Lasers to Store Information1037

Context 8 The Cosmic Connection1042

28 Quantum Physics1044

28.1 Blackbody Radiation and Planck’s Theory1045

28.2 The Photoelectric Effect1049

28.3 The Compton Effect1054

28.4 Photons and Electromagnetic Waves1058

28.5 The Wave Properties of Particles1058

28.6 The Quantum Particle1062

28.7 The Double-Slit Experiment Revisited1066

28.8 The Uncertainty Principle1068

28.9 An Interpretation of Quantum Mechanics1071

28.10 A Particle in a Box1073

28.11 The Quantum Particle Under Boundary Conditions1076

28.12 The Schrodinger Equation1077

28.13 Tunneling Through a Potengyal Energy Barrier1080

28.14 Context Connection—The Cosmic Temperature1083

Summary1085

29 Atomic Physics1093

29.1 Early Structural Models of the Atom1094

29.2 The Hydrogen Atom Revisited1096

29.3 The Spin Magnetic Quantum Number1098

29.4 The Wave Functions for Hydrogen1099

29.5 Physical Interpretation of the Quantum Numbers1103

29.6 The Exclusion Principle and the Periodic Table1110

29.7 Atomic Spectra： Visible and X-Ray1115

29.8 Context Connection—Atoms in Space1120

Summary1122

30 Nuclear Physics1129

30.1 Some Properties of Nuclei1130

30.2 Binding Energy1138

30.3 Radioactivity1140

30.4 The Radioactive Decay Processes1143

30.5 Nuclear Reactions1151

30.6 Context Connection—The Engine of the Stars1153

Summary1155

31 Particle Physics1164

31.1 The Fundamental Forces in Nature1165

31.2 Positrons and Other Antiparticles1166

31.3 Mesons and the Beginning of Particle Physics1169

31.4 Classification of Particles1172

31.5 Conservation Laws1174

31.6 Strange Particles and Strangeness1177

31.7 Making Elementary Particles and Measuring Their Properties1178

31.8 Finding Patterns in the Particles1182

31.9 Quarks1183

31.10 Colored Quarks1187

31.11 The Standard Model1189

31.12 Context Connection—Investigating the Smallest System to Understand theLargest1192

Summary1197

Context 8 Conclusion Problems and Perspectives1204