Simple Nature

619 Pages·2003·18.28 MB·english

by  СrowelI B.

Simple Nature
An Introduction to Physics
for Engineering and
Physical Science Students
Benjamin Crowell
www.lightandmatter.com
Light and Matter
Fullerton, California
www.lightandmatter.com
Copyright (cid:13)c 2001 Benjamin Crowell
All rights reserved.
Edition 0.1 — 2001
rev. July 1, 2003
ISBN 0-9704670-7-9
Permission is granted to copy, distribute and/or modify this doc-
ument under the terms of the GNU Free Documentation License,
Version 1.1, with no invariant sections, no front-cover texts and no
back-cover texts. A copy of the license is provided in the appendix
titled GNU Free Documentation License. The license applies to
the entire text of this book, plus all the illustrations that are by
Benjamin Crowell. All the illustrations are by Benjamin Crowell
except as noted in the photo credits or in parentheses in the cap-
tion 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
1 Conservation of Mass 11
2 Conservation of Energy 31
3 Conservation of Momentum 81
4 Conservation of Angular Momentum 149
5 Thermodynamics 191
6 Waves 219
7 Relativity 258
8 Atoms and Electromagnetism 289
9 DC Circuits 339
10 Fields 373
11 Electromagnetism 435
12 Quantum Physics 495
3
4
Contents
1 Conservation of Mass
1.1 Mass . . . . . . . . . . . . . . . . . . . . . . 11
Problem-solving techniques, 13.—Delta notation, 15.
1.2 Equivalence of Gravitational and Inertial Mass . . . . . 16
1.3 Galilean Relativity. . . . . . . . . . . . . . . . . 19
Applications of calculus, 22.
1.4 A Preview of Some Modern Physics . . . . . . . . . 25
Problems . . . . . . . . . . . . . . . . . . . . . . 27
2 Conservation of Energy
2.1 Energy . . . . . . . . . . . . . . . . . . . . . 31
Theenergyconcept,31.—Logicalissues,33.—Kineticenergy,34.—
Power, 37.—Gravitational energy, 38.—Equilibrium and stability,
43.—Predicting the direction of motion, 44.
2.2 Numerical Techniques . . . . . . . . . . . . . . . 46
2.3 Gravitational Phenomena. . . . . . . . . . . . . . 51
Kepler’s laws, 51.—Circular orbits, 53.—The sun’s gravitational
field,54.—Gravitationalenergyingeneral,55.—Theshelltheorem,
58.
2.4 Atomic Phenomena . . . . . . . . . . . . . . . . 64
Heat is kinetic energy., 64.—All energy comes from particles mov-
ing or interacting., 65.
2.5 Oscillations . . . . . . . . . . . . . . . . . . . 68
Problems . . . . . . . . . . . . . . . . . . . . . . 73
3 Conservation of Momentum
3.1 Momentum in One Dimension. . . . . . . . . . . . 81
Mechanicalmomentum,81.—Nonmechanicalmomentum,84.—Momentum
comparedtokineticenergy,85.—Collisionsinonedimension,86.—
Thecenterofmass,90.—Thecenterofmassframeofreference,93.
3.2 Force in One Dimension . . . . . . . . . . . . . . 94
Momentumtransfer,94.—Newton’slaws,95.—Forcesbetweensolids,
96.—Work, 98.—Simple machines, 104.—Force related to interac-
tion energy, 105.
3.3 Resonance. . . . . . . . . . . . . . . . . . . . 107
Damped,freemotion,108.—Thequalityfactor,111.—Drivenmotion,
111.
3.4 Motion in Three Dimensions . . . . . . . . . . . . 118
TheCartesianperspective,118.—Rotationalinvariance,120.—Vectors,
122.—Calculuswithvectors,132.—Thedotproduct,134.—Gradients
and line integrals (optional), 137.
Problems . . . . . . . . . . . . . . . . . . . . . . 140
4 Conservation of Angular Momentum
4.1 Angular Momentum in Two Dimensions. . . . . . . . 149
Angularmomentum,149.—Applicationtoplanetarymotion,153.—
Two Theorems About Angular Momentum, 155.—Torque, 157.—
Applicationstostatics,161.—ProofofKepler’sellipticalorbitlaw,
163.
4.2 Rigid-Body Rotation . . . . . . . . . . . . . . . . 166
Kinematics, 166.—Relations between angular quantities and mo-
tionofapoint,167.—Dynamics,169.—Findingmomentsofinertia
by integration, 171.
4.3 Angular Momentum in Three Dimensions . . . . . . . 174
Rigid-body kinematics in three dimensions, 174.—Angular mo-
mentum in three dimensions, 176.—Rigid-body dynamics in three
dimensions, 180.
Problems . . . . . . . . . . . . . . . . . . . . . . 184
5 Thermodynamics
5.1 Pressure and Temperature . . . . . . . . . . . . . 192
Pressure, 192.—Temperature, 196.
5.2 Microscopic Description of an Ideal Gas . . . . . . . 199
Evidenceforthekinetictheory,199.—Pressure,volume,andtemperature,
199.
5.3 Entropy as a Macroscopic Quantity. . . . . . . . . . 202
Efficiencyandgradesofenergy,202.—Heatengines,202.—Entropy,
204.
5.4 Entropy as a Microscopic Quantity (Optional) . . . . . 208
Amicroscopicviewofentropy,208.—Phasespace,209.—Microscopic
definitions of entropy and temperature, 209.—The arrow of time,
or “This way to the Big Bang”, 213.—Quantum mechanics and
zero entropy, 214.
Problems . . . . . . . . . . . . . . . . . . . . . . 216
6 Waves
6.1 Free Waves . . . . . . . . . . . . . . . . . . . 220
Wave motion, 220.—Waves on a string, 224.—Sound and light
waves, 227.—Periodic waves, 229.—The Doppler effect, 232.
6.2 Bounded Waves . . . . . . . . . . . . . . . . . 237
Reflection,transmission,andabsorption,237.—Quantitativetreat-
mentofreflection,242.—Interferenceeffects,245.—Wavesbounded
on both sides, 247.
Problems . . . . . . . . . . . . . . . . . . . . . . 252
7 Relativity
7.1 Basic Relativity . . . . . . . . . . . . . . . . . . 258
The principle of relativity, 258.—Distortion of time and space,
259.—Applications, 262.
7.2 The Lorentz transformation . . . . . . . . . . . . . 266
Coordinate transformations in general, 266.—Derivation of the
Lorentz transformation, 267.—Spacetime, 270.
6 Contents
7.3 Dynamics . . . . . . . . . . . . . . . . . . . . 275
Invariants,275.—Combinationofvelocities,275.—Momentumand
force,276.—Kineticenergy,278.—Equivalenceofmassandenergy,
280.
Problems . . . . . . . . . . . . . . . . . . . . . . 284
8 Atoms and Electromagnetism
8.1 The Electric Glue . . . . . . . . . . . . . . . . . 289
Thequestfortheatomicforce,290.—Charge,electricityandmagnetism,
291.—Atoms, 295.—Quantization of charge, 300.—The electron,
303.—The raisin cookie model of the atom, 307.
8.2 The Nucleus . . . . . . . . . . . . . . . . . . . 309
Radioactivity, 309.—The planetary model of the atom, 312.—
Atomic number, 315.—The structure of nuclei, 320.—The strong
nuclear force, alpha decay and fission, 323.—The weak nuclear
force;betadecay,326.—Fusion,329.—Nuclearenergyandbinding
energies, 329.—Biological effects of ionizing radiation, 331.—The
creation of the elements, 333.
Problems . . . . . . . . . . . . . . . . . . . . . . 336
9 DC Circuits
9.1 Current and Voltage . . . . . . . . . . . . . . . . 339
Current, 339.—Circuits, 342.—Voltage, 344.—Resistance, 347.—
Current-conducting properties of materials, 354.
9.2 Parallel and Series Circuits . . . . . . . . . . . . . 358
Schematics,358.—Parallelresistancesandthejunctionrule,358.—
Series resistances, 362.
Problems . . . . . . . . . . . . . . . . . . . . . . 367
10 Fields
10.1 Fields of Force. . . . . . . . . . . . . . . . . . 373
Whyfields?,373.—Thegravitationalfield,375.—Theelectricfield,
378.
