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Unformatted text preview: ms 123 $6.9. waxlvzw “71qu ac... git.“ L1 '10“le (23 pts) Problem 1: Multiple choice conceptual questions. Choose the best answer and ﬁll in the appropriate bubble on your bubble { sheet. You may also want to circle the letter of your top choice on this paper. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. Which of the following is the best resolution of the barn paradox, as discussed in class and analyzed for homework? (Lee. is
the one” running with the ladderj Cathy is the one at rest relative to the barn.)
CE; Cathy sees theladdner ﬁt entirely within the barn, but Lee does not.
b. Lee" sees. the ladder ﬁt entirely within the barn, but Cathy does not.
c. Each of them sees the ladder ﬁt entirely within the barn. LQ8)C’ 9‘( L254 i ‘C Caug‘erir‘fD In théelativ‘ity context, which of the following would be an eXample of an “event”?
. A light beam hits a sensor. _ . V .1 h Aw. b. ’ Alrightbeam traVels'through space. swim? ale LWQWJ an; “L (k, L 0. Bill travels on a very fast train. t,qu .9» +2.... a“ d. Ted observes Bill traveling on a fast train. i
Frodo isveating breakfast ona train which moves at 2>I<l_1087.m/s. Sam is sitting at a picnic table near the train tracks, also
eating breakfast. Which pair of statements is correct (note, “slow motion” refers to the eating motions only, not to the
overall train speed of 2x108 m/s, which is obviously anything but slow): a. To Frodo, it looks like Sam is eating in fast motion..To Sam, it looks like Frodo is eating in slow motion. b. To Frodo, it looks like Sam is eating in fast'motion. To Sam, it looks like Frodo is eating in fast motion. 3Q To Frodo, it looks like Sam is eating in slow motion. To Sam, it looks like Frodo is eating in slow motion. d. To Frodo, it looks like Sam is eating in slow motion. To Sam, it looks like Frodo is eating in fast motion. '1th W Db‘kl‘fk '37mm—ciiim’i 1M 5m aJkgrg
What is the maximum momentum that a particle with mass m and velocity v can have?
a. mv ‘ . _ 6. 27710
b. 1720 ,f X m v, f. 2771012
c. mcv \0 \ There is no maximum
d. 27711) Kb Q“ h" arb'irw'l7 A reference frame in which objects which do not experience forces do not accelerate is called a(n) reference frame. ' a. accelerating e. Lorentz b. depressed f. null c. Einsteinian g. proper
relativisitic inertial h. Suppose Dr. Colton slams a book down on a desk, twice. The two book slams are (in Dr. Colton’s frame) separated by 10
seconds. To an observer in a rocket moving at 0.70 relative to Dr. Colton, the two slams will be: I
a. separated by less than 10 seconds _ W”, I OJ « l ” [A 51g“, M pm
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c. separated by exactly 10 seconds at Emily is moving at 0.90 relative to Joshua. David is moving at 0.8c relative to Joshua. Emily’s speed relative to David will
be: a. less than 0.10 Moi 9,13? VJ. sq “m L
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c. exactly O.lc [ x e a so O“wa :5 A! A ballet dancer (mass m) stands on her toes during a performance with area A in contact with the ﬂoor. What is the pressure
exerted by the ﬂoor over the area of contact if the dancer is jumping upwards with an acceleration of a? a. mg 9/
b. m(g+a) E F: 9 mg I c. m.(g—a) « m3 1vvxq L 2
d. mg/A
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f. m(g—a)/A a W N 2 Milli: )
9mg 8 Wk » We ’ A A Phys 123 Final Exam — pg 2 1.9. boat is on a lake. If an anvil (that sinks) is pushed from the boat into the water, will the overall water level of the lake
rise, fall or stay the same? (compared to when the anvil was in the boat) (lg/gs; i W : an.me WW 4» was,“
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c. staythe same li’\ wile! ’~ AWQWH VolvVWL 1.10. Water (no viscosity, incompressible) ﬂows from a little pipe into a big pipe with no height change. The ﬂow speed (m/s) in th little pipe will be in the big pipe. \ .
greater than A! v 1. [An Vb #3 § Wm. H A ; to .6} “lamb
b. the same as ‘
c. less than 1.11. Water (no viscosity, incompressible) ﬂows from a little pipe into a big pipe while also increasing in height. (That is, the water is ﬂowing uphill.) The volume ﬂow rate (mg/s) in the little pipe will be in the big pipe.
. greater than
. the same as \hCVL : Cmsiﬁe’d’ L: ikv)
0. less than Q’i CVU‘S‘J'L émﬂgﬁi i‘ Limdﬂ)
1.12. A gas in contact with a thermal reservoir undergoes an isothermal expansion. The gas and the thermal reservoir are
isolated from the rest of the universe. Which of the followmg is true. «wt; \Nkm’ (will; 308 a. The entropy of the gas will increase. The entropy of the reservoir Will increase. ‘
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The entropy of the gas Will increase. The entropy of the reservon Will decrease. Q01 N“ n CW? v c. The entropy of the gas Will increase. The entropy of the reservoir will stay the same. d“, W a; WWLQi] d. The entropy of the gas will decrease. The entropy of the reservoir will increase. F _ e. The entropy of the gas Will decrease. The entropy of the reservoir Will decrease. \q SJ—ic a 7L 3 'x k f. The entropy of the gas will decrease. The entropy of the reservoir will stay the same. Q 1)“) > g. The entropy of the gas Will stay the same. The entropy of the reservoir Will increase. Sm . h. The entropy of the gas will stay the same. The entropy of the reservoir will decrease. twigw: laced” WW9 i. The entropy of the gas Will stay the same. The entropy of the reservoir will stay the same. (‘ngr JQLr (w lire A d“; J
1.13. Whenagas expands: WA; 1 SSC “’3 P 973 f»
@ The gas does positive work on its surroundings. WM ‘1} 2 A V '2 «five '9?“ b. The surroundings do positive work on the gas. 7 (3 \ K ‘1‘ Mk 5? Iggy «’0 f c. Work is not necessarily done. _ i, V? Fm (My/S
1.14. If a gas undergoes a thermodynamic change whereby it somehow ends up in the same state it started in: a. The internal energy of the gas will be less than when it started. 1% larvon QALrj 1 :5 g b. The intenial energy of the gas Will be greater than when it started. 31mg Wm “3&ng C9 The internal energy of the gas will be the same as when it staited.
d. The change in internal energy will depend on the direction of the change (clockwise vs. counter—clockwise). 1.15. Suppose you ﬂip 13 coins simultaneously. How many different ways could the coins land to give you 8 heads and 5 tails?
(1.e., What is the number of microstates in the 8H 5T inacrostate?) a. 32 i i c f. 8192
b. 256 (W) 2 «ii/t C if“? g. 13980 c. 520 % tr 5  h. 432432 d. 688 i. 67108864
Q 1287 1.16. A “closed—’clgged” pipe and a “closedopen” pipe are the same length. Which will have the lower fundamental ﬁ‘e uenc ? \n
q y “We @\ W a. closedclosed . V b. closedo en
9' p 1:9" )‘ ) 50 “MM”! same ﬁmdamental frequency 1,17. In which case will there be no reﬂection from a wave on a string hitting a boundary?
a. when the wave’s frequency is the same on both sides of the boundary
b. when the wave’s speed is the same on both sides of the boundary
0. when the wave’s wavelength is the same on both sides of the boundary (t V «J CAM E 3 3 if V/
v.) t more than one of the above “mg (q) lac/lid 'ifot f {raga I g S Q
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Phys 123 Final Exam — pg 3 f(x, t) plotted as f(x) for t=O . —3
1.18. Which wave function f(x,t) is represented by the two graphs displayed? The left—hand‘graph is the wave functiOn
plotted for t=0; the right hand graph is the wave function plotted for t=1. V _
f(x,t) = 3 cos(2x  2t) 6 0N1 bi/\9 NIL V» l”\ f. f(x,t) = 6 cos(2x  2t)
. f(x,t) = 3 cos(2x  4t) L: L w: l H4 } g. f(x,t) = 6 cos(2x — 4t)
0. f(x,t) = 3 cos(3x — 3t) \ ' h. f(x,t) = 6 cos(3x  3t)
(1. f(x,t) = 3 cos(4x  2t) i. f(x,t) = 6 cos(4x  2t)
e. f(x,t) = 3 cos(4x  4t) j. f(x,t) = 6 .cos(4x  4t) TV i
A? 1.19. 7 Light going from a low index of refraction to a high index of refraction will always experience a 180° phase shift,
regardless of the angle of the light ray relative to the boundary. 7A+ m, w/qu MexWm Mi aka 1; kqmagi l ‘1'
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WLS ‘ihL bow/Liij 1.20. The critical angle for total internal reﬂection exists on both sides of a material interface. Q31 N new 1422’“ n +0 low in 1.21. When you are designing a coating for a piece of glass that needs to minimize reﬂections for a given wavelength, there
is only one coating thickness d that is allowed. _ \ k H _ Q4 4. l A
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1.22. When light difﬁacts through two wide slits, the resulting difﬁaction pattern will be the same as the pattern from a sinﬁwide slit, times the pattern of two inﬁnitely narrow slits. . a: gig W cm mm w W 1
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false 1.23. <Stiransparent glass, which travels faster: red light (7t=630 Inn) or green light (7t=500 nm)?
red light
b. green light c. both travel at the same speed ﬂame (U;”:‘ ) Phys 123 Final Exam — pg 4 W, \é/ ‘3 ‘ Zfl‘f (10 pts) Problem 2,Di/sgﬁs/te/d:vith their ﬁnal exam, the Physics 123 students gang up and ship Dr. Colton out from Earth on a fast
rocket traveling aw? to live the remainder of his days in isolation from the rest of humanity. He lives for 60 more years (in his
ﬂame of reference), a the while wishing he had been kinder to the students. How far is he irons the Earth when he dies (in the Earth’s frame of reference)? ‘ Jr (53?“ So 3cm; 9V (V
g) 40 Lima J3 AVA ﬁan’Lﬁi I ﬂ N K A“ g . N I
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C 3 l ’* (it, ﬁt: I "l (WC?) (b) John and Cathy both ﬁre laser guns at Lee, and coincidentally both of their shots (traveling at the speed of light) arrive at Lee at
the same time. Draw the situation on three different spacetime diagrams: from John’s perspective, from Lee’s perspective, and from
Cathy’s perspective. On each diagram label the worldlines from each of the three people, the two laser beams, and label these three
events: 1 = John ﬁres laser gun 2 = Cathy ﬁres laser gun 3 = Lee gets hit by both guns all
A) at ; his”? Jo (q A NC“)?th .
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J C (c) In J ohn’s frame of reference, who ﬁres ﬁrst? In Lee’s frame? In Cathy’s frame? (You should be able to use your pictures from
part (b) to answer this; no equations needed.) F / .
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\ Phys 123 Final Exam — pg 6 (12 pts) Problem 4. (a) How fast would a 1 kg block need to be traveling in order to have as much momentum as a 0.999 electron? L \Y; 22,364. 0 mchr (etch/m, nm/quhwgvk (b) When you burn a match, about 1000 J of energy are released. If all of that energy goes into accelerating an electron (that is, it all
gets turned into kinetic energy), how fast would that electron be traveling? Note: because your answer will be very close to the speed of light, please write your answer as, for example, (1 — 7.7x10‘“)c, instead of 09999999999230 (or whatever the correct answer
turns out to be). Hint: remember that (1+x)n w 1+nx when x = small. \(E —; (Y‘ (\mc 2‘ ‘ loOO » ﬂ ,(‘2
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(14 pts) Problem 5. ( S ( 7 ~
(a) A Utube, open on both ends, is ﬁlled with water. The right end is then shielded while air is blown across the left end. This
creates a decrease in pressure by the :left end,:which “sucks” the water'up; How fast must'the air be blown in‘order for the water in the left—hand section to end up 10 cm higher than the water in the righthand section. (Densities of air and water can be found on
page 1.) i J V 2‘ ‘\& \
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bubble when it reaches the surface? Assume that the temperature and the number of air molecules in the bubble remain constant during the ascent. ﬂ
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of 0.06 in standard SI units. (a) What are the standard SI units for thermal conductivity? Eqm‘. P: kits/V N) \L: 371‘ Siqﬁ \" aL ;; OT gaw‘K,¢3 ‘0\ (GT \u 53" Eh \ mg. Qicvh‘\V“VQ“~ gﬁ’KVQ‘LVQ—l l9“Q. 3mm!“ \NI big—3"") W): Hi5
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(16 pts) Problem 7. An engine using 0.12 moles of a diatomic ideal gas is driven by this cycle: starting ﬁom "state A, the gas is
cOmpresseduadiabaticallyuntil it reaches state B, Then, the gas is heated at constant pr‘essUre untilit reaches state C. Finally, the gas is cooled at constant volume back to the original state. Various pressures, volumes, and temperature are given in the table. ' Pr . 
II W: nM «a T = A Emma was; Nj 05M T :zmn. TL‘LA ‘6‘ \“P‘QCNV kcubl POM w 2 \fh‘sikﬁ ‘3th {a {CA "\W‘AJKQ (b) Find the heat added to the gas during each of the three legs. arm” ﬂ Alohoiraﬁcv a Q‘QcQ ( 32:9 eel54 9— (Sta nCPth 412%; “‘HLW'S‘K)
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QM“ “x :(‘u t \‘ M0? \ Phys 123 Final Exam ~ pg 10 ("12 pts) lgroblem 8. While attempting to tune the note C at 523.3 Hz, a piano tuner hears 236mm between a reference oscillator (at
523.3 Hz) and the string. 1,9 {3 = €113 t. a (a) When she tightens the string slightly, the beat frequency she hears rises smoothly to 3.5 beats/s. What is the frequency of the
string now? \A P 3
«Fm/WV} vak kfj LAW M 3 I Tumkgwg—e "P (am An f Big H? (b) By what percentage should the piano tuner now change the tension in the string to bring it into tune? at“ WA?
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(14 ptS) Problem 9. As a car drives paSt Steve, the driver sounds the hom. Steve has perfect pitch, and notices that as {the car
approached, the horn sounded the A above middle C (440.0 Hz). After the car passed, the pitch dropped dowri'three half steps to an
Fsharp. How fast was the car going? W0 mutt/31cm '. moo” 4&7, on: gm 3 3g??? I” \/:\/a 1
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m Phys 123 Final Exam — pg 12 (l0 pts) P‘roblem 10. You book lists this as the “lensmaker’s equation”:
i =(,7_1)(_1___L]
f R1 R2 However, when I consulted Wikipedia, htt ://en.wiki edia.or /wiki/Lens o tics , I found a slightly different version of that
equation:
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f 7 R1 R2 anR2 In that equation, d is the thickness of the lens. Assuming the Wikipedia equation is correct (which I believe it is), apparently the
textbook’s equation is making an approximation that the lens is infinitely thin. But, of course, lenses are not inﬁnitely thin. If I have a biconvex lens (the normal lens shape, curved outward on both sides), with both radii of curvature equal to 10 cm in
magnitude, and my lens is 0.6 cm thick, what is the difference in the focal lengths predicted by the two equations? (The index of refraction of the material is 1.55.)
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2 (diverging, f = —40 cm). How far (in magnitude) from lens 2 will the ﬁnal image be formed? Will the image be to the left or the
right of lens 2? Will it be real or virtual? What will be the total magniﬁCation? You do not have to provide any ray diagrams for this problem. HSQ 7 H I
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Phys 123 Final Exam ~ pg 14 / i pts, no» partial credit) Extra Credit. You may pick one of the following extra credit problems to do. (If you work more than one,
only the first one will be graded.) (a) Use the Lorentz transformations to prove the relativistic velocity addition formula. Hint: Pick an arbitrary velocity in reference
frame 1, ﬁnd a point on the worldline corresponding to that velocity, do the Lorentz transformation to reference frame 2, then ﬁnd the slope (and hence velocity) of the worldline in that reference ﬁ‘ame.
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(b) Suppose I developed the ability to travel faster than the speed of light. That means (in the Earth frame of reference) I could travel
one light year in 0.5 years. This would cause a tremendous problem for causality! Namely, the endpoint of my trip and the start of
my trip will have a “spacelike” relationship to each other instead of a “timelike” relationship. And, as I claimed in class, if two
points on a spacetime diagram have a spacelike relationship, then one can always find a reference frame where one point happened
before the other, and another reference frame where it’s the other way around. Therefore, there is some reference frame where my
trip’s endpoint happened before my trip’s start! In that frame, cause and effect are reversed! In fact, there are an inﬁnite number of
such reference ﬂames. Find the speed of the speciﬁc reference frame where I arrived 0.5 years before I left. Hint: that reference frame will be traveling in the same direction that I’m traveling. WWII“
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