Simple Nature - Light and Matter

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Fullerton, Californiawww.lightandmatter.comCopyright c○2001-2008 Benjamin Crowellrev. February 3, 2014Permission is granted to copy, distribute and/or modify this documentunder the terms of the Creative Commons Attribution Share-Alike License, which can be found at creativecommons.org. Thelicense applies to the entire text of this book, plus all the illustrationsthat are by Benjamin Crowell. (At your option, you may alsocopy this book under the GNU Free Documentation License version1.2, with no invariant sections, no front-cover texts, and noback-cover texts.) All the illustrations are by Benjamin Crowell exceptas noted in the photo credits or in parentheses in the captionof the figure. This book can be downloaded free of charge fromwww.lightandmatter.com in a variety of formats, including editableformats.
Brief Contents0 Introduction 131 Conservation of Mass 552 Conservation of Energy 733 Conservation of Momentum 1294 Conservation of Angular Momentum 2455 Thermodynamics 2976 Waves 3397 Relativity 3818 Atoms and Electromagnetism 4539 DC Circuits 50910 Fields 55711 Electromagnetism 64712 Optics 73313 Quantum Physics 8215
Page 7 and 8: Contents0 Introduction and Review0.
Page 9 and 10: 5.5 More About Heat Engines . . . .
Page 11 and 12: 669.11.3 Magnetic Fields by Ampère
Page 13 and 14: The Mars Climate Orbiter is prepare
Page 15: temperatures and with many combinat
Page 19 and 20: idence that quarks have smaller par
Page 21 and 22: give clearer explanations.Finally,
Page 23 and 24: It can also be handy to have a rela
Page 25 and 26: The prefix centi-, meaning 10 −2
Page 27 and 28: goes like this:V = 1 3 Ah[1]A = πr
Page 29 and 30: the notation 10 0 to stand for one,
Page 32 and 33: calculation, 5.04 cm, was really no
Page 34 and 35: 0.2 Scaling and Order-of-Magnitude
Page 36 and 37: to many times your own height. The
Page 38 and 39: g / 1. This plank is as long as it
Page 40 and 41: the front panels of the three violi
Page 42 and 43: Correct solution #4: The area of a
Page 44 and 45: here?” The scientific Mr. Spock w
Page 46 and 47: 1. Don’t even attempt more than o
Page 48 and 49: Problem 10.mean, however, is define
Page 50 and 51: (d) Find the person’s acceleratio
Page 52 and 53:
Albert Einstein, and his moustache,
Page 54 and 55:
54 Chapter 0 Introduction and Revie
Page 56 and 57:
a / Portrait of Monsieur Lavoisiera
Page 58 and 59:
1.1.1 Problem-solving techniquesHow
Page 60 and 61:
∆m = 0, where m is the total mass
Page 62 and 63:
different substances will have diff
Page 64 and 65:
c / Left: In a frame of referenceth
Page 66 and 67:
f / Discussion question B.(discusse
Page 68 and 69:
Self-check D.since the derivative o
Page 70 and 71:
ProblemsThe symbols √ , , etc. ar
Page 72 and 73:
difficult? ⊲ Solution, p. 932Key
Page 74 and 75:
Heat energy can be convertedto ligh
Page 76 and 77:
a new form of invisible “mystery
Page 78 and 79:
f / A realistic drawing of Joule’
Page 80 and 81:
numbers. With a purely numerical ap
Page 82 and 83:
of gravity doesn’t change much if
Page 84 and 85:
field. If the plane can start from
Page 86 and 87:
m / Discussion question C.n / A hyd
Page 88 and 89:
88 Chapter 2 Conservation of Energy
Page 90 and 91:
A car drives over a cliff.new frame
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How long does it take to move 1 met
Page 94 and 95:
a / Approximations to thebrachistoc
Page 96 and 97:
a / An ellipse is circle that hasbe
Page 98 and 99:
to deduce the general equation for
Page 100 and 101:
to the mass of the object that inte
Page 102 and 103:
The minimum velocity required for t
Page 104 and 105:
and since sin θ dθ occurs in the
Page 106 and 107:
that is deeper than r. Under the as
Page 108 and 109:
2.3.6 ⋆ Evidence for repulsive gr
Page 110 and 111:
a / A vivid demonstration thatheat
Page 112 and 113:
ture. This is a very good question,
Page 114 and 115:
Three functions with thesame curvat
Page 116 and 117:
This looks like a cosine function,
Page 118 and 119:
Page 120 and 121:
Problem 16.13 Anya and Ivan lean ov
Page 122 and 123:
Problem 27.then we’d have U/m =
Page 124 and 125:
37 Two springs with spring constant
Page 126 and 127:
ExercisesExercise 2A: Reasoning wit
Page 128 and 129:
128 Chapter 2 Conservation of Energ
Page 130 and 131:
3.1 Momentum In One Dimensiona / Sy
Page 132 and 133:
eing to the right. The initial mome
Page 134 and 135:
3.1.3 Momentum compared to kinetic
