Vanessa Cueva

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Apr 3, 2024

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Name VQ‘\Q‘;SQ C\JE\IO Q el Homework Questions for Physics and Reality Week 1 Due the week of February 12 Metric System Prefixes Table Useful Values Speed of light in a vacuum ¢ =3.0 x 10° m/s T “terra” IOO Gravitational constant G = 6.7 x 10" m’ kg™ s G “giga” 10 Re (Radius of Earth) = 6.4 x 10°m I A g ME (Mass of Earth) = 6.0 x 10** kg M mega 10. 17 =1 kg m¥s? k “kilo™ 10 1 mile = 1.61 km=1.61 X 10°m & “centi” 10° linch=2.54cm 5 1 foot = 12 inches m “milli” 10 1 light year (ly) = 9.5 X 10'5m [ “micro” 104, n “npano” IO_Q 3 212! P “pico™ 10 Useful Equations Speed and time d=vt d = distance, v = speed, = time Gamma factor y= ._17 v = velocity, ¢ = speed of light =z Time dilation and length contraction time elapsed for stati bj (time elapsed for moving object/observer) = ¢ pEee /| tznar‘y eblect/gnserver) length of stationary object (Ienythl)fmovlngab/cct)=( gthof > Y 2tact) Energy of a massive particle E=ymc? m = rest mass of object, ¢ = speed of light

{ 1. The Vast Universe ‘ eaTE TEY ) o 1A. Astronomers often use units of light years to express the vast distances between stars and | 2563 < \( | galaxies. A light yeans defined as the distance that light (in a vacuum) travels in one year, which is equal I\WFM each of the following report or calculate the size/distance in units of lightyear: 2 UxI0 X 5% 10%) LA. (i) The distance to Voyager 1: the most distant human-made objec ﬂ 10"°4m. (45%0%) 8 pn ; Bulaadoe B 200100 4163 —ZG x [0 M TS x WS 1A. (ii) The distance to Sagittarius A*, the black hole in the center of our galaxy: 2.4 x 102°m. 20 e i 4 2 %l Py fzsé - 10 % 1012 1A. (iii)) The distagggq Andromeda: our galactic neighbor: 2.5 Mly. 7 6 2.5 10| 1B. Plot the distances from part A on the logarithmic scale provided in Figure 1 below. Be sure to label the major ticks on the axis first, then plot and label the points. a \) C. | : y J e 02 Bigls 0 Topiiok 1% 103 o 5168 o° Ntk e ey T W Figure 1. A logarithmic scale of distances 1C. Would you be able to plot your own distance from Earth on the plot above (that is 0 m since you are on Earth)? Explain why or why not in one sentence No becose 15 1o Passib\? o p\o*’ 0O o @ \(\9 Sule. 2. Relativity and the Fundamental Limit of the Speed of Light 2A. Consider the set of spaceships flying by an asteroid, as shown in Figure 2 (next page). Motion of each spaceship relative to the asteroid (which is not changing speed or direction) is designated by the corresponding arrow. All spaceships are moving at a constant speed and do not change direction. The length of the arrow indicates the magnitude of the speed of the spaceship: for example, spaceship A is traveling in the same direction as spaceship B, but about twice as fast. e eec————— T T T ]

Figure 2. Diagram of an asteroid, and objects flying near it. Objects are not to scale, but the arrows indicate speed and direction of each object relative to the asteroid, P 9 with longer arrows implying 3 ks E faster speeds. A asteroid 2A. (i) Which, if any, of the spaceships can validly claim to be at rest? Explain your answer _choice in 1-2 sentences. ( /\‘ All spaceships can claim to be at rest. B2 None of the spaceships can claim to be at rest. > Only spaceships B and E may claim to be at rest. “>d_ The answer cannot be determined from the information provided. There ore not 2 prspactives gem\ Cmsldfil"’j hat ol ashonaots congant velochy ndhi6n - This meons Jicechion “aF spacehs mgkien 2A. (ii) Select the largest group of ships that would agree on the speed of the asteroid. —'b\p Explain your answer choice in 1-2 sentences. Aand B Band E B,Cand E & A, B, C, D, and E (all five spaceships will agree on the speed) All spaceships will disagree on the speed of the asterond 5\60\6 \WLS& 3 bove Y gc\y\e sascecj bc Cast the Grrow levﬂ‘h« For 1\~L<E 3 2A. (iii) Spaceship A sends messages the olher spaceships using flashes of light from a beacon on its tip. Assume all four other ships can see the light flashes from this beacon. Select the largest group of ships that would agree on the speed of a flash of light from spaceship A. Explain your answer choice in 1-2 scntcnces AandB The g{)((’{ ;i\ ~ Band E r ool e 93 OP{)‘V B,Cand E “’\(l 5(( A, B, C, D, and E (all five spaceships will agree on the speed) % All spaceships will disagree on the speed of a flash of light are 0 g *’\’, SaNe€ - dwg Y\U\' C\’\C\‘\f}t/ ‘(V(’L’\ﬂi"\j

