Simple Nature - Light and Matter

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Contents0 Introduction and Review0.1 Introduction and Review . . . . . . . . . . . . . . 13The scientific method, 13.—What is physics?, 16.—How to learnphysics, 19.—Velocity and acceleration, 21.—Self-evaluation, 23.—Basics of the metric system, 24.—Less common metric prefixes,28.—Scientific notation, 28.—Conversions, 29.—Significant figures,31.0.2 Scaling and Order-of-Magnitude Estimates . . . . . . 34Introduction, 34.—Scaling of area and volume, 35.—Order-of-magnitudeestimates, 43.Problems . . . . . . . . . . . . . . . . . . . . . . 471 Conservation of Mass1.1 Mass . . . . . . . . . . . . . . . . . . . . . . 55Problem-solving techniques, 58.—Delta notation, 59.1.2 Equivalence of Gravitational and Inertial Mass . . . . . 601.3 Galilean Relativity . . . . . . . . . . . . . . . . . 62Applications of calculus, 66.1.4 A Preview of Some Modern Physics . . . . . . . . . 68Problems . . . . . . . . . . . . . . . . . . . . . . 702 Conservation of Energy2.1 Energy . . . . . . . . . . . . . . . . . . . . . 73The energy concept, 73.—Logical issues, 75.—Kinetic energy, 76.—Power, 80.—Gravitational energy, 81.—Equilibrium and stability,86.—Predicting the direction of motion, 89.2.2 Numerical Techniques . . . . . . . . . . . . . . . 912.3 Gravitational Phenomena. . . . . . . . . . . . . . 96Kepler’s laws, 96.—Circular orbits, 98.—The sun’s gravitationalfield, 99.—Gravitational energy in general, 99.—The shell theorem,102.—⋆ Evidence for repulsive gravity, 108.2.4 Atomic Phenomena . . . . . . . . . . . . . . . . 109Heat is kinetic energy., 110.—All energy comes from particles movingor interacting., 111.2.5 Oscillations . . . . . . . . . . . . . . . . . . . 113Problems . . . . . . . . . . . . . . . . . . . . . . 118Exercises . . . . . . . . . . . . . . . . . . . . . . 1263 Conservation of Momentum3.1 Momentum In One Dimension . . . . . . . . . . . . 130Mechanical momentum, 130.—Nonmechanical momentum, 133.—
Page 4 and 5: Fullerton, Californiawww.lightandma
Page 8 and 9: Momentum compared to kinetic energy
Page 10 and 11: 8.6 ⋆ The Creation of the Element
Page 12 and 13: 12 Contents13.3 Matter As a Wave .
Page 14 and 15: Building its centerpiece, the steam
Page 18 and 19: of light is such a big number, a la
Page 20 and 21: of an object sliding down an inclin
Page 22 and 23: about the function x(t), given info
Page 24 and 25: 0.1.6 Basics of the metric systemTh
Page 26 and 27: The kilogramThe third base unit of
Page 28 and 29: 0.1.7 Less common metric prefixesg
Page 30: force, and the best unit to use for
Page 33 and 34: significant figures of precision, t
Page 35 and 36: million cubic centimeters — they
Page 37 and 38: in proportion to their size. There
Page 39 and 40: while discussing conversions of the
Page 41 and 42: The symbol “∝” means “is pr
Page 43 and 44: Scaling of a more complex shape exa
Page 45 and 46: dimensions of the bin are probably
Page 47 and 48: ProblemsThe symbols √ , , etc. ar
Page 49 and 50: 14 You are looking into a deep well
Page 51 and 52: from rest with an acceleration of 1
Page 53 and 54: 41 Estimate the number of man-hours
Page 55 and 56: The universe has been recyclingits
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y scientists who actually specializ
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yesterday’s. One way of stating a
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happens because the greater gravita
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m/s. From my point of view, the fri
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special “rest frame.” Since the
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derivative v = dx/ dt is called the
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only certain values of mass are pos
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kind used, for example, to test des
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Chapter 2Conservation of EnergyDo y
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Conservation of energy tells us ∆
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Although the story is picturesque a
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a symbols.kg · m21 J = 1= 1s 2kg
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since we don’t know how the perso
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elated to gravitational mass, but s
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proportion to one another, so this
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lock in figure o/3. Even if the blo
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Water in a U-shaped tube example 13
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2.2 Numerical TechniquesEngineering
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But by increasing n to ten thousand
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17 ds = math.sqrt(dx**2+dy**2) # Py
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d / As the earth and Mars revolvear
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In one second, the satellite moves
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Determining G example 15The constan
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the apple. A kilogram of dirt a few
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at its center. We already know that
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1 import math2 def tmoon(vi,ri,rf,n
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This was the state of things until
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it becomes possible to answer at on
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Discussion QuestionsA I’m not mak
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1 import math2 def u(k,x):3 return
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so the energy in the spring isU = 1
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5 A grasshopper with a mass of 110
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trical energy is the Lennard-Jones
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the sun was to increase its light o
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time in the case of a 21 g ball of
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Exercise 2C: VibrationsEquipment:
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Forces transfer momentum to thegirl
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As in the one-particle argument on
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all the exhaust has been expelled.
