Simple Nature - Light and Matter

983 Pages·2016·40.9 MB·English

2
Simple Nature
An Introduction to Physics for Engineering
and Physical Science Students
Benjamin Crowell
www.lightandmatter.com
Fullerton, California
www.lightandmatter.com
Copyright (cid:13)c 2001-2008 Benjamin Crowell
rev. April 26, 2017
Permission is granted to copy, distribute and/or modify this docu-
ment under the terms of the Creative Commons Attribution Share-
Alike License, which can be found at creativecommons.org. The
license applies to the entire text of this book, plus all the illustra-
tions that are by Benjamin Crowell. (At your option, you may also
copy this book under the GNU Free Documentation License ver-
sion 1.2, with no invariant sections, no front-cover texts, and no
back-cover texts.) All the illustrations are by Benjamin Crowell ex-
cept as noted in the photo credits or in parentheses in the caption
of the figure. This book can be downloaded free of charge from
www.lightandmatter.com in a variety of formats, including editable
formats.
Brief Contents
0 Introduction and Review 13
1 Conservation of Mass 55
2 Conservation of Energy 73
3 Conservation of Momentum 129
4 Conservation of Angular Momentum 245
5 Thermodynamics 299
6 Waves 343
7 Relativity 385
8 Atoms and Electromagnetism 459
9 Circuits 515
10 Fields 563
11 Electromagnetism 653
12 Optics 739
13 Quantum Physics 829
5
6
Contents
0 Introduction and Review
0.1 Introduction and Review . . . . . . . . . . . . . . 13
The scientific method, 13.—What is physics?, 16.—How to learn
physics,19.—Velocityandacceleration,21.—Self-evaluation,23.—
Basics of the metric system, 24.—Less common metric prefixes,
28.—Scientificnotation,28.—Conversions,29.—Significantfigures,
31.—A note about diagrams, 33.
0.2 Scaling and Order-of-Magnitude Estimates . . . . . . 35
Introduction,35.—Scalingofareaandvolume,36.—Order-of-magnitude
estimates, 44.
Problems . . . . . . . . . . . . . . . . . . . . . . 48
1 Conservation of Mass
1.1 Mass . . . . . . . . . . . . . . . . . . . . . . 55
Problem-solving techniques, 58.—Delta notation, 59.
1.2 Equivalence of Gravitational and Inertial Mass . . . . . 60
1.3 Galilean Relativity. . . . . . . . . . . . . . . . . 62
Applications of calculus, 66.
1.4 A Preview of Some Modern Physics . . . . . . . . . 68
Problems . . . . . . . . . . . . . . . . . . . . . . 70
2 Conservation of Energy
2.1 Energy . . . . . . . . . . . . . . . . . . . . . 73
Theenergyconcept,73.—Logicalissues,75.—Kineticenergy,76.—
Power, 80.—Gravitational energy, 81.—Equilibrium and stability,
86.—Predicting the direction of motion, 89.
2.2 Numerical Techniques . . . . . . . . . . . . . . . 91
2.3 Gravitational Phenomena. . . . . . . . . . . . . . 96
Kepler’s laws, 96.—Circular orbits, 98.—The sun’s gravitational
field,99.—Gravitationalenergyingeneral,99.—Theshelltheorem,
102.—Evidence for repulsive gravity, 108.
2.4 Atomic Phenomena . . . . . . . . . . . . . . . . 109
Heatiskineticenergy.,110.—Allenergycomesfromparticlesmov-
ing or interacting., 111.
2.5 Oscillations . . . . . . . . . . . . . . . . . . . 113
Problems . . . . . . . . . . . . . . . . . . . . . . 118
Exercises . . . . . . . . . . . . . . . . . . . . . . 126
3 Conservation of Momentum
3.1 Momentum In One Dimension. . . . . . . . . . . . 130
Mechanical momentum, 130.—Nonmechanical momentum, 133.—
Momentum compared to kinetic energy, 134.—Collisions in one
dimension, 136.—The center of mass, 140.—The center of mass
frame of reference, 144.
3.2 Force In One Dimension . . . . . . . . . . . . . . 145
Momentum transfer, 145.—Newton’s laws, 147.—What force is
not,150.—Forcesbetweensolids,152.—Fluidfriction,155.—Analysis
offorces,156.—Transmissionofforcesbylow-massobjects,158.—
Work, 160.—Simple Machines, 167.—Force related to interaction
energy, 168.
3.3 Resonance. . . . . . . . . . . . . . . . . . . . 171
Damped, free motion, 172.—The quality factor, 175.—Driven mo-
tion, 176.
3.4 Motion In Three Dimensions . . . . . . . . . . . . 187
TheCartesianperspective,187.—Rotationalinvariance,190.—Vectors,
193.—Calculuswithvectors,208.—Thedotproduct,212.—Gradients
and line integrals (optional), 215.
Problems . . . . . . . . . . . . . . . . . . . . . . 218
Exercises . . . . . . . . . . . . . . . . . . . . . . 239
4 Conservation of Angular Momentum
4.1 Angular Momentum In Two Dimensions. . . . . . . . 245
Angularmomentum,245.—Applicationtoplanetarymotion,250.—
Two theorems about angular momentum, 251.—Torque, 254.—
Applicationstostatics,258.—ProofofKepler’sellipticalorbitlaw,
262.
4.2 Rigid-Body Rotation . . . . . . . . . . . . . . . . 265
Kinematics, 265.—Relations between angular quantities and mo-
tion of a point, 266.—Dynamics, 268.—Iterated integrals, 270.—
Finding moments of inertia by integration, 273.
4.3 Angular Momentum In Three Dimensions . . . . . . . 278
Rigid-body kinematics in three dimensions, 278.—Angular mo-
mentum in three dimensions, 280.—Rigid-body dynamics in three
dimensions, 285.
Problems . . . . . . . . . . . . . . . . . . . . . . 288
Exercises . . . . . . . . . . . . . . . . . . . . . . 297
5 Thermodynamics
5.1 Pressure and Temperature . . . . . . . . . . . . . 300
Pressure, 300.—Temperature, 304.
5.2 Microscopic Description of An Ideal Gas . . . . . . . 307
Evidence for the kinetic theory, 307.—Pressure, volume, and tem-
perature, 308.
5.3 Entropy As a Macroscopic Quantity . . . . . . . . . 312
Efficiencyandgradesofenergy,312.—Heatengines,313.—Entropy,
315.
5.4 Entropy As a Microscopic Quantity. . . . . . . . . . 319
Amicroscopicviewofentropy,319.—Phasespace,320.—Microscopic
definitions of entropy and temperature, 321.—The arrow of time,
or“thiswaytotheBigBang”,329.—Quantummechanicsandzero
entropy, 330.—Summary of the laws of thermodynamics, 331.
8 Contents
5.5 More About Heat Engines . . . . . . . . . . . . . 331
Problems . . . . . . . . . . . . . . . . . . . . . . 338
6 Waves
6.1 Free Waves . . . . . . . . . . . . . . . . . . . 344
Wave motion, 344.—Waves on a string, 350.—Sound and light
waves, 353.—Periodic waves, 355.—The Doppler effect, 358.
6.2 Bounded Waves . . . . . . . . . . . . . . . . . 364
Reflection,transmission,andabsorption,364.—Quantitativetreat-
mentofreflection,369.—Interferenceeffects,372.—Wavesbounded
on both sides, 374.
Problems . . . . . . . . . . . . . . . . . . . . . . 381
7 Relativity
7.1 Time Is Not Absolute . . . . . . . . . . . . . . . 385
Thecorrespondenceprinciple,385.—Causality,385.—Timedistor-
tion arising from motion and gravity, 386.
7.2 Distortion of Space and Time . . . . . . . . . . . . 388
The Lorentz transformation, 388.—The γ factor, 393.—The uni-
versalspeedc,398.—Noactionatadistance,403.—Thelightcone,
406.—The spacetime interval, 406.—Four-vectors and the inner
product, 411.—Doppler shifts of light and addition of velocities,
412.
7.3 Dynamics . . . . . . . . . . . . . . . . . . . . 415
Momentum,415.—Equivalenceofmassandenergy,419.—Theenergy-
momentum four-vector, 423.—Proofs, 426.
7.4 General Relativity . . . . . . . . . . . . . . . . . 429
Ouruniverseisn’tEuclidean,429.—Theequivalenceprinciple,432.—
Black holes, 436.—Cosmology, 439.
Problems . . . . . . . . . . . . . . . . . . . . . . 443
Exercises . . . . . . . . . . . . . . . . . . . . . . 451
8 Atoms and Electromagnetism
8.1 The Electric Glue . . . . . . . . . . . . . . . . . 459
Thequestfortheatomicforce,460.—Charge,electricityandmag-
netism, 461.—Atoms, 466.—Quantization of charge, 471.—The
electron, 474.—The raisin cookie model of the atom, 478.
8.2 The Nucleus . . . . . . . . . . . . . . . . . . . 480
Radioactivity, 480.—The planetary model, 483.—Atomic number,
487.—The structure of nuclei, 492.—The strong nuclear force, al-
pha decay and fission, 495.—The weak nuclear force; beta decay,
498.—Fusion, 500.—Nuclear energy and binding energies, 502.—
Biological effects of ionizing radiation, 503.—The creation of the
elements, 508.
Problems . . . . . . . . . . . . . . . . . . . . . . 510
Exercises . . . . . . . . . . . . . . . . . . . . . . 514
Contents 9
9 Circuits
9.1 Current and Voltage . . . . . . . . . . . . . . . . 516
Current, 516.—Circuits, 519.—Voltage, 520.—Resistance, 525.—
Current-conducting properties of materials, 534.
9.2 Parallel and Series Circuits . . . . . . . . . . . . . 538
Schematics,538.—Parallelresistancesandthejunctionrule,539.—
Series resistances, 543.
Problems . . . . . . . . . . . . . . . . . . . . . . 550
Exercises . . . . . . . . . . . . . . . . . . . . . . 558
10 Fields
10.1 Fields of Force. . . . . . . . . . . . . . . . . . 563
Whyfields?,563.—Thegravitationalfield,565.—Theelectricfield,
569.
10.2 Voltage Related To Field . . . . . . . . . . . . . 573
One dimension, 573.—Two or three dimensions, 576.
10.3 Fields by Superposition . . . . . . . . . . . . . . 578
Electric field of a continuous charge distribution, 578.—The field
near a charged surface, 584.
10.4 Energy In Fields . . . . . . . . . . . . . . . . . 587
Electricfieldenergy,587.—Gravitationalfieldenergy,592.—Magnetic
field energy, 592.
10.5 LRC Circuits . . . . . . . . . . . . . . . . . . 594
Capacitanceandinductance,594.—Oscillations,598.—Voltageand
current, 600.—Decay, 605.—Review of complex numbers, 608.—
Euler’sformula,610.—Impedance,612.—Power,615.—Impedance
matching, 618.—Impedances in series and parallel, 620.
10.6 Fields by Gauss’ Law . . . . . . . . . . . . . . . 622
Gauss’ law, 622.—Additivity of flux, 626.—Zero flux from outside
charges, 626.—Proof of Gauss’ theorem, 630.—Gauss’ law as a
fundamental law of physics, 630.—Applications, 631.
10.7 Gauss’ Law In Differential Form . . . . . . . . . . 634
Problems . . . . . . . . . . . . . . . . . . . . . . 639
Exercises . . . . . . . . . . . . . . . . . . . . . . 649
11 Electromagnetism
11.1 More About the Magnetic Field . . . . . . . . . . . 653
Magnetic forces, 653.—The magnetic field, 657.—Some applica-
tions, 661.—No magnetic monopoles, 662.—Symmetry and hand-
edness, 665.
11.2 Magnetic Fields by Superposition. . . . . . . . . . 667
Superpositionofstraightwires,667.—Energyinthemagneticfield,
671.—Superposition of dipoles, 671.—The Biot-Savart law (op-
tional), 675.
11.3 Magnetic Fields by Ampe`re’s Law. . . . . . . . . . 679
Amp`ere’s law, 679.—A quick and dirty proof, 681.—Maxwell’s
equations for static fields, 682.
11.4 Ampe`re’s Law In Differential Form (Optional) . . . . . 684
The curl operator, 684.—Properties of the curl operator, 685.
10 Contents