Physics For Scientists And Engineers 6E - part 338

Approximating, 13–14

and limiting techniques, 721
with rays, 1097–1098
and series expansions, 1250, 1269, A.23
and small angles, 351, 1138–1139, 1180
and small values, 588, A.23

Aqueous humor, 1155
Arago, Dominique, 1207
Archimedes, 427, 429
Archimedes’s principle, 427–430
Area

and dimensional analysis, 11t
of geometric shapes, A.20t

Areas under curves. See Integration
Arguments of trigonometric functions,

455

Aristotle, 40, 215–216
Associative law of addition

for vectors, 62

Astigmatism, 1158
Astronomical units (AU), 399, 414
Astronomy and astrophysics. See also

Gravitation; Kepler’s laws; Planetary
motion; Planets; Relativity; Stars;
Sun; Universe

and Doppler shift, 525
history of, 396–399

Atmospheres

escape speeds from, 408
and heat engines, 669
law of, 663
and molecular speed distributions, 656
and polarization by scattering in, 1231
pressure of, 426, 446–447
and radiation, 628

Atomic clocks, 5–6
Atomic mass, 9–10, 592, A.4t–A.13t,

A.30t–A.31t

Atomic mass units (u), 9–10
Atomic nucleus

liquid drop model of, 791

Atomic number (Z), 8, A.4t–A.13t,

A.30t–A.31t

Atomic spectroscopy, 1220
Atomic spectrum, 1222
Atomizers, 437
Atoms, 8

Bohr model of hydrogen, 352–353,

731, 791, 852

magnetic dipole moments of, 944–946

Atwood machines, 129–130, 311–312
Audio systems, 1053, 1056
Audiovisual devices. See also Movies;

Musical instruments; Sound
recording

compact discs (CDs), 299, 529–532,

1203, 1221, 1236

digital video discs (DVD), 1203
loudspeakers, 548–549
and magnetic recording, 951
phonographs, 528–529

Audiovisual devices (Continued)

pickup coils, 971–972
radio, 813, 1051, 1061
television, 728, 765, 900, 1156–1157

Auroras, 910
Autobiography [Cellini], 1117
Automobiles

airbags for, 257
and diesel engines, 650, 680–681,

682–683, 701

and energy, 205–208, 828
and gasoline engines, 679–682
and hybrid drive systems, 985
intermittent windshield wipers for, 877
shock absorbers for, 472
and simple harmonic motion, 465
suspension systems of, 460–461
taillights of, 1100–1101

Average, 643
Average acceleration (a

!

), 31, 79–80

Average angular acceleration (!

!

),

293–296, 295

Average angular speed (&

!

), 293–296,

294

Average coefficient of linear expansion

(!), 587–588t

Average coefficient of volume

expansion ('), 588t

Average power ( ), 203, 1047
Average speed (v

(

), 27, 656–657

Average velocity (v

!

), 26–27, 78–79

Avogadro’s number (N

A

), 592

Back-of-the-envelope calculations, 14.

See also Approximating

Bainbridge mass spectrometers, 911
Balances

current, 933
equal-arm, 987–988
torsional, 393–394, 895, 1077

Ball-park figures, 13. See also

Approximating

Balloons, hot-air, 420
Banked curves, 155
Barometers, 426
Barometric pressure (P

0

), 426

Base of logarithms, A.19
Base quantities, 4, A.32t
Batteries, 858–861

chemical energy in, 799, 845–846
recharging, 1014–1015, 1061

Beam splitters, 1194
Beams, 368–369
Beat frequency (f

b

), 564–565

Beats, 544, 564–566
Belknap, C. J., 249
Bell, Alexander Graham, 519
Bernoulli, Daniel, 433, 434
Bernoulli effect, 435, 436
Bernoulli’s equation, 433–436, 434

!