10.2 Voltage Related to Field. . . . . . . . . . . . . . 381
One dimension, 381.—Two or three dimensions, 382.
10.3 Fields by Superposition . . . . . . . . . . . . . . 384
Electric field of a continuous charge distribution, 384.—The field
near a charged surface, 390.
10.4 Energy in Fields . . . . . . . . . . . . . . . . . 392
Electricfieldenergy,392.—Gravitationalfieldenergy,396.—Magnetic
field energy, 396.
10.5 LRC Circuits . . . . . . . . . . . . . . . . . . 397
Capacitanceandinductance,397.—Oscillations,399.—Voltageand
current,402.—Decay,404.—Impedance,406.—Power,408.—Impedance
Matching, 410.—Complex Impedance, 412.
10.6 Fields by Gauss’ Law . . . . . . . . . . . . . . . 415
Gauss’ law, 415.—Additivity of flux, 418.—Zero flux from outside
charges, 419.—Proof of Gauss’ theorem, 420.—Gauss’ law as a
fundamental law of physics, 420.—Applications, 421.
Contents 7
10.7 Gauss’ Law in Differential Form. . . . . . . . . . . 423
Problems . . . . . . . . . . . . . . . . . . . . . . 427
11 Electromagnetism
11.1 More About the Magnetic Field . . . . . . . . . . . 435
Magneticforces,435.—Themagneticfield,438.—Someapplications,
441.—No magnetic monopoles, 442.—Symmetry and handedness,
444.
11.2 Magnetic Fields by Superposition. . . . . . . . . . 446
Superpositionofstraightwires,446.—Energyinthemagneticfield,
449.—Superpositionofdipoles,449.—TheBiot-Savartlaw(optional),
452.
11.3 Magnetic Fields by Ampe`re’s Law. . . . . . . . . . 456
Amp`ere’s law, 456.—A quick and dirty proof, 457.—Maxwell’s
equations for static fields, 458.
11.4 Ampe`re’s Law in Differential Form (optional) . . . . . 460
The curl operator, 460.—Properties of the curl operator, 461.
11.5 Induced Electric Fields . . . . . . . . . . . . . . 465
Faraday’sexperiment,465.—Whyinduction?,467.—Faraday’slaw,
469.
11.6 Maxwell’s Equations . . . . . . . . . . . . . . . 474
Induced magnetic fields, 474.—Light waves, 476.
Problems . . . . . . . . . . . . . . . . . . . . . . 484
12 Quantum Physics
12.1 Rules of Randomness . . . . . . . . . . . . . . 495
Randomness isn’t random., 496.—Calculating randomness, 496.—
Probability distributions, 499.—Exponential decay and half-life,
501.—Applications of calculus, 505.
12.2 Light as a Particle . . . . . . . . . . . . . . . . 507
Evidenceforlightasaparticle,508.—Howmuchlightisonephoton?,
509.—Wave-particle duality, 512.—Photons in three dimensions,
516.
12.3 Matter as a Wave . . . . . . . . . . . . . . . . 518
Electrons as waves, 518.—Dispersive waves, 522.—Bound states,
524.—Theuncertaintyprincipleandmeasurement,526.—Electrons
in electric fields, 529.—The Schr¨odinger equation, 531.
12.4 The Atom. . . . . . . . . . . . . . . . . . . . 534
Classifying states, 534.—Angular momentum in three dimensions,
536.—The hydrogen atom, 537.—Energies of states in hydrogen,
538.—Electron spin, 541.—Atoms with more than one electron,
543.
Problems . . . . . . . . . . . . . . . . . . . . . . 545
Appendix 1: Programming with Python 553
Appendix 2: Miscellany 555
Appendix 3: Acknowledgments 563
Appendix 4: Photo Credits 565
Appendix 5: Hints and Solutions 567
8 Contents
Appendix 6: Useful Data 581
Notation and terminology, compared with other books, 581.—
Notation and units, 582.—Metric prefixes, 582.—Nonmetric units,
583.—The Greek alphabet, 583.—Fundamental constants, 583.—
Subatomic particles, 583.—Earth, moon, and sun, 584.—The pe-
riodic table, 584.—Atomic masses, 584.
Appendix 7: Summary 587
Appendix 8: Glossary 605
Contents 9
10 Contents