Solution Manuals for Physics, 10th Edition John D. Cutnell

1 Introduction and Mathematical Concepts 1

1.1 The Nature of Physics 1

1.2 Units 1

1.3 The Role of Units in Problem Solving 3

1.4 Trigonometry 6

1.5 Scalars and Vectors 8

1.6 Vector Addition and Subtraction 10

1.7 The Components of a Vector 12

1.8 Addition of Vectors by Means of Components 15

CONCEPT SUMMARY 18

2 Kinematics in One Dimension 26

2.1 Displacement 26

2.2 Speed and Velocity 27

2.3 Acceleration 29

2.4 Equations of Kinematics for Constant Acceleration 33

2.5 Applications of the Equations of Kinematics 36

2.6 Freely Falling Bodies 40

2.7 Graphical Analysis of Velocity and Acceleration 44

CONCEPT SUMMARY 46

3 Kinematics in Two Dimensions 54

3.1 Displacement, Velocity, and Acceleration 54

3.2 Equations of Kinematics in Two Dimensions 55

3.3 Projectile Motion 59

3.4 Relative Velocity 67

CONCEPT SUMMARY 71

4 Forces and Newton’s Laws of Motion 79

4.1 The Concepts of Force and Mass 79

4.2 Newton’s First Law of Motion 79

4.3 Newton’s Second Law of Motion 81

4.4 The Vector Nature of Newton’s Second Law of Motion 84

4.5 Newton’s Third Law of Motion 85

4.6 Types of Forces: An Overview 86

4.7 The Gravitational Force 87

4.8 The Normal Force 91

4.9 Static and Kinetic Frictional Forces 94

4.10 The Tension Force 100

4.11 Equilibrium Applications of Newton’s Laws of Motion 101

4.12 Nonequilibrium Applications of Newton’s Laws of Motion 105

CONCEPT SUMMARY 110

5 Dynamics of Uniform Circular Motion 121

5.1 Uniform Circular Motion 121

5.2 Centripetal Acceleration 122

5.3 Centripetal Force 125

5.4 Banked Curves 128

5.5 Satellites in Circular Orbits 129

5.6 Apparent Weightlessness and Artifi cial Gravity 133

5.7 Vertical Circular Motion 135

CONCEPT SUMMARY 136

6 Work and Energy 142

6.1 Work Done by a Constant Force 142

6.2 The Work–Energy Theorem and Kinetic Energy 145

6.3 Gravitational Potential Energy 152

6.4 Conservative Versus Nonconservative Forces 154

6.5 The Conservation of Mechanical Energy 156

6.6 Nonconservative Forces and the Work–Energy Theorem 159

6.7 Power 160

6.8 Other Forms of Energy and the Conservation of Energy 162

6.9 Work Done by a Variable Force 162

CONCEPT SUMMARY 164

7 Impulse and Momentum 173

7.1 The Impulse–Momentum Theorem 173

7.2 The Principle of Conservation of Linear Momentum 177

7.3 Collisions in One Dimension 182

7.4 Collisions in Two Dimensions 187

7.5 Center of Mass 187

CONCEPT SUMMARY 189

8 Rotational Kinematics 197

8.1 Rotational Motion and Angular Displacement 197

8.2 Angular Velocity and Angular Acceleration 200

8.3 The Equations of Rotational Kinematics 202

8.4 Angular Variables and Tangential Variables 204

8.5 Centripetal Acceleration and Tangential Acceleration 206

8.6 Rolling Motion 209

8.7 The Vector Nature of Angular Variables 210

CONCEPT SUMMARY 210

9 Rotational Dynamics 218

9.1 The Action of Forces and Torques on Rigid Objects 218

9.2 Rigid Objects in Equilibrium 220

9.3 Center of Gravity 225

9.4 Newton’s Second Law for Rotational Motion About a Fixed Axis 230

9.5 Rotational Work and Energy 236

9.6 Angular Momentum 239

CONCEPT SUMMARY 241

10 Simple Harmonic Motion and Elasticity 251

10.1 The Ideal Spring and Simple Harmonic Motion 251

10.2 Simple Harmonic Motion and the Reference Circle 255

10.3 Energy and Simple Harmonic Motion 260

10.4 The Pendulum 263

10.5 Damped Harmonic Motion 266

10.6 Driven Harmonic Motion and Resonance 267

10.7 Elastic Deformation 268

10.8 Stress, Strain, and Hooke’s Law 271

CONCEPT SUMMARY 272

11 Fluids 281

11.1 Mass Density 281

11.2 Pressure 282

11.3 Pressure and Depth in a Static Fluid 284

11.4 Pressure Gauges 287

11.5 Pascal’s Principle 288

11.6 Archimedes’ Principle 291

11.7 Fluids in Motion 295

11.8 The Equation of Continuity 297

11.9 Bernoulli’s Equation 299

11.10 Applications of Bernoulli’s Equation 301

11.11 Viscous Flow 304

CONCEPT SUMMARY 306

12 Temperature and Heat 316

12.1 Common Temperature Scales 316

12.2 The Kelvin Temperature Scale 317

12.3 Thermometers 318

12.4 Linear Thermal Expansion 320

12.5 Volume Thermal Expansion 326

12.6 Heat and Internal Energy 328

12.7 Heat and Temperature Change: Specific Heat Capacity 328

12.8 Heat and Phase Change: Latent Heat 331

12.9 Equilibrium Between Phases of Matter 336

12.10 Humidity 339

CONCEPT SUMMARY 340

13 The Transfer of Heat 348

13.1 Convection 348

13.2 Conduction 351

13.3 Radiation 357

13.4 Applications 361

CONCEPT SUMMARY 362

14 The Ideal Gas Law and Kinetic Theory 367

14.1 Molecular Mass, the Mole, and Avogadro’s Number 367

14.2 The Ideal Gas Law 370

14.3 Kinetic Theory of Gases 375

14.4 Diffusion 379

CONCEPT SUMMARY 382

15 Thermodynamics 388

15.1 Thermodynamic Systems and Their Surroundings 388

15.2 The Zeroth Law of Thermodynamics 388

15.3 The First Law of Thermodynamics 389

15.4 Thermal Processes 391

15.5 Thermal Processes Using an Ideal Gas 395

15.6 Specifi c Heat Capacities 398

15.7 The Second Law of Thermodynamics 399

15.8 Heat Engines 400

15.9 Carnot’s Principle and the Carnot Engine 401

15.10 Refrigerators, Air Conditioners, and Heat Pumps 404

15.11 Entropy 408

15.12 The Third Law of Thermodynamics 412

CONCEPT SUMMARY 412

16 Waves and Sound 422

16.1 The Nature of Waves 422

16.2 Periodic Waves 424

16.3 The Speed of a Wave on a String 425

16.4 The Mathematical Description of a Wave 428

16.5 The Nature of Sound 428

16.6 The Speed of Sound 431

16.7 Sound Intensity 435

16.8 Decibels 437

16.9 The Doppler Effect 439

16.10 Applications of Sound in Medicine 444

16.11 The Sensitivity of the Human Ear 446

CONCEPT SUMMARY 446

17 The Principle of Linear Superposition and Interference Phenomena 456

17.1 The Principle of Linear Superposition 456

17.2 Constructive and Destructive Interference of Sound Waves 457

17.3 Diffraction 461

17.4 Beats 463

17.5 Transverse Standing Waves 465

17.6 Longitudinal Standing Waves 469

17.7 Complex Sound Waves 472

CONCEPT SUMMARY 473

18 Electric Forces and Electric Fields 481

18.1 The Origin of Electricity 481

18.2 Charged Objects and the Electric Force 482

18.3 Conductors and Insulators 484

18.4 Charging by Contact and by Induction 485

18.5 Coulomb’s Law 486

18.6 The Electric Field 491

18.7 Electric Field Lines 496

18.8 The Electric Field Inside a Conductor: Shielding 499

18.9 Gauss’ Law 501

18.10 Copiers and Computer Printers 505

CONCEPT SUMMARY 506

19 Electric Potential Energy and the Electric Potential 514

19.1 Potential Energy 514

19.2 The Electric Potential Difference 515

19.3 The Electric Potential Difference Created by Point Charges 521

19.4 Equipotential Surfaces and Their Relation to the Electric Field 525

19.5 Capacitors and Dielectrics 528

19.6 Biomedical Applications of Electric Potential Differences 532

CONCEPT SUMMARY 534

20 Electric Circuits 541

20.1 Electromotive Force and Current 541

20.2 Ohm’s Law 543

20.3 Resistance and Resistivity 544

20.4 Electric Power 547

20.5 Alternating Current 549

20.6 Series Wiring 552

20.7 Parallel Wiring 555

20.8 Circuits Wired Partially in Series and Partially in Parallel 559

20.9 Internal Resistance 560

20.10 Kirchhoff’s Rules 561

20.11 The Measurement of Current and Voltage 564

20.12 Capacitors in Series and in Parallel 566

20.13 RC Circuits 568

20.14 Safety and the Physiological Effects of Current 569

CONCEPT SUMMARY 570

21 Magnetic Forces and Magnetic Fields 580

21.1 Magnetic Fields 580

21.2 The Force That a Magnetic Field Exerts on a Moving Charge 582

21.3 The Motion of a Charged Particle in a Magnetic Field 585

21.4 The Mass Spectrometer 589

21.5 The Force on a Current in a Magnetic Field 590

21.6 The Torque on a Current-Carrying Coil 592

21.7 Magnetic Fields Produced by Currents 594

21.8 Ampère’s Law 601

21.9 Magnetic Materials 602

CONCEPT SUMMARY 605

22 Electromagnetic Induction 615

22.1 Induced Emf and Induced Current 615

22.2 Motional Emf 616

22.3 Magnetic Flux 622

22.4 Faraday’s Law of Electromagnetic Induction 624

22.5 Lenz’s Law 627

22.6 Applications of Electromagnetic Induction to the Reproduction of Sound 630

22.7 The Electric Generator 631

22.8 Mutual Inductance and Self-Inductance 636

22.9 Transformers 639

CONCEPT SUMMARY 642

23 Alternating Current Circuits 651

23.1 Capacitors and Capacitive Reactance 651

23.2 Inductors and Inductive Reactance 653

23.3 Circuits Containing Resistance, Capacitance, and Inductance 655

23.4 Resonance in Electric Circuits 660

23.5 Semiconductor Devices 662

CONCEPT SUMMARY 667

24 Electromagnetic Waves 673

24.1 The Nature of Electromagnetic Waves 673

24.2 The Electromagnetic Spectrum 677

24.3 The Speed of Light 679

24.4 The Energy Carried by Electromagnetic Waves 681

24.5 The Doppler Effect and Electromagnetic Waves 685

24.6 Polarization 686

CONCEPT SUMMARY 692

25 The Refl ection of Light: Mirrors 699

25.1 Wave Fronts and Rays 699

25.2 The Refl ection of Light 700

25.3 The Formation of Images by a Plane Mirror 701

25.4 Spherical Mirrors 703

25.5 The Formation of Images by Spherical Mirrors 706

25.6 The Mirror Equation and the Magnification Equation 710

CONCEPT SUMMARY 715

26 The Refraction of Light: Lenses and Optical Instruments 721

26.1 The Index of Refraction 721

26.2 Snell’s Law and the Refraction of Light 722

26.3 Total Internal Refl ection 727

26.4 Polarization and the Refl ection and Refraction of Light 733

26.5 The Dispersion of Light: Prisms and Rainbows 733

26.6 Lenses 735

26.7 The Formation of Images by Lenses 736

26.8 The Thin-Lens Equation and the Magnification Equation 739

26.9 Lenses in Combination 742

26.10 The Human Eye 744

26.11 Angular Magnifi cation and the Magnifying Glass 748

26.12 The Compound Microscope 750

26.13 The Telescope 751

26.14 Lens Aberrations 753

CONCEPT SUMMARY 754

27 Interference and the Wave Nature of Light 766

27.1 The Principle of Linear Superposition 766

27.2 Young’s Double-Slit Experiment 768

27.3 Thin-Film Interference 771

27.4 The Michelson Interferometer 775

27.5 Diffraction 776

27.6 Resolving Power 780

27.7 The Diffraction Grating 785

27.8 Compact Discs, Digital Video Discs, and the Use of Interference 787

27.9 X-Ray Diffraction 789

CONCEPT SUMMARY 790

28 Special Relativity 798

28.1 Events and Inertial Reference Frames 798

28.2 The Postulates of Special Relativity 799

28.3 The Relativity of Time: Time Dilation 801

28.4 The Relativity of Length: Length Contraction 805

28.5 Relativistic Momentum 807

28.6 The Equivalence of Mass and Energy 809

28.7 The Relativistic Addition of Velocities 814

CONCEPT SUMMARY 816

29 Particles and Waves 822

29.1 The Wave–Particle Duality 822

29.2 Blackbody Radiation and Planck’s Constant 823

29.3 Photons and the Photoelectric Effect 824

29.4 The Momentum of a Photon and the Compton Effect 830

29.5 The De Broglie Wavelength and the Wave Nature of Matter 833

29.6 The Heisenberg Uncertainty Principle 835

CONCEPT SUMMARY 839

30 The Nature of the Atom 844

30.1 Rutherford Scattering and the Nuclear Atom 844

30.2 Line Spectra 845

30.3 The Bohr Model of the Hydrogen Atom 847

30.4 De Broglie’s Explanation of Bohr’s Assumption About Angular Momentum 852

30.5 The Quantum Mechanical Picture of the Hydrogen Atom 852

30.6 The Pauli Exclusion Principle and the Periodic Table of the Elements 856

30.7 X-Rays 859

30.8 The Laser 863

30.9 Medical Applications of the Laser 865

30.10 Holography 867

CONCEPT SUMMARY 869

31 Nuclear Physics and Radioactivity 876

31.1 Nuclear Structure 876

31.2 The Strong Nuclear Force and the Stability of the Nucleus 878

31.3 The Mass Defect of the Nucleus and Nuclear Binding Energy 879

31.4 Radioactivity 882

31.5 The Neutrino 887

31.6 Radioactive Decay and Activity 888

31.7 Radioactive Dating 891

31.8 Radioactive Decay Series 895

31.9 Radiation Detectors 895

CONCEPT SUMMARY 897

32 Ionizing Radiation, Nuclear Energy, and Elementary Particles 903

32.1 Biological Effects of Ionizing Radiation 903

32.2 Induced Nuclear Reactions 907

32.3 Nuclear Fission 909

32.4 Nuclear Reactors 911

32.5 Nuclear Fusion 912

32.6 Elementary Particles 915

32.7 Cosmology 920

CONCEPT SUMMARY 923

Appendices A-1

Appendix A Powers of Ten and Scientifi c Notation A-1

Appendix B Significant Figures A-1

Appendix C Algebra A-2

Appendix D Exponents and Logarithms A-3

Appendix E Geometry and Trigonometry A-4

Appendix F Selected Isotopes A-5

Answers to Check Your Understanding A-9

Answers to Odd-Numbered Problems A-16

Index I-1