Betatrons, 1001
Big Bang, 1088
Bimetallic strips, 589, 601
Binary numbers, 530, 531t
Binary stars, 409
Binding energy, 245, 404, 406
Binomial expansions, 1250, 1269, A.23
Biophysics. See also Health; Medicine

eyes, 1080, 1087, 1155–1159, 1216–1217
hearing, 519–522, 564

Biot, Jean-Baptiste, 927
Biot–Savart law, 927–932
Birefringent materials, 1229
Black bodies, 629, 1076
Black holes, 409–410, 1275, 1282
Blue shifts, 1281
Bode plots, 1064
Bohr, Niels, 352, 957
Bohr magneton ()

B

), 946

Boiling. See Vaporization
Boiling points, 612t
Boltzmann, Ludwig, 656
Boltzmann distribution law, 654–655
Boltzmann’s constant (k

B

), 593

Bond energy, 605. See also Internal energy
Bound systems, 397, 406
Boundaries

of systems, 183

Boundary conditions

and standing waves, 552–553, 555, 560

Boyle’s law, 584, 592
Bragg, William Lawrence, 1225
Bragg’s law, 1225
Brahe, Tycho, 396
Brewster, David, 1228
Brewster’s angle, 1119, 1228
Brewster’s law, 1228
Bridges

Tacoma Narrows, 473–474
trusses for, 372–373

British thermal units (Btu), 606
Brown, Robert, 579
Brownian motion, 579
Bubble chambers, 918
Bulk modulus (B), 373–375, 374t

and speed of sound waves, 513–514,

516

Bunsen, Robert, 870
Buoyant forces (B), 163, 164, 427–430,

782

Burn rates, 279

Calculus, A.23–A.28. See also Chain rule;

Definite integrals; Derivatives;
Differential equations;
Differentiation; Fourier series;
Gradient; Integration; Mean value
theorem; Partial derivatives

development of, 3, 28, 392, A.23
vs. numerical modeling, 168–169

I.2

Index

Caloric, 605
Calorie (cal), 212, 606
Calorimeters, 609

flow, 637

Calorimetry, 609–611

and entropy changes, 689–690

Cameras, 1153–1155

pinhole, 1239

Candela (cd), 4
Capacitance (C), 795–830

calculation of, 797–802
equivalent (C

eq

), 803–805

Capacitive reactance (X

C

), 1042,

1056

Capacitors, 795–796

in AC circuits, 1041–1043
charging of, 873–876
circuits of, 800, 802–806, 870, 873
construction of, 812t–814
cylindrical, 801–802
discharging of, 876–878
electrolytic, 813
parallel-plate, 767, 798–800
spherical, 802
variable, 813

Carlson, Chester, 784
Carnot, Sadi, 675
Carnot cycles, 675–676

entropy changes in, 685

Carnot engines, 675–678
Carnot’s theorem, 675
Cars. See Automobiles
Cartesian coordinate systems, 59. See

also Coordinate systems

Cartesian coordinates (x, y, z), 59
Cataracts, 1174
Categorizing problems, 46–47. See also

Problem-solving strategies

Cathode ray tubes (CRT), 727–728
Cavendish, Henry, 393, 711
Cavities

electric fields in, 780
thermal expansion of, 587

CCD. See Charge-coupled devices
CD. See Compact discs
CDS. See Cinema Digital Sound
Celestial equator, 412
Cellini, Benvenuto, 1117
Celsius, Anders, 585
Celsius temperature scale, 583, 610
Center of gravity, 272

vs. center of mass, 365–366

Center of mass (r

CM

), 270–274, 

272

vs. center of gravity, 365–366

Center of percussion, 333
Central forces (F), 403
Central maxima, 1206
Centrifugal casting, 172–173
“Centrifugal” forces, 159–160
Centrifuges, 665

Centripetal acceleration (a

c

), 92–93

and rotation about a fixed axis, 298
and second law of motion, 150–152
and speed of waves on a string,

496–497

and universal gravitation, 391–392

Ceramics

superconductivity in, 844

Cerenkov effect, 539
Cesium-133

and standard second, 5

Chain rule, 193–194, 313, A.24
Change (#) in a quantity, 25
Charge carriers, 833

and Hall effect, 914–916

Charge-coupled devices (CCD), 1154
Charge density (*, +, or ,), 720
Charges. See Electric charge
Charles’s and Gay–Lussac’s law, 584, 592
Charon, 1217–1218
Chemical energy

in batteries, 799, 845–846
in fuel, 278, 679

Chemistry. See Physical chemistry
Chimneys, falling, 310, 329
Chromatic aberration, 1153, 1165
Ciliary muscles, eye, 1156, 1158
Cinema. See Movies
Cinema Digital Sound (CDS), 532
Circles, A.20
Circuit breakers, 880
Circuit diagrams, 802
Circuit elements, 796. See also Batteries;

Capacitors; Diodes; Inductors;
Junctions; Resistors; Transformers;
Transistors

Circuit symbols

for AC sources, 1034
for batteries, 802
for capacitors, 802
for diodes, 1054
for ground, 710
for inductors, 1006
for resistors, 845
for switches, 802
for transformers, 1051