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increase, because kinetic energy is
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or permanently bend them. Cars, in
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h / Chadwick’s subatomic pool tab
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interaction with the felt surface i
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The center of mass as an average ex
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center of mass frame. Chapter 7 dis
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(1) The collision is instantaneous.
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1. It always relates exactly two fo
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is used up, so forces can exist bet
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that the paper makes an upward norm
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l / Example 26.friction is F s = µ
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The following is another example in
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n / If we imagine dividing a taut r
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F > 0 dx > 0 dK > 0F < 0 dx < 0 dK
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Work in generalI derived the expres
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K. Differentiating K cm , we havedK
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s / Discussion question B.3.2.9 Sim
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we need to use positive and negativ
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3.3 ResonanceResonance is a phenome
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the time ∆t = ∆x/v required to
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second derivatives are v = e −ct
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the steady-state motion, we’re go
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force will simply displace the osci
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j / Dependence of the amplitudeand
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trous. With very strong damping, th
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is also a solution of the driven eq
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3.4 Motion In Three Dimensions3.4.1
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y a gas or liquid, like the turbine
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etter not matter which directions t
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3.4.3 VectorsRemember the title of
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e eliminated by dividing each equat
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one point and ends at another. Addi
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A shortcut example 62⊲ A split se
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where the vectors ˆx, ŷ, and ẑ,
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three vectors. This is the Pythagor
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figure t/2, and we assume that the
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G New York and Rome are at about th
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ordrdt = dx dy ˆx +dt dt ŷ + dzdt
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this to the x component of the acce
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two vectors that we want to multipl
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As in the proof on page 130, the fi
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increasing most rapidly, and it tel
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design won’t work. (For the sake
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20 A tugboat of mass m pulls a ship
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29 A person is rowing a boat, with
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the bond stretch by any appreciable
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of the falls at the same moment, si
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59 Your hand presses a block of mas
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71 (a) We observe that the amplitud
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73 A microwave oven works by twisti
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79 For safety, mountain climbers of
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83 Problem 79 discussed a possible
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Exercise 3B: VibrationsEquipment:
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Exercise D is on the following two
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Exercises 243
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Chapter 4Conservation of Angular Mo
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doesn’t repeat or even curve arou
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her rate of rotation. That is, by p
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The area can thus be rewritten asar
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planet A, angular momentum is still
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zero total torque.Conversely we can
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of F ⊥ can thus be expressed asF
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4.1.5 Applications to staticsIn cha
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Art! example 9⊲ The abstract scul
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from his equations, leaving only sp
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4.2 Rigid-Body Rotation4.2.1 Kinema
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axis. We adopt a coordinate system,
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isI = ∑ m i ri 2 , [definition of
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each one of them. Using the sigma n
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∫ avolume ==∫ az=0 y=0∫ a ∫
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In the most general case where ther
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meters to the first power requiresk
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about y gives one result, while doi
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two vectors to produce a third vect
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momentum of the top is zero, which
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4.3.3 Rigid-body dynamics in three
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surfaces consists only of the two p
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9 A uniform ladder of mass m and le
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19 Use analogies to find the equiva
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28 Find a vector that is perpendicu
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38 Suppose an object has mass m, an
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Chapter 5ThermodynamicsS = k log WI
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the force will still be the same in
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Variation of pressure with depthThe
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But physics deals with operational
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Although we can achieve as good an
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The proportionality of volume to te
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5.3 Entropy As a Macroscopic Quanti
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than any other. The grade of heat e
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Entropy increases in heat conductio
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Hawking radiation example 19Any pro
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pressing on a piston rather than si
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of heat to be transferred into eith
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where “. . .” indicates terms t
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energy in the electrical energy due
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Integrating both sides gives(α + 2
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ecause low-entropy states are short
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l / The Otto cycle. 1. In the exhau
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compression or expansion is T ∝ P
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ALρ, where L is the length of the
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ProblemsThe symbols √ , , etc. ar
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10 Example 25 on page 332 suggests
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The vibrations of this electric bas
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The two circular patterns ofripples
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The incorrect belief that the mediu
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Discussion QuestionsA The left pane
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As always, the velocity of a wave d
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mathematical statement of the intui
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the story are more fittingly reserv
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The size of a radio antenna is clos
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the familiar dropping-pitch sound o
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football player with a serious nico
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of light would look like to a perso
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waves to be partly reflected at the
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AbsorptionSo far we have tacitly as
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in the cable; this minimizes the am
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s − sR = s(v 1 /v 2 )T , or1 −
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as a coating to prevent reflection.