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4. Length Contraction and Time Dilation Some of the most surprising consequences of special relativity have to do with the effects that moving close to the speed of light has on time and length. In lecture, Prof. Greene explained that because time passes more slowly for a moving clock, compared to a stationary clock, this means that less time elapses for moving objects. Furthermore, due to the intimate relationship between length and time, the length of a moving object along the direction of motion is actually shorter than the length of the same object when it is stationary. Let’s consider how this works. Lieutenant Greene is in charge of the spacecraft docking bay on Deep Space 10, a space station. He notices a spaceship flying past Deep Space 10 at a whopping 2.77 x 10® m/s, as shown in Figure 3 below. Lieutenant Greene signals the spaceship, and discovers it is being piloted by Commander Hughes. v=207T] % IO%m (e S Figure 3. Diagram of Lieutenant Greene on board Deep Space 10 and Commander Hughes on board her spaceship. The arrow indicates the direction the spaceship is ying relative to Deep Space 10. 4A. (i) Fill in the blank and circle the correct choice in the statement below. Use the space below the question for any necessary calculations, According to Lieutenant Greene, time passes Z-b_times more qunckl)‘/@ l_\)on the spaceship relative to on the space station Deep Space 10.” ~ » }\ =96 ko Ea ﬂmj (3.0x0'2) o

4A. (i) According to Lieutenant Greene, while 1-hour elapses on the clocks on Deep Space 10, how much time will elapse on Commander Hughes’ clock on the spaceship? Express your answer in units of minutes. ‘;mm\l(.\ for e\(»{){(} Jime \fim o 2’5.\ mins 206 (‘ﬂﬂ\\"(‘#l(‘/‘} Just at the moment that Commander Hughes’ spacecraft passes Lieutenant Greene on Deep Space 10, both she and Lieutenant Greene happen to turn on their music. Commander Hughes turns on “Supersonic Rocket Ship™ by The Kinks, and Lieutenant Greene turns on “Supermassive Black Hole” by Muse. By coincidence, both tracks are 3 minutes and 30 seconds long. Hoa?s v,fib \lte W i3 g odec Y { \ ® Comm o mwi Sl (hve (s daws ) h 4B. (i) From Lieutenant Greene’s perspective, which song will end first? Circle the correct choice: sa-Commander Hughes' song, “Supersonic Rocket Ship™ ieutenant Greene's song, “Supermassive Black Hole™ 4B. (ii) According to Lieutenant Greene, 3 minutes and 30 seconds will pass on his clock before the song he is listening to, Supermassive Black Hole ends. How many seconds will pass on his clock before Commander Hughes’ song, “Supersonic Rocket Ship,” ends? ‘56 secs will o5 on e clock beere f1supesonic rocked g endS \pecause Hre mindes (3:34) ;f( 02 e ONoc f is wonng: fim (3 5 mm‘Q’% G(/)S— = SL}( <ecS y [ \iminy 4B, (iii) From Commander Hughes’ perspective, which song will end first? Circle the correct “ghoice: (@ Commander Hughes' song, “Supersonic Rocket Ship” “bLieutenant Greene's song, “Supermassive Black Hole” 6 < [/‘r (,‘ NOre

R s o WS O s (\ \\F, \“\{\VI‘V ' \ \\\\‘ » ,.\ AN . WO 4egy ’ W ‘ \ Taye) ng k: (‘1 Mimay, Hus Mmuni. 0 s, I ) \ Nicatjq, © Deg, h 1ee ding (| '])l Pace | \ K\ \m:\nd g} Spac in Chany . Seg time . A mc“‘“" 10 b ;: ‘l’u“\" es | can ¢, ""'n:'ml Tugh,. “"'l"'“ <M long “Utengyy, “Ship at D “nds 5 \ 4(‘,( ‘ 26 %19 (tip o tail Il‘cc[|“n)~ 3 "G NCasyp, m:\p’ Pace | \ c“‘“’ding to o \° €, and 3my | Pacesp; \ he l’l-lnks and y, . blm"undt.r l“l:heq wh B ) © Space beloy, e 1At are the g; o~ the quecs: © ‘llmum.,n Lengp. ~Spaa “’W‘l 1estion for ay, Ol her e . e 312 % Width: 3 Y ecessan Caley nli.'.:.: D2 Filp i — Heighy. 3 Y \ -3 \ o % < R 10 31.2 ‘ S (Qs\mf) S A2m \"Pr;;.(\q \en\jn =\2m 9 3 ocking bay o, Space 1 leutenap¢ Greene ajjgy oo P Sp. < 0is 15 1 | 2 4 m wige senlences usin 5. (i) What is the total energy contained in tomato, which ig' 125 grams/ _—- K( =] 125 % (073 g & (3%108 Ty )’? O-\I/)(’ x Qq ( mu) ; — [H) /;(,"’hi’) | 7 a hamster at rest? Use the > b‘qqff ¥ Eguivalencx of Mass and Energy In lecture You were introduced to the most famous €quation in Specia| Relativity, £ - me?. This €quation tells ys that mass and energy are really just differeng manifestations of the same thing, related by the universal speed limit, the speed of light. Evep 5 relatively Jighe object, such as 5 tomato, intrinsicall)' contains a |ot of energy. average mass of 5 %.h T p——

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5. (ii) According to the US Energy Information Administration, the daily energy consumