Simple Nature - Light and Matter

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Momentum compared to kinetic energy, 134.—Collisions in onedimension, 136.—The center of mass, 140.—The center of massframe of reference, 144.3.2 Force In One Dimension . . . . . . . . . . . . . . 145Momentum transfer, 145.—Newton’s laws, 147.—What force isnot, 150.—Forces between solids, 152.—Fluid friction, 155.—Analysisof forces, 156.—Transmission of forces by low-mass objects, 158.—Work, 160.—Simple Machines, 167.—Force related to interactionenergy, 168.3.3 Resonance. . . . . . . . . . . . . . . . . . . . 171Damped, free motion, 172.—The quality factor, 175.—Driven motion,176.3.4 Motion In Three Dimensions . . . . . . . . . . . . 187The Cartesian perspective, 187.—Rotational invariance, 190.—Vectors,193.—Calculus with vectors, 208.—The dot product, 212.—Gradientsand line integrals (optional), 215.Problems . . . . . . . . . . . . . . . . . . . . . . 218Exercises . . . . . . . . . . . . . . . . . . . . . . 2384 Conservation of Angular Momentum4.1 Angular Momentum In Two Dimensions . . . . . . . . 245Angular momentum, 245.—Application to planetary motion, 250.—Two theorems about angular momentum, 252.—Torque, 254.—Applications to statics, 259.—Proof of Kepler’s elliptical orbit law,262.4.2 Rigid-Body Rotation . . . . . . . . . . . . . . . . 265Kinematics, 265.—Relations between angular quantities and motionof a point, 266.—Dynamics, 268.—Iterated integrals, 270.—Finding moments of inertia by integration, 273.4.3 Angular Momentum In Three Dimensions . . . . . . . 278Rigid-body kinematics in three dimensions, 278.—Angular momentumin three dimensions, 280.—Rigid-body dynamics in threedimensions, 285.Problems . . . . . . . . . . . . . . . . . . . . . . 288Exercises . . . . . . . . . . . . . . . . . . . . . . 2965 Thermodynamics5.1 Pressure and Temperature . . . . . . . . . . . . . 298Pressure, 298.—Temperature, 302.5.2 Microscopic Description of An Ideal Gas . . . . . . . 305Evidence for the kinetic theory, 305.—Pressure, volume, and temperature,306.5.3 Entropy As a Macroscopic Quantity . . . . . . . . . 309Efficiency and grades of energy, 309.—Heat engines, 310.—Entropy,312.5.4 Entropy As a Microscopic Quantity . . . . . . . . . . 316A microscopic view of entropy, 316.—Phase space, 317.—Microscopicdefinitions of entropy and temperature, 318.—The arrow of time,or “this way to the Big Bang”, 326.—Quantum mechanics and zeroentropy, 327.—Summary of the laws of thermodynamics, 328.8 Contents
5.5 More About Heat Engines . . . . . . . . . . . . . 328Problems . . . . . . . . . . . . . . . . . . . . . . 3356 Waves6.1 Free Waves . . . . . . . . . . . . . . . . . . . 340Wave motion, 340.—Waves on a string, 346.—Sound and lightwaves, 349.—Periodic waves, 351.—The Doppler effect, 354.6.2 Bounded Waves . . . . . . . . . . . . . . . . . 360Reflection, transmission, and absorption, 360.—Quantitative treatmentof reflection, 365.—Interference effects, 368.—Interferenceeffects, 368.—Interference effects, 368.—Waves bounded on bothsides, 370.Problems . . . . . . . . . . . . . . . . . . . . . . 3777 Relativity7.1 Time Is Not Absolute . . . . . . . . . . . . . . . 381The correspondence principle, 381.—Causality, 381.—Time distortionarising from motion and gravity, 382.7.2 Distortion of Space and Time . . . . . . . . . . . . 384The Lorentz transformation, 384.—The γ factor, 389.—The universalspeed c, 394.—No action at a distance, 398.—The light cone,401.—⋆ The spacetime interval, 401.—⋆ Four-vectors and the innerproduct, 406.—⋆ Doppler shifts of light and addition of velocities,407.7.3 Dynamics . . . . . . . . . . . . . . . . . . . . 410Momentum, 410.—Equivalence of mass and energy, 413.—⋆ Theenergy-momentum four-vector, 418.—⋆ Proofs, 420.7.4 ⋆ General Relativity . . . . . . . . . . . . . . . . 423Our universe isn’t Euclidean, 423.—The equivalence principle, 426.—Black holes, 430.—Cosmology, 433.Problems . . . . . . . . . . . . . . . . . . . . . . 437Exercises . . . . . . . . . . . . . . . . . . . . . . 4448 Atoms and Electromagnetism8.1 The Electric Glue . . . . . . . . . . . . . . . . . 453The quest for the atomic force, 454.—Charge, electricity and magnetism,455.—Atoms, 460.—Quantization of charge, 465.—The electron,468.—The raisin cookie model of the atom, 472.8.2 The Nucleus . . . . . . . . . . . . . . . . . . . 474Radioactivity, 474.—The planetary model, 477.—Atomic number,481.—The structure of nuclei, 486.—The strong nuclear force, alphadecay and fission, 490.—The weak nuclear force; beta decay,493.8.3 Fusion. . . . . . . . . . . . . . . . . . . . . . 4958.4 Nuclear Energy and Binding Energies . . . . . . . . 4968.5 Biological Effects of Ionizing Radiation . . . . . . . . 498Units used to measure exposure, 498.—Effects of exposure, 499.—Effects of high doses of radiation, 500.—Effects of low doses radiation,500.—The green case for nuclear power, 501.Contents 9
Page 4 and 5: Fullerton, Californiawww.lightandma
Page 7: Contents0 Introduction and Review0.
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
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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
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1.1.1 Problem-solving techniquesHow
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∆m = 0, where m is the total mass
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different substances will have diff
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c / Left: In a frame of referenceth
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f / Discussion question B.(discusse
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Self-check D.since the derivative o
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ProblemsThe symbols √ , , etc. ar
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difficult? ⊲ Solution, p. 932Key
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Heat energy can be convertedto ligh
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a new form of invisible “mystery
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f / A realistic drawing of Joule’
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numbers. With a purely numerical ap
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of gravity doesn’t change much if
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field. If the plane can start from
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m / Discussion question C.n / A hyd
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88 Chapter 2 Conservation of Energy
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A car drives over a cliff.new frame
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How long does it take to move 1 met
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a / Approximations to thebrachistoc
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a / An ellipse is circle that hasbe
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to deduce the general equation for
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to the mass of the object that inte
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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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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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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
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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
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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
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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
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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
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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
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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
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the two resistors in figure h/3.We
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Choice of high voltage for power li
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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
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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
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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
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space, 2 while charge doesn’t, we
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a / The symbol for a capacitor.b /
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ounding each capacitor will be half
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in time:x ↔ qv ↔ Iself-check GH
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due to its own momentum. It perform
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or|V | =∣ LdIdt ∣ ,which in man
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the inductor resists such a sudden
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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
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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
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a purely inductive or capacitive lo
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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
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The symmetry between the two sides
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where dv is the volume of the cube.