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itself, and since the body is very
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series has two important roles in m
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The only difference is that the wav
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10 Singing that is off-pitch by mor
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Chapter 7Relativity7.1 Time Is Not
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arithmetic transparent, suppose tha
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parts. Now the background comes to
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means that observers 1 and 2 disagr
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pick the time unit to be the second
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An interstellar road trip example 1
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An example of length contraction ex
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t / The Michelson-Morley experiment
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frequencies in the burst differed b
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some physical reality to these ripp
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C Resolve the following paradox by
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ecause this case can be obtained as
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equals half the interval, and the a
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which is greater than the Betty’s
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self-check BTurn your book upside-d
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a / An unequal collision, viewed in
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At very low velocities, γ is close
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Gravity bending light example 14Gra
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talking about relativity, so an obj
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we’d defined p = (E, p x , p y ,
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How does this energy-shift factor d
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7.4 ⋆ General RelativityWhat you
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c / Left: A 90-90-90 triangle. Its
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are two possible explanations for t
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you have no way of determining from
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Although the light rays in figure n
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interstellar gas flowing into it wo
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sity of matter from that. It turns
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8 (a) A free neutron (as opposed to
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15 Expand the equation K = m(γ −
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29 The angular defect d of a triang
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Groups 1-4 work in the sun’s fram
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Exercise 7C: Events and SpacetimeEx
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Exercises 449
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Exercise 7E: The sum of observer-ve
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Chapter 8Atoms and Electromagnetism
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as vigorous as the beating of a hea
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Use of positive and negative signs
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come in two general types. Permanen
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tinguished the different types from
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atios of the different atoms’ mas
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tion for Brown’s observation: the
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The table on the left shows a few o
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Were cathode rays a form of light,
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Thomson played with the electric an
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a four-electron atom. All four elec
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nomenon of phosphorescence, in whic
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nately necessary for physics studen
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g / Alpha particles being scattered
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y moving charges; we have not yet d
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so that he could attempt to do phys
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us that the ones scattered from cop
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The neutronIt would have been nice
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Isotopes can be named by giving the
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q / 1. The forces cancel. 2. The fo
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8.2.6 The weak nuclear force; beta
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Discussion QuestionsA In the reacti
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energy as would be produced in a nu
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ing sports statistics or weather re
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tion better against diptheria; incr
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8.6.2 We are stardustIn that case,
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7 In the semifinals of an electrost
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16 [See section 0.2 for help on how
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Chapter 9CircuitsMadam, what good i
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“charge” to describe the proper
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current as a function of time, we c
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If his job is to toss them up into
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loss of electrical energy will just
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Discussion QuestionsA A roller coas
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your mouth is analogous to a voltag
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Constant voltage means that no work
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short-circuit: a circuit in which a
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in units of volts based on the know
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imagine them passing between the cr
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eality, it would be a matter of min
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9.2.2 Parallel resistances and the
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The cutting in half of the resistan
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Now if we are carrying out this mea
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can now be rewritten by applying Oh
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ohmic, so substituting ∆V T = IR
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Interpreting this result, we see th
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linearly with time, giving a charge
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next gauge in the series?18 In the
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28 You are given a battery, a flash
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to lose PE while gaining KE.√Key
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Exercise 9B: The Loop and Junction
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3. A wire is added as shown to the
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Chapter 10Fields“Okay. Your dutie
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More evidence that fields of force
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places where we didn’t measure it
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surface of a pond. Although we have
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negative charge with equal magnitud
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Alternative definition of the elect
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voltage is defined as electrical en
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10.2.2 Two or three dimensionsThe t
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10.3 Fields by Superposition10.3.1
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puter software:V = kλ ln(z + √ )
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Field of a uniformly charged disk e
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10.3.2 The field near a charged sur
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dimensionality of the charged objec
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as dU e ∝ E 2 dv, or dU e = aE 2
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No. Consider, for instance, an alte
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Discussion QuestionsA The figure sh
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10.5 LRC CircuitsThe long road lead
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a stylized solenoid, d, is the symb
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gap. For a given amount of charge o
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phone company filters out all the e
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of the charges on the plates from q
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throws a positively charged bowling
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The RC circuitWe first analyze the
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in your front yard, and the lights
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factored as (x − i)(x + i). In ge
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10.5.7 ImpedanceSo far we have been
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impedances. The ones that represent
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their maxima at the same time. In a
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function V (t), take its average (m
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When the impedances are matched, ha
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10.6 Fields by Gauss’ Law10.6.1 G
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Gauss herself leads one of the expe
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Note that although region and its s
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extended to the case where the char
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the information reaches the right s
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shown in the figure. The length, L,
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10.7 Gauss’ Law In Differential F
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Mathematically, let the x axis be t
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The partial derivative ∂r/∂x is
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(b) Generalize the result of part a
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that are closest to the central axi
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for the purposes of this problem, a
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values to find on the shelf at Radi
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(x, y, z) byx = u + py = v + qz = w
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3. The figure below is a cross-sect
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Chapter 11ElectromagnetismThink not
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lone charge is therefore zero:E 1 =
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11.1.2 The magnetic fieldDefinition
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the magnetic field.If the loop is o
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is a pretty big number. To get a di
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electric dipoles does the same thin
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Since the particle in our example w
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11.2 Magnetic Fields by Superpositi
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the two wires of example 8: current
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11.2.2 Energy in the magnetic field
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where dB z is the contribution to t
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Field at the center of a circular l
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to the loop. The field is∫ kIa dl
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11.3 Magnetic Fields by Ampère’s
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self-check EBased on how l entered
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Discussion QuestionsA Figure g/1 sh
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Note that the curl, just like a der
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is very much as it was before, exce
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socurl E = cos ẑThis is visually
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ture of 19th century England. Farad
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The generator example 18A basic gen
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figure h/1, which implies the exist
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perpendicular to the front and back
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variation of the magnetic field is
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11.6 Maxwell’s Equations11.6.1 In
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chosen moment. Unadorned with the
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wave terminology, we say that the w
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waves, then this might be surprisin
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Multiplying these last two equation
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piece of wire of length l is bathed
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11.7 Electromagnetic Properties of
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voltage difference between the plat
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An iron-core electromagnet example
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their differential-mode fields woul
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and nickel, which explains the orig
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(b) Suppose the currents are in the
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and the forces on them were measure
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26 The first step in the proof of A
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plane, falls through a nonuniform m
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equations are the electric and magn
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53 The purpose of this problem is t
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ExercisesExercise 11B: Polarization
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Chapter 12Optics12.1 The Ray Model
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Today, photography provides the sim
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propagation of light.Discussion Que
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Numerical measurement of the bright
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ut a full understanding of this app
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until the twentieth century it was
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e used for video games and computer
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vacuum and light undergoing reflect
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Imagine that the person in figure a
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12.2.2 Curved mirrorsAn image in a
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given point on the object are too s
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k / The person uses a mirror toget
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CLocate the images formed by the pe
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The only way to find out anything m
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figure a/1. Second, it is usually e
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Letting d o be less than f is equiv
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are assigned negative focal lengths
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degree panorama, the problem would
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l / The Hubble Space Telescopewas p
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Refractive properties of mediaWhat
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Finding an angle using Snell’s la
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proportional to their velocities. C
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concept of the focal length of a le
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of memorization. The positive sign
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ight side consists of a superpositi
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make patterns of strong and weak wa
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lead to the creation of a new and m
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We know from our discussion of the
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Double-slit diffraction of blue and
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u / 1. There is a bright central ma
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ing corresponding to the large dist
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9 In section 12.2 we’ve only done
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22 A concave surface that reflects
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33 The figure shows four lenses. Le
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40 A nearsighted person is one whos
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44 The figure shows a diffraction p
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Problem 51. This image ofthe Pleiad
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57 Suppose we have a polygonal room
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ExercisesExercise 12A: Exploring Im
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5. Now imagine the following experi
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Exercise 12C: How strong are your g
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Exercises 817
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Exercises 819
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Chapter 13Quantum Physics13.1 Rules
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eliminated by natural selection. Do
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has ever succeeded in detecting dif
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nonsensical sequence of letters and
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sure of the amount of variation abo
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Using the rule for calculating aver
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Mathematically, differentating an e
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Average lifetime example 6You might
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passes into and back out of a mediu
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13.2.2 How much light is one photon
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Numerical relationship between ener
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constitute more detailed informatio
Page 845 and 846:
e like firing a hail of bullets thr
Page 847 and 848:
proportional to the square of the w
Page 849 and 850:
Discussion QuestionsA Referring bac
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13.3 Matter As a Wave[In] a few min
Page 853 and 854:
a / A double-slit interference patt
Page 855 and 856:
voltage differences on the order of
Page 857 and 858:
Here’s how the now-legendary stud
Page 859 and 860:
energy and momentum is E = p 2 /2m,
Page 861 and 862:
and according to classical physics,
Page 863 and 864:
traveling waves going in opposite d
Page 865 and 866:
objects like atoms but of human-sca
Page 867 and 868:
l / A typical wavefunction of an el
Page 869 and 870:
The detailed study of the solution
Page 871 and 872:
The correspondence principle for E
Page 873 and 874:
A classically allowed region with c
Page 875 and 876:
for example, arbitrarily say that e
Page 877 and 878:
13.4 The AtomYou can learn a lot by
Page 879 and 880:
Quantization of angular momentumThe
Page 881 and 882:
the electron is close to the nucleu
Page 883 and 884:
E Criticize the following incorrect
Page 885 and 886:
Now comes the approximation. In rea
Page 887 and 888:
Wave phases in the hydrogen molecul
Page 889 and 890:
internal motion within the electron
Page 891 and 892:
The relatively complex spectra of e
Page 893 and 894:
Page 895 and 896:
11 All helium on earth is from the
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19 In a television, suppose the ele
Page 899 and 900:
29 Before the quantum theory, exper
Page 901 and 902:
39 Americium-241 is an artificial i
Page 903 and 904:
45 Suppose that an electron, in one
Page 905 and 906:
Three Essential Mathematical Skills
Page 907 and 908:
The distance from San Diego to Las
Page 909 and 910:
calculator, but it’s a good way t
Page 911 and 912:
all is at rest relative to the eart
Page 913 and 914:
direction to avoid breaking rotatio
Page 915 and 916:
div E = 4πkρdiv B = 0curl E = −
Page 917 and 918:
licensed. 384 Satellite: From a pub
Page 919 and 920:
This is similar to example 23 on pa
Page 921 and 922:
Page 810, problem 60: Expand sin θ
Page 923 and 924:
Page 174: The two graphs start off
Page 925 and 926:
Answers to Self-Checks for Chapter
Page 927 and 928:
towards the center of the circle. W
Page 929 and 930:
Page 828: The area under the curve
Page 931 and 932:
Page 47, problem 8: (a) Let’s do
Page 933 and 934:
Page 118, problem 5:E total,i = E t
Page 935 and 936:
Page 229, problem 63: Since its vel
Page 937 and 938:
Solving for w,w = 1 − A1 + A(1 +
Page 939 and 940:
Page 643, problem 58: We can think
Page 941 and 942:
Appendix 5: Useful Data.0.7 Notatio
Page 943 and 944:
.0.10 Metric prefixesM- mega- 10 6k
Page 945 and 946:
Appendix 6: SummaryNotation and uni
Page 947 and 948:
in everyday life, which is why we c
Page 949 and 950:
A moving object’s momentum equals
Page 951 and 952:
angular momentum is related to rate
Page 953 and 954:
absolute zero, the temperature at w
Page 955 and 956:
All of these strange effects, howev
Page 957 and 958:
Many important electrical phenomena
Page 959 and 960:
or|V L | =∣ LdIdt ∣ .In the equ
Page 961 and 962:
Ampère’s law is another way of r
Page 963 and 964:
Refraction: Refraction is a change
Page 965 and 966:
A particle that is bound within a c
Page 967 and 968:
Indexaberration, 766chromatic, 779a
Page 969 and 970:
partial, 216Descartes, René, 129,
Page 971 and 972:
generator, 598, 687geothermal vents
Page 973 and 974:
Millikan, Robert, 465Millikan, Robe
Page 975 and 976:
scalardefined, 193scaling, 35schema
Page 977:
medium not transported with, 342on
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Simple Nature - Light and Matter

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