Page 136 and 137:
3.1.4 Collisions in one dimensiong
Page 138 and 139:
could never do that again in a mill
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i / The highjumper’s body passeso
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where x 1 is the mass of the first
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3.1.6 The center of mass frame of r
Page 146 and 147:
The airbag increases ∆tso as to r
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d / Two magnets exert forceson each
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x (m) t (s)10 1.8420 2.8630 3.8040
Page 152 and 153:
3.2.4 Forces between solidsConserva
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Maximum acceleration of a car examp
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Discussion QuestionA Criticize the
Page 158 and 159:
C A pool ball is rebounding from th
Page 160 and 161:
forces, as if the hand were a pair
Page 162 and 163:
This may not sound like an impressi
Page 164 and 165:
stroke are both executed in straigh
Page 166 and 167:
Accelerating a cart example 35If yo
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w / A wedge.x / Archimedes’ screw
Page 170 and 171:
As in the preceding example, we hav
Page 172 and 173:
that have the same frequency is a s
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around until I got this result, sin
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quality factor, Q, is defined as Q
Page 178 and 179:
ight direction to add energy to the
Page 180 and 181:
i / Example 45: a viola withouta mu
Page 182 and 183:
Collapse of the Nimitz Freeway exam
Page 184 and 185:
end up canceling out, however:Q =
Page 186 and 187:
186 Chapter 3 Conservation of Momen
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c / Bullets are dropped and shot at
Page 190 and 191:
the asteroid’s energy and boostin
Page 192 and 193:
coordinate axes. Even though ∆x,
Page 194 and 195:
of the three components,∆p x = 0
Page 196 and 197:
A useless vector operation example
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Solving for the unknowns gives∆x
Page 200 and 201:
o / Example 64.p / Adding vectors g
Page 202 and 203:
How to generalize one-dimensional e
Page 204 and 205:
needed to support the object in fig
Page 206 and 207:
The easiest method is the one demon
Page 208 and 209:
Incorrect solution #4:(same notatio
Page 210 and 211:
The magnitude of the acceleration i
Page 212 and 213:
dropped out like a trap door, showi
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af / Breaking trail, by WalterE. Bo
Page 216 and 217:
know how to integrate with respect
Page 218 and 219:
Page 220 and 221:
Problem 16.Problem 19.resistance.)1
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of gravity on Mars.(a) Find the tim
Page 224 and 225:
partner force. (a) A swimmer speeds
Page 226 and 227:
Problem 45the 0.4-gram masses would
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53 If you walk 35 km at an angle 25
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(b) Interpret this equation in the
Page 232 and 233:
Problem 71.232 Chapter 3 Conservati
Page 234 and 235:
77 A car accelerates from rest. At
Page 236 and 237:
Problem 81.81 Complete example 71 o
Page 238 and 239:
ExercisesExercise 3A: Force and Mot
Page 240 and 241:
Exercise 3C: Worksheet on Resonance
Page 242 and 243:
Exercise 3D: Vectors and MotionEach
Page 244 and 245:
244 Chapter 3 Conservation of Momen
Page 246 and 247:
An overhead view of apiece of putty
Page 248 and 249:
inward toward the hinge will have n
Page 250 and 251:
special case, we can choose to visu
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j / Two asteroids collide.k / Every
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Note that although the factors of 2
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Relationship between force and torq
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is straight down, which is perpendi
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⊲ All three objects in the figure
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aa / Example 10.to either side of e
Page 264 and 265:
momentum tells us that L = mrv sin
Page 266 and 267:
In the absence of any torque, a rig
Page 268 and 269:
Radial acceleration at the surface
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The parallel axis theorem example 1
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differential. The result isarea ===
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of inertia as if the object was smo
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h / Moments of inertia of somegeome
Page 278 and 279:
4.3 Angular Momentum In Three Dimen
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14 deg, and it points along an axis
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manner like this, then the definiti
Page 284 and 285:
k / Example 27.torque to the left w
Page 286 and 287:
We can also generalize the plane-ro
Page 288 and 289:
Problem 1.Problem 6.Problem 8.Probl
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14 (a) The bar of mass m is attache
Page 292 and 293:
Problem 22.22 The sun turns on its
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35 The nucleus 168 Er (erbium-168)
Page 296 and 297:
ExercisesExercise 4A: TorqueEquipme
Page 298 and 299:
pesky set of constraints on heat en
Page 300 and 301:
mit more air into the cavity behind
Page 302 and 303:
Pressure of lava underneath a volca
Page 304 and 305:
h / A simplified version of anideal
Page 306 and 307:
for us to construct a simple connec
Page 308 and 309:
For the first time we have an inter
Page 310 and 311:
a / 1. The temperature differencebe
Page 312 and 313:
Carnot engines operating between a
Page 314 and 315:
from A to B, he lets it by, but whe
Page 316 and 317:
B When we run the Carnot engine in
Page 318 and 319:
f / A phase space for a singleatom
Page 320 and 321:
time, the energy sharing is very un
Page 322 and 323:
will the the one that maximizes the
Page 324 and 325:
If the gas is monoatomic, then we k
Page 326 and 327:
5.4.4 The arrow of time, or “this
Page 328 and 329:
5.4.6 Summary of the laws of thermo
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may be in the form of microscopic d
Page 332 and 333:
significant amount of heat to flow
Page 334 and 335:
while the smaller area under the bo
Page 336 and 337:
7 (a) Determine the ratio between t
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338 Chapter 5 Thermodynamics
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end of this book, we’ll even see
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c / As the wave pattern passes the
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the wave move ahead faster and get
Page 346 and 347:
k / Hitting a key on a pianocauses
Page 348 and 349:
Our final result for the speed of t
Page 350 and 351:
care, because the delay is the same
Page 352 and 353:
An easy way to visualize this is in
Page 354 and 355:
can be constructed as a superpositi
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⊲ Looking up the speed of light i
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scientists, to speak of the Big Ban
Page 360 and 361:
6.2 Bounded WavesSpeech is what sep
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d / An uninverted reflection. There
Page 364 and 365:
our intuitive expectation of strong
Page 366 and 367:
valid solutions. In the following s
Page 368 and 369:
j / In the mirror image, theareas o
Page 370 and 371:
m / A pulse bounces backand forth.i
Page 372 and 373:
q / Graphs of loudness versusfreque
Page 374 and 375:
s / Standing waves on a rope. (PSSC
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“cavity” and “neck” parts o
Page 378 and 379:
Problem 5.Problem 8.5 The figure sh
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Problem 16.16 A Fabry-Perot interfe
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c / Newton’s laws do not distingu
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f / The correspondence principlereq
Page 386 and 387:
d / A Galilean version of therelati
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g / Three types of transformations
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system, velocities are always unitl
Page 392 and 393:
p / Apparatus used for the testof r
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sumption, the assumption that it ma
Page 396 and 397:
at rest relative to the water. But
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7.2.4 No action at a distanceThe Ne
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so that Alice can complete her moti
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time into different regions accordi
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position relative to the sun at exa
Page 406 and 407:
7.2.7 ⋆ Four-vectors and the inne
Page 408 and 409:
would depend on the relative veloci
Page 410 and 411:
7.3 DynamicsSo far we have said not
Page 412 and 413:
In this frame, as expected, the sma
Page 414 and 415:
But this whole argument was based o
Page 416 and 417:
meters per second, so converting to
Page 418 and 419:
Expressing γ as ( 1 − v 2 /c 2)
Page 420 and 421:
7.3.4 ⋆ ProofsThis optional secti
Page 422 and 423:
these lines. For example, a car sit
Page 424 and 425:
An Einstein’s ring. Thedistant ob
Page 426 and 427:
two-dimensional universe as if it w
Page 428 and 429:
h / 1. A ray of light is emittedupw
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object that that isn’t influenced
Page 432 and 433:
it impossible for any observer to b
Page 434 and 435:
a variant on the Penrose singularit
Page 436 and 437:
in it. Instead, it is currently spe
Page 438 and 439:
2 Astronauts in three different spa
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(d) Simplify your answer to part c
Page 442 and 443:
Problem 25b. Redrawn fromVan Baak,
Page 444 and 445:
ExercisesExercise 7A: The Michelson
Page 446 and 447:
Exercise 7B: Sports in Slowlightlan
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448 Chapter 7 Relativity
Page 450 and 451:
Exercise 7D: Misconceptions about R
Page 452 and 453:
452 Chapter 7 Relativity
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sun, moon, stars, and planets were
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Two types of chargeWe can easily co
Page 458 and 459:
the other acquires an equal amount
Page 460 and 461:
to get the beam up to speed in the
Page 462 and 463:
telling us that we know about matte
Page 464 and 465:
the muddle. The row-and-column sche
Page 466 and 467:
the force of air friction canceled
Page 468 and 469:
ectly evaluate the implications of
Page 470 and 471:
that they were indeed electrically
Page 472 and 473:
C Thomson found that the m/q of an
Page 474 and 475:
the object with a net positive char
Page 476 and 477:
thickness of material the radioacti
Page 478 and 479:
It was already known that although
Page 480 and 481:
particle. It turned out that it was
Page 482 and 483:
For example they could easily strip
Page 484 and 485:
cording to Mosely, the atomic numbe
Page 486 and 487:
that fly off to see what was inside
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solution was found by measuring the
Page 490 and 491:
o / A nuclear power plant at Catten
Page 492 and 493:
neutrons. In a nuclear fission bomb
Page 494 and 495:
We can now list all four of the kno
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1. Our sun’s source of energy is
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a / The known nuclei, represented o
Page 500 and 501:
killed, because the DNA becomes una
Page 502 and 503:
e / Wild Przewalski’s horsesprosp
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Problem 1. Top: A realisticpicture
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12 The subatomic particles called m
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ExercisesExercise 8A: Nuclear decay
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saxophone, every technological tool
Page 512 and 513:
Example 1Ions moving across a cell
Page 514 and 515:
ut the original meaning was to trav
Page 516 and 517:
Force depends only on position. Sin
Page 518 and 519:
Here are a few questions and answer
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flow through it.For many substances
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superconductivity in metals that wo
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j / Example 9. In 1 and 2,charges t
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look like the usual resistor. The f
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9.1.5 Current-conducting properties
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attery acid becomes depleted of hyd
Page 532 and 533:
9.2 Parallel and Series CircuitsIn
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to each resistance, resulting inI t
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where “...” means that the sum
Page 538 and 539:
the two resistors in figure h/3.We
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Choice of high voltage for power li
Page 542 and 543:
A complicated circuit example 20⊲
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Problem 2.ProblemsThe symbols √ ,
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Problem 16.only count that as one u
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knob turned all the way clockwise,
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A printed circuit board, likethe ki
Page 552 and 553:
ExercisesExercise 9A: Voltage and C
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Exercise 9C: Reasoning About Circui
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556 Chapter 9 Circuits
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a / A bar magnet’s atoms are(part
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defined. The ship’s captain can m
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Reduction in gravity on Io due to J
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j / Example 3.self-check AFind an e
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a dipole moment — they are define
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10.2.1 One dimensionVoltage is elec
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The interpretation is that if you b
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Figure c shows some examples of way
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For large values of d, this express
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where Q is the total charge of the
Page 578 and 579:
g / Example 12: variation of the fi
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corners to the disk and transform i
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10.4 Energy In Fieldsa / Two opposi
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self-check DWe can think of the qua
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of the inward field contributed by
Page 588 and 589:
space, 2 while charge doesn’t, we
Page 590 and 591:
a / The symbol for a capacitor.b /
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ounding each capacitor will be half
Page 594 and 595:
in time:x ↔ qv ↔ Iself-check GH
Page 596 and 597:
due to its own momentum. It perform
Page 598 and 599:
or|V | =∣ LdIdt ∣ ,which in man
Page 600 and 601:
the inductor resists such a sudden
Page 602 and 603:
Example 26.Death by solenoid; spark
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ordering.( 1 √2+√ i ) 2 = √ 1
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x / The complex number e iφlies on
Page 608 and 609:
Figure aa shows a useful way to vis
Page 610 and 611:
Inductors tend to be big, heavy, ex
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The reason for using the trig ident
Page 614 and 615:
a purely inductive or capacitive lo
Page 616 and 617:
Resonance with damping example 33
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orE outward, on side 1 A + E outwar
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|E| = kq totalr 2 ,where r is the r
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y considering its point charges ind
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Discussion Questionsg / Discussion
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with charge, change the Coulomb con
Page 628 and 629:
The symmetry between the two sides
Page 630 and 631:
where dv is the volume of the cube.
Page 632 and 633:
The three terms in the divergence a
Page 634 and 635:
Page 636 and 637:
Problem 19.Problem 20.proton, for e
Page 638 and 639:
the lightning strike.(b) Based on y
Page 640 and 641:
units.(b) Verify that RC has units
Page 642 and 643:
lating freely (without any driving
Page 644 and 645:
ExercisesExercise 10A: Field Vector
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5. Now hook up the two solenoids in
Page 648 and 649:
A large current is createdby shorti
Page 650 and 651:
time I used it implicitly was in fi
Page 652 and 653:
f / A standard dipole madefrom a sq
Page 654 and 655:
and substituting q = λh and v = m/
Page 656 and 657:
o / Magnetic forces cause abeam of
Page 658 and 659:
electric field, a magnetic one, can
Page 660 and 661:
u / In this scene from SwanLake, th
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so the total field in the z directi
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For the y component, we havee / A s
Page 666 and 667:
We can pin down the result even mor
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i / The field of a dipole.where r i
Page 670 and 671:
circulates around the y axis, so at
Page 672 and 673:
to be, not where it is now. Coulomb