Circuits. See also Kirchhoff’s rules;

Parallel combinations; Series
combinations

alternating-current, 1033–1065
of capacitors, 800, 802–806, 870, 873
direct-current, 858–893
filter, 1055–1056
household, 865, 880–882
LC, 1015–1020
LRC, 1020–1022, 1043–1047,

1049–1051

RC, 873–878
of resistors, 845
RL, 1006–1011, 1007
short, 881–882

Circular motion, 150–180

and angular momentum, 341
nonuniform, 157–158
and orbits, 406
uniform, 91–93, 151–156, 465–467

Civil engineering

and banked curves, 155
and bridges, 372–373, 473–474
and chimneys, 310, 329
and concrete, 375–376
and dams, 425–426

Cladding, in optical fibers, 1114
Classical mechanics, 1. See also

Mechanics

Classical physics, 3. See also Quantum

mechanics

Clausius, Rudolf, 671, 683
Clausius statement of the second law of

thermodynamics, 671–672

Clocks

atomic, 5–6
mechanical, 2
moving, 1255
and pendulums, 140

Coaxial cables, 801, 840, 1012–1013
Coefficients

of damping (b), 471
of drag (D), 164, 206
Hall (R

H

), 915

of kinetic friction ()

k

), 132t

of linear expansion (!), 587–588t
of performance (COP), 672, 677
of resistivity, temperature (!), 837t,

843, 855

of rolling friction ()

r

), 205

of static friction ()

s

), 132t

of volume expansion ('), 588t

Coherence, 1177
Coils

Helmholtz, 963
pickup, 971–972
primary, 949, 968–969
Rogowski, 993–994
saddle, 963
search, 999
secondary, 949, 968–969

Collins, S. C., 1030
Collision frequency ( f ), 658
Collisions, 260

elastic, 260–267
glancing, 267
inelastic, 260–261
in one dimension, 260–267
perfectly inelastic, 261, 278
in two dimensions, 267–270

Columbia [space shuttle], 0, 278
Comets

Halley, 360, 397, 414

Common logarithms, A.19
Commutative law of addition

for vectors, 62

Index

I.3

Commutative law of multiplication

for scalar (dot) products, 187
and vector (cross) products, 337

Commutators, 984
Compact discs (CDs), 299, 529–532,

1203, 1221, 1236

Compasses, 895

dip, 962

Component vectors, 65

and scalar (dot) products, 187

Components of vectors, 65–70
Compound microscopes, 1160–1162
Compressibility (-), 375, 664

and speed of sound waves, 513–514

Compression, 515
Compression ratios, 680
Compression strokes, 679
Compton, Arthur, 177
Computer modeling, 169–170
Concave mirrors, 1131–1133. See also

Mirrors

Conceptualizing problems, 46–47. See

also Problem-solving strategies

Concrete, prestressed, 375–376
Condensation

latent heat of, 611–612t

Conduction

electrical, 710, 841–843
thermal, 197, 623–627, 687–688

Conduction electrons, 709, 841
Conductivity (+), 835, 842
Conductors, 709

electric potential due to charged,

778–781

in electrostatic equilibrium, 750–752
motion in magnetic fields of, 970,

973–977, 980–981

resistivity of, 837t

Cones, eye, 1156
Conservation of electric charge, 708, 870
Conservation of energy, 182, 196–199

and calorimetry, 609–611
and first law of thermodynamics,

618–619

and Kirchhoff’s rules, 870
and Lenz’s law, 978–979
mechanical, 220–228, 221, 313
and motional emf, 975, 977
and planetary motion, 406
and reflection and transmission of

waves, 500

relativistic, 1268–1272
and simple harmonic motion, 463

Conservation of momentum

angular, 345–349
linear, 252–256, 254, 275, 277–280
relativistic, 1267–1268, 1270

Conservative fields, 768
Conservative forces, 218, 221, 228–229

and potential energy, 234–236, 403
work done by, 228–229, 403, 768

Constant-volume gas thermometers,

584–586

Constructive interference, 545–549,

1177–1180, 1190

Contact forces, 112–113
Contact lenses, 1169
Continuity equation for fluids, 432
Convection, 627–628

and energy transfer, 197

Conversion of units, 12–13, A.1t–A.2t
Converters, AC–DC, 1053–1054
Convex mirrors, 1134. See also Mirrors
Cooper, Gordon, 1278
Coordinate systems, 59–60

Cartesian or rectangular, 59
polar, 59
right-handed, 66
rotating, 159
transformations between, Galilean, 98,

1247

transformations between, Lorentz,

1262–1267, 1263

Copernicus, Nicholaus, 46, 396
Coplanar vectors, 364
Coriolis forces, 159–160, 323
Corneas, 1155
Corner cube reflectors, 1119
Cornu, Marie, 1199
Corona discharge, 780–782
Cosine function, A.21. See also

Trigonometric functions

and components of vectors, 65, 83
and direction cosines, 213
and law of cosines, 64, A.22
and power factor (cos .), 1048,

1051

Cosmic background radiation, 1088
Cosmic rays, 1082

in Earth’s magnetic field, 910
and time dilation, 1255

Coulomb, Charles, 705, 711
Coulomb (C), 711, 933
Coulomb constant (k

e

), 711

Coulomb’s law, 711–715
Crests, 492
Critical angle (%

c

), 1111–1112

Critical temperature (T

c

), 844–845t

Critically damped oscillators, 471–472,

1022

Cross product, 337–339
CRT. See Cathode ray tubes
Crystalline lenses, 1155
Crystalline solids, 1229

diffraction of X-rays by, 1224–1225

Curie, Pierre, 951
Curie temperature (T

Curie

), 951t

Curie’s constant (C), 952
Curie’s law, 951–952
Current, electric. See Electric current
Current, fluid. See Flow
Current balances, 933

Current density ( J ), 835, 842
Cutoff ratio, 682
Cyclic processes, 619

and heat engines, 670
vs. one-time isothermal processes, 671

Cycloids, 316
Cyclotron frequency (&), 908–909
Cyclotrons, 908, 913–914

Dalton, John, 606
Dalton’s law of partial pressures, 602
Damped oscillators, 471–472,

1020–1022

Damping coefficients (b), 471
Dams, 425–426
D’Arsonval galvanometers, 879, 907
DC. See Direct-current
de Maricourt, Pierre, 895
Deceleration, 32
Decibels (dB), 519
Declination, magnetic, 954
Dees, cyclotron, 913
Defibrillators, 810, 825
Definite integrals, 45, A.26, A.28t. See

also Integration

Deformable systems. See also Rigid objects

moment of inertia of, 346
work done on, 605, 615–617

Degree of freedom, 644
Delta (#), 25
Demagnetization, 950
Democritus, 7
Density (*), 9t–10, 422t

of air, 446–447
and Archimedes’s principle, 428–430
of the Earth, 395
and incompressible liquids, 423
linear mass (, or )), 273–274, 302,

488, 496

and mean free path, 658
measurement of, 443
and moment of inertia, 302
and resistive forces, 164, 206
and speed of sound waves, 513–514
surface charge (+), 720, 779, 818
surface mass (+), 302
volumetric mass (*), 302

Depth of field, 1154
Derivatives, 29, 79–80, A.23–A.25t. See

also Differentiation

of exponential functions, 34, 164
partial, 235, 495, 503–504, 516, 773,

1069–1070

second, 31, A.24

Derived quantities, 4, A.32t
Destructive interference, 545–549,

1177–1180, 1190

Determinants, 338
Deuterium

as moderator, 266–267

I.4

Index

Devices. See Audiovisual devices;

Electronic devices; Mechanical
devices; Optical devices

Dewar, James, 629
Dewar flasks, 629
Diagrams. See Energy diagrams; Energy-

level diagrams; Free-body diagrams;
Graphs; Motion diagrams; PV
diagrams

Dialogue Concerning Two New World

Systems [Galilei], 46

Diamagnetism, 947–948, 952

perfect, 952, 1031

Diamonds, 1112
Dielectric constant (-), 810, 812t
Dielectric strength, 812t

of air, 782, 791, 812

Dielectrics, 796, 810–814

atomic description of, 817–820

Diesel engines, 650, 680–681, 682–683,

701

Differential equations, 163–164, 168

second-order, 454–455, 1069
separable, 875, 1007–1008

Differentials, perfect, A.27
Differentiation, A.23–A.25. See also

Derivatives

inexact, 618
partial, 235
total, 649

Diffraction, 1069, 1097, 1178. See also

Interference

of X-rays by crystals, 1224–1225

Diffraction grating spectrometers, 1219
Diffraction gratings, 1187, 1217–1224

resolution of, 1221–1222

Diffraction patterns, 1188, 1205–1241.

