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Simple Nature - Light and Matter
Simple Nature - Light and Matter
Simple Nature - Light and Matter
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54 Chapter 0 Introduction <strong>and</strong> Review
54 Chapter 0 Introduction <strong>and</strong> Review
The universe has been recyclingits contents ever since the BigBang, 13.7 billion years ago.Chapter 1Conservation of MassIt took just a moment for that head to fall, but a hundred yearsmight not produce another like it.Joseph-Louis Lagrange, referring to the execution of Lavoisieron May 8, 17941.1 MassChange is impossible, claimed the ancient Greek philosopher Parmenides.His work was nonscientific, since he didn’t state his ideasin a form that would allow them to be tested experimentally, butmodern science nevertheless has a strong Parmenidean flavor. Hismain argument that change is an illusion was that something can’tbe turned into nothing, <strong>and</strong> likewise if you have nothing, you can’tturn it into something. To make this into a scientific theory, we haveto decide on a way to measure what “something” is, <strong>and</strong> we can then55
- Page 4 and 5: Fullerton, Californiawww.lightandma
- 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 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
- Page 92 and 93: 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
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and since sin θ dθ occurs in the
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that is deeper than r. Under the as
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2.3.6 ⋆ Evidence for repulsive gr
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a / A vivid demonstration thatheat
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ture. This is a very good question,
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Three functions with thesame curvat
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This looks like a cosine function,
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ProblemsThe symbols √ , , etc. ar
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Problem 16.13 Anya and Ivan lean ov
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Problem 27.then we’d have U/m =
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37 Two springs with spring constant
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ExercisesExercise 2A: Reasoning wit
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128 Chapter 2 Conservation of Energ
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3.1 Momentum In One Dimensiona / Sy
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eing to the right. The initial mome
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3.1.3 Momentum compared to kinetic
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3.1.4 Collisions in one dimensiong
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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
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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
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3.2.4 Forces between solidsConserva
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Maximum acceleration of a car examp
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Discussion QuestionA Criticize the
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C A pool ball is rebounding from th
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forces, as if the hand were a pair
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This may not sound like an impressi
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stroke are both executed in straigh
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Accelerating a cart example 35If yo
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w / A wedge.x / Archimedes’ screw
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As in the preceding example, we hav
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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
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ight direction to add energy to the
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i / Example 45: a viola withouta mu
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Collapse of the Nimitz Freeway exam
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end up canceling out, however:Q =
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186 Chapter 3 Conservation of Momen
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c / Bullets are dropped and shot at
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the asteroid’s energy and boostin
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coordinate axes. Even though ∆x,
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of the three components,∆p x = 0
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A useless vector operation example
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Solving for the unknowns gives∆x
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o / Example 64.p / Adding vectors g
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How to generalize one-dimensional e
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needed to support the object in fig
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The easiest method is the one demon
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Incorrect solution #4:(same notatio
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The magnitude of the acceleration i
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dropped out like a trap door, showi
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af / Breaking trail, by WalterE. Bo
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know how to integrate with respect
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ProblemsThe symbols √ , , etc. ar
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Problem 16.Problem 19.resistance.)1
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of gravity on Mars.(a) Find the tim
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partner force. (a) A swimmer speeds
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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
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Problem 71.232 Chapter 3 Conservati
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77 A car accelerates from rest. At
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Problem 81.81 Complete example 71 o
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ExercisesExercise 3A: Force and Mot
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Exercise 3C: Worksheet on Resonance
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Exercise 3D: Vectors and MotionEach
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244 Chapter 3 Conservation of Momen
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An overhead view of apiece of putty
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inward toward the hinge will have n
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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
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momentum tells us that L = mrv sin
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In the absence of any torque, a rig
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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
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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
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k / Example 27.torque to the left w
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We can also generalize the plane-ro
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Problem 1.Problem 6.Problem 8.Probl
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14 (a) The bar of mass m is attache
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Problem 22.22 The sun turns on its
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35 The nucleus 168 Er (erbium-168)
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ExercisesExercise 4A: TorqueEquipme
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pesky set of constraints on heat en
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mit more air into the cavity behind
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Pressure of lava underneath a volca
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h / A simplified version of anideal
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for us to construct a simple connec
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For the first time we have an inter
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a / 1. The temperature differencebe
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Carnot engines operating between a
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from A to B, he lets it by, but whe
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B When we run the Carnot engine in
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f / A phase space for a singleatom
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time, the energy sharing is very un
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will the the one that maximizes the
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If the gas is monoatomic, then we k
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5.4.4 The arrow of time, or “this
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5.4.6 Summary of the laws of thermo
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may be in the form of microscopic d
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significant amount of heat to flow
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while the smaller area under the bo
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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
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k / Hitting a key on a pianocauses
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Our final result for the speed of t
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care, because the delay is the same
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An easy way to visualize this is in
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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
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6.2 Bounded WavesSpeech is what sep
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d / An uninverted reflection. There
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our intuitive expectation of strong
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valid solutions. In the following s
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j / In the mirror image, theareas o
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m / A pulse bounces backand forth.i
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q / Graphs of loudness versusfreque
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s / Standing waves on a rope. (PSSC
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“cavity” and “neck” parts o
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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
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d / A Galilean version of therelati
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g / Three types of transformations
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system, velocities are always unitl
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p / Apparatus used for the testof r
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sumption, the assumption that it ma
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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
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7.2.7 ⋆ Four-vectors and the inne
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would depend on the relative veloci
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7.3 DynamicsSo far we have said not
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In this frame, as expected, the sma
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But this whole argument was based o
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meters per second, so converting to
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Expressing γ as ( 1 − v 2 /c 2)
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7.3.4 ⋆ ProofsThis optional secti
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these lines. For example, a car sit
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An Einstein’s ring. Thedistant ob
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two-dimensional universe as if it w
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h / 1. A ray of light is emittedupw
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object that that isn’t influenced
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it impossible for any observer to b
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a variant on the Penrose singularit
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in it. Instead, it is currently spe
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2 Astronauts in three different spa
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(d) Simplify your answer to part c
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Problem 25b. Redrawn fromVan Baak,
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ExercisesExercise 7A: The Michelson
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Exercise 7B: Sports in Slowlightlan
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448 Chapter 7 Relativity
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Exercise 7D: Misconceptions about R
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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
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the other acquires an equal amount
- Page 460 and 461:
to get the beam up to speed in the
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telling us that we know about matte
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the muddle. The row-and-column sche
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the force of air friction canceled
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ectly evaluate the implications of
- Page 470 and 471:
that they were indeed electrically
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C Thomson found that the m/q of an
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the object with a net positive char
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thickness of material the radioacti
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It was already known that although
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particle. It turned out that it was
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For example they could easily strip
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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
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o / A nuclear power plant at Catten
- Page 492 and 493:
neutrons. In a nuclear fission bomb
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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
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killed, because the DNA becomes una
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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
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Example 1Ions moving across a cell
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ut the original meaning was to trav
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Force depends only on position. Sin
- Page 518 and 519:
Here are a few questions and answer
- Page 520 and 521:
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
- Page 526 and 527:
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
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9.2 Parallel and Series CircuitsIn
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to each resistance, resulting inI t
- Page 536 and 537:
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⊲
- Page 544 and 545:
Problem 2.ProblemsThe symbols √ ,
- Page 546 and 547:
Problem 16.only count that as one u
- Page 548 and 549:
knob turned all the way clockwise,
- Page 550 and 551:
A printed circuit board, likethe ki
- Page 552 and 553:
ExercisesExercise 9A: Voltage and C
- Page 554 and 555:
Exercise 9C: Reasoning About Circui
- Page 556 and 557:
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
- Page 562 and 563:
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
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g / Example 12: variation of the fi
- Page 580 and 581:
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
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space, 2 while charge doesn’t, we
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a / The symbol for a capacitor.b /
- Page 592 and 593:
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
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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
- Page 604 and 605:
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
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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
- Page 618 and 619:
orE outward, on side 1 A + E outwar
- Page 620 and 621:
|E| = kq totalr 2 ,where r is the r
- Page 622 and 623:
y considering its point charges ind
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Discussion Questionsg / Discussion
- Page 626 and 627:
with charge, change the Coulomb con
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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:
ProblemsThe symbols √ , , etc. ar
- 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
- Page 646 and 647:
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
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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
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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
- Page 674 and 675:
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
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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
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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
- Page 698 and 699:
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
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esulting in cancellation.The opposi
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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
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Problem 42.beam of light usually co
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(c) Discuss the relationship betwee
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(f) Use conservation of energy to r
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5. Now position yourself with your
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12.1.1 The nature of lightThe cause
- Page 736 and 737:
An image of Jupiter andits moon Io
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d / Two self-portraits of theauthor
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ultimate truth about light, but the
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• 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
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12.2 Images by ReflectionInfants ar
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Discussion QuestionA The figure sho
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down magnification is AB/DE. A repe
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i / A Newtonian telescopebeing used
- Page 756 and 757:
B Locate the images formed by two p
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12.3 Images, QuantitativelyIt sound
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⊲ The object and image angles are
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12.3.2 Other cases with curved mirr
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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
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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
- Page 782 and 783:
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
- Page 788 and 789:
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
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6 The figure on the next page shows
- Page 798 and 799:
14 Here’s a game my kids like to
- Page 800 and 801:
27 Suppose a converging lens is con
- Page 802 and 803:
same depth, but not quite. [Check:
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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
- Page 872 and 873:
Three dimensionsFor simplicity, we
- Page 874 and 875:
1. Oscillations can go backand fort
- Page 876 and 877:
C The figure shows a skateboarder t
- Page 878 and 879:
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
- Page 900 and 901:
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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