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We have found one specific example
Page 676 and 677:
to a flagpole, we can cancel out a
Page 678 and 679:
11.4 Ampère’s Law In Differentia
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y evaluating the field at the midpo
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i.e.,F = axˆx + byˆx + cˆx + dx
Page 684 and 685:
k / A summary of the derivative, gr
Page 686 and 687:
c / Detail from Ascending andDescen
Page 688 and 689:
the magnet. Are these atomic curren
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field in her region of space has be
Page 692 and 693:
A changing magnetic flux makes a cu
Page 694 and 695:
nearly zero. By Faraday’s law, th
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c / An Ampèrian surface superimpos
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and Maxwell’s equations becomeΦ
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k / Red and blue light travelat the
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second, the zero-point is located a
Page 704 and 705:
is the magnitude of the momentum ve
Page 706 and 707:
Discussion question A.Discussion qu
Page 708 and 709:
only penetrates to a very small dep
Page 710 and 711:
elationship D = ɛE would actually
Page 712 and 713:
esulting in cancellation.The opposi
Page 714 and 715:
a low permeability, while the other
Page 716 and 717:
n / A fluxgate compass.is externall
Page 718 and 719:
6 Two parallel wires of length L ca
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an instant at the upper right, but
Page 722 and 723:
Problem 25.20 Four long wires are a
Page 724 and 725:
Problem 35.Problem 37.32 Verify Amp
Page 726 and 727:
Problem 42.beam of light usually co
Page 728 and 729:
(c) Discuss the relationship betwee
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(f) Use conservation of energy to r
Page 732 and 733:
5. Now position yourself with your
Page 734 and 735:
12.1.1 The nature of lightThe cause
Page 736 and 737:
An image of Jupiter andits moon Io
Page 738 and 739:
d / Two self-portraits of theauthor
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ultimate truth about light, but the
Page 742 and 743:
• There is a tendency to conceptu
Page 744 and 745:
self-check AEach of these diagrams
Page 746 and 747:
m / Discussion question B.Discussio
Page 748 and 749:
12.2 Images by ReflectionInfants ar
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Discussion QuestionA The figure sho
Page 752 and 753:
down magnification is AB/DE. A repe
Page 754 and 755:
i / A Newtonian telescopebeing used
Page 756 and 757:
B Locate the images formed by two p
Page 758 and 759:
12.3 Images, QuantitativelyIt sound
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⊲ The object and image angles are
Page 762 and 763:
12.3.2 Other cases with curved mirr
Page 764 and 765:
signs also have to be memorized for
Page 766 and 767:
h / A diverging mirror in the shape
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j / Spherical mirrors are thecheape
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general type of eye that we share w
Page 772 and 773:
shown on this graph and then attemp
Page 774 and 775:
the mechanical model would predict
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that your calculator will flash an
Page 778 and 779:
D Classify the examples shown in fi
Page 780 and 781:
12.4.6 ⋆ Microscopic description
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12.5 Wave OpticsElectron microscope
Page 784 and 785:
of a crystal? Sound waves are used
Page 786 and 787:
j / Thomas Youngk / Double-slit dif
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object that diffracts it, so the tr
Page 790 and 791:
Although the equation λ/d = sin θ
Page 792 and 793:
things we’ve learned about diffra
Page 794 and 795:
apidly changing distances; on reuni
Page 796 and 797:
6 The figure on the next page shows
Page 798 and 799:
14 Here’s a game my kids like to
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27 Suppose a converging lens is con
Page 802 and 803:
same depth, but not quite. [Check:
Page 804 and 805:
Problem 42.42 Panel 1 of the figure
Page 806 and 807:
46 The figure below shows two diffr
Page 808 and 809:
53 The beam of a laser passes throu
Page 810 and 811:
Problem 59.the ancient problem of i
Page 812 and 813:
3. Now imagine the following new si
Page 814 and 815:
Exercise 12B: Object and Image Dist