See also Interference

defined, 1206–1207
from slits, 1207–1214

Diffuse reflection, 1098–1099
Diffusion, 658
Digital cameras, 1154
Digital micromirror devices (DMD),

1101–1102, 1220

Digital sound recording, 530–532
Digital Theater Sound (DTS), 533
Digital video discs (DVD), 1203
Dimensional analysis, 10–12
Dimensions, 10, A.2t–A.3t
Diodes, 838, 1053–1054
Diopters, 1158
Dipole antennas, 1079–1080
Dipoles. See Electric dipoles; Magnetic

dipoles

Direct-current (DC) circuits, 858–893

and electrical meters, 879–880
and electrical safety, 881–882
and emf, 859–861
and household wiring, 880–882
and Kirchhoff’s rules, 869–873

Direct-current (DC) circuits (Continued)

and RC circuits, 873–878
resistor combinations in, 862–869

Direct-current (DC) generators, 984
Direction cosines, 213
Direction of propagation, 1069
Disorder. See Entropy
Dispersion, 488, 1109–1111, 1239
Displacement (#x), 25–26, 61

angular (#%), 293–296, 294

Displacement amplitude (s

max

), 515

Displacement current (I

d

), 942–944, 

943

Displacement vectors (#r), 78–80
Displacement volume, 681
Dissimilar metals

and bimetallic strips, 589

Distance (d), 26, A.20
Distribution functions, 654–657
Distribution of molecular speeds,

655–657

Distributive law of multiplication

for scalar (dot) products, 187
for vector (cross) products, 338

Diverging mirrors, 1134. See also Mirrors
Division

and significant figures, 15
and uncertainty, A.29

DMD. See Digital micromirror devices
Dolby Digital Sound, 533
Domain walls, 949
Domains, 949
Doppler, Christian Johann, 522
Doppler effect

non-relativistic, for sound, 522–528,

541

relativistic, for light, 1262

Dot product, 186–188
Double rainbows, 1094, 1111
Double-refracting materials, 1229
Double-slit interference patterns. See

Young’s double-slit experiment

Drag, aerodynamic, 436
Drag coefficients (D), 164, 206
Drag racing, 23, 144
Drift speed (v

d

), 834, 841–842

Drude, Paul, 841
DTS. See Digital Theater Sound
Dulong–Petit law, 654
DVD. See Digital video discs
Dynamics. See also Laws of motion

and numerical modeling, 167–170

e (Euler’s number), 163, 875, A.19
Ear trumpets, 518
Ears, 512, 519–522, 564. See also

Biophysics

Earth, 399t. See also Planetary motion

atmosphere of, 408
density of, 395

Earth (Continued)

escape speed from, 408t
magnetic field of, 895, 910,

953–954

Mohorovicic discontinuity of, 540
orbit of, 397
orbital velocity of, 1248–1250
Van Allen belts of, 910

Earthquakes

and Richter scale, 240–241
and waves, 489

Eccentricity (e), 396
Eddy currents, 986–988

in transformers, 987, 1051

Edison, Thomas, 528, 1053
Efficiency, thermal. See Thermal

efficiency

Eigenzeit. See Proper time intervals
Einstein, Albert, 1244, 1251

and Brownian motion, 579
and development of special relativity,

3, 988, 1243, 1245, 1249–1250

and general relativity, 402, 1195,

1273–1275

and photoelectric effect, 1093,

1095–1096

and special relativity, 6, 1249–1252,

1254, 1263

Elastic collisions, 260–267
Elastic limit, 374
Elastic modulus, 373, 374t
Elastic potential energy (U

s

), 197,

222–228

Elasticity, 373–376
Electric charge (q), 707–709

distributions of, 719–723, 746–750,

774–778

electromagnetic radiation from

accelerating, 988, 1079–1080

and electrostatic equilibrium,

750–752

fundamental (e), 708, 712, 781–782
induction of, 709–711
point, 711, 724, 768–771
positive and negative, 707
source and test, 715–716
of subatomic particles, 712t

Electric current (I ), 4, 831–857, 833

average (I

av

), 832

direct, 859
displacement (I

d

), 942–944, 943

eddy, 986–988
induced, 968–970
instantaneous (i), 833, 1034
magnetic field of, 927–932
magnetic force on, 900–904
model of, 833–835
root-mean-square (I

rms

), 1037

Electric current density ( J ), 835, 842
Electric dipole moment (p), 815, 905

induced, 817

Index

I.5