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The three terms in the divergence a
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Problem 19.Problem 20.proton, for e
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the lightning strike.(b) Based on y
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units.(b) Verify that RC has units
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lating freely (without any driving
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ExercisesExercise 10A: Field Vector
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5. Now hook up the two solenoids in
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A large current is createdby shorti
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time I used it implicitly was in fi
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f / A standard dipole madefrom a sq
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and substituting q = λh and v = m/
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o / Magnetic forces cause abeam of
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electric field, a magnetic one, can
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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
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circulates around the y axis, so at
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to be, not where it is now. Coulomb
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We have found one specific example
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to a flagpole, we can cancel out a
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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
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k / A summary of the derivative, gr
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c / Detail from Ascending andDescen
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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
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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
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is the magnitude of the momentum ve
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Discussion question A.Discussion qu
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only penetrates to a very small dep
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elationship D = ɛE would actually
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esulting in cancellation.The opposi
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a low permeability, while the other
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n / A fluxgate compass.is externall
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6 Two parallel wires of length L ca
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an instant at the upper right, but
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Problem 25.20 Four long wires are a
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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
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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
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self-check AEach of these diagrams
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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
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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
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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
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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
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D Classify the examples shown in fi
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12.4.6 ⋆ Microscopic description
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12.5 Wave OpticsElectron microscope
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of a crystal? Sound waves are used
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j / Thomas Youngk / Double-slit dif
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object that diffracts it, so the tr
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Although the equation λ/d = sin θ
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things we’ve learned about diffra
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apidly changing distances; on reuni
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6 The figure on the next page shows
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14 Here’s a game my kids like to
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27 Suppose a converging lens is con
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same depth, but not quite. [Check:
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Problem 42.42 Panel 1 of the figure
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46 The figure below shows two diffr
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53 The beam of a laser passes throu
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Problem 59.the ancient problem of i
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3. Now imagine the following new si
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Exercise 12B: Object and Image Dist
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Exercise 12D: Double-Source Interfe
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Exercise 12E: Single-slit diffracti
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Exercise 12F: Diffraction of LightE
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energy, instead of being spread out
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correlated. If they have been playi
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small.The statement that the rule f
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But the y axis can no longer be a u
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for a long time once it gets there,
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j / Calibration of the 14 C dating
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given by(probability of a ≤ x ≤
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k / In recent decades, a huge hole
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A wave is partially absorbed.c / A
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f / The hamster in her hamsterball
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How would you extract h from the gr
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F Does E = hf imply that a photon c
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of approaching this issue.)j / Bull
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We assume v is small enough so that
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the probability distribution will b
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trons that we have already used for
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equations of general validity are t
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wave carries high probability and w
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An infinite sine wave can only tell
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momentum implies a definite kinetic
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of snapshots would amount to a desc
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close are the electrons to the limi
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dimensional particle in a box, and
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Applying this to conservation of en
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the probability of making it throug
Page 872 and 873:
Three dimensionsFor simplicity, we
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1. Oscillations can go backand fort
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C The figure shows a skateboarder t
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a / Eight wavelengths fit aroundthi
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As shown by these examples, the unc
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e / The three states of the hydroge
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f / The energy levels of a particle
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∂r/∂x = x/r comes in handy. Com
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50% of its time in each atom. It’
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tus to the z axis) and more memorab
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ut why does that have anything to d
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the data are only inaccurate due to
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14 The photoelectric effect can occ
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Problem 25.(b) Sketch a graph showi
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conservation of energy and momentum
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Problem 43.43 On pp. 884-885 of sub
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ExercisesExercise 13A: Quantum Vers
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⊲ First we convert the equation i
Page 908 and 909:
Programming With PythonThe purpose
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Appendix 2: MiscellanyUnphysical
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18 bestt = t19 c1 = bestc120 c2 = b
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p i + ∑ iThe spin theoremTheorem:
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Appendix 3: Photo CreditsExcept as
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Appendix 4: Hints and SolutionsHint
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Hints for Chapter 6Page 377, proble
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Answers to Self-Checks for Chapter
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Page 301: (1) Not valid. The equati
Page 926 and 927:
Page 584:N −1 m −2 C 2 V 2 m
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the dashed ray.Page 748: You should
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direction it was initially going (i
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Page 52, problem 38: The cone of mi
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Page 224, problem 37: (a) Spring co
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object, we have static friction, wh
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Page 549, problem 29:(a) Conservati
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Page 798, problem 19: (a) The objec
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.0.8 Notation and unitsquantity uni
Page 944 and 945:
surfaces. For comparison, a typical
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elations:a = ∆v∆tx = 1 2 at2 +
Page 948 and 949:
we are moving along with the projec
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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
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signs for charge is that with this
Page 958 and 959:
know that there is a delay in time
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is related byΦ = 4πkq into the ch
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to use sophisticated models such as
Page 964 and 965:
Chapter 13, Quantum Physics, page 8
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oth position and momentum, the Heis
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Schrödinger’s, 864cathode rays,
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unstable, 87equipartition theorem,
Page 972 and 973:
Joule, James, 73paddlewheel experim
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Einstein’s early theory, 838energ
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Nikola, 178tesla (unit), 652thermal
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Simple Nature - Light and Matter

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