Page 816 and 817:
Exercise 12D: Double-Source Interfe
Page 818 and 819:
Exercise 12E: Single-slit diffracti
Page 820 and 821:
Exercise 12F: Diffraction of LightE
Page 822 and 823:
energy, instead of being spread out
Page 824 and 825:
correlated. If they have been playi
Page 826 and 827:
small.The statement that the rule f
Page 828 and 829:
But the y axis can no longer be a u
Page 830 and 831:
for a long time once it gets there,
Page 832 and 833:
j / Calibration of the 14 C dating
Page 834 and 835:
given by(probability of a ≤ x ≤
Page 836 and 837:
k / In recent decades, a huge hole
Page 838 and 839:
A wave is partially absorbed.c / A
Page 840 and 841:
f / The hamster in her hamsterball
Page 842 and 843:
How would you extract h from the gr
Page 844 and 845:
F Does E = hf imply that a photon c
Page 846 and 847:
of approaching this issue.)j / Bull
Page 848 and 849:
We assume v is small enough so that
Page 850 and 851:
the probability distribution will b
Page 852 and 853:
trons that we have already used for
Page 854 and 855:
equations of general validity are t
Page 856 and 857:
wave carries high probability and w
Page 858 and 859:
An infinite sine wave can only tell
Page 860 and 861:
momentum implies a definite kinetic
Page 862 and 863:
of snapshots would amount to a desc
Page 864 and 865:
close are the electrons to the limi
Page 866 and 867:
dimensional particle in a box, and
Page 868 and 869:
Applying this to conservation of en
Page 870 and 871:
the probability of making it throug
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Three dimensionsFor simplicity, we
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1. Oscillations can go backand fort
Page 876 and 877:
C The figure shows a skateboarder t
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a / Eight wavelengths fit aroundthi
Page 880 and 881:
As shown by these examples, the unc
Page 882 and 883:
e / The three states of the hydroge
Page 884 and 885:
f / The energy levels of a particle
Page 886 and 887:
∂r/∂x = x/r comes in handy. Com
Page 888 and 889:
50% of its time in each atom. It’
Page 890 and 891:
tus to the z axis) and more memorab
Page 892 and 893:
ut why does that have anything to d
Page 894 and 895:
the data are only inaccurate due to
Page 896 and 897:
14 The photoelectric effect can occ
Page 898 and 899:
Problem 25.(b) Sketch a graph showi
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conservation of energy and momentum
Page 902 and 903:
Problem 43.43 On pp. 884-885 of sub
Page 904 and 905:
ExercisesExercise 13A: Quantum Vers
Page 906 and 907:
⊲ First we convert the equation i
Page 908 and 909:
Programming With PythonThe purpose
Page 910 and 911:
Appendix 2: MiscellanyUnphysical
Page 912 and 913:
18 bestt = t19 c1 = bestc120 c2 = b
Page 914 and 915:
p i + ∑ iThe spin theoremTheorem:
Page 916 and 917:
Appendix 3: Photo CreditsExcept as
Page 918 and 919:
Appendix 4: Hints and SolutionsHint
Page 920 and 921:
Hints for Chapter 6Page 377, proble
Page 922 and 923:
Answers to Self-Checks for Chapter
Page 924 and 925:
Page 301: (1) Not valid. The equati
Page 926 and 927:
Page 584:N −1 m −2 C 2 V 2 m
Page 928 and 929:
the dashed ray.Page 748: You should
Page 930 and 931:
direction it was initially going (i
Page 932 and 933:
Page 52, problem 38: The cone of mi
Page 934 and 935:
Page 224, problem 37: (a) Spring co
Page 936 and 937:
object, we have static friction, wh
Page 938 and 939:
Page 549, problem 29:(a) Conservati
Page 940 and 941:
Page 798, problem 19: (a) The objec
Page 942 and 943:
.0.8 Notation and unitsquantity uni
Page 944 and 945:
surfaces. For comparison, a typical
Page 946 and 947:
elations:a = ∆v∆tx = 1 2 at2 +
Page 948 and 949:
we are moving along with the projec
Page 950 and 951:
the number of oscillations required
Page 952 and 953:
In general, the cross product of ve
Page 954 and 955:
Sound waves consist of increases an
Page 956 and 957:
signs for charge is that with this
Page 958 and 959:
know that there is a delay in time
Page 960 and 961:
is related byΦ = 4πkq into the ch
Page 962 and 963:
to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
Page 966 and 967:
oth position and momentum, the Heis
Page 968 and 969:
Schrödinger’s, 864cathode rays,
Page 970 and 971:
unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
Page 974 and 975:
Einstein’s early theory, 838energ
Page 976 and 977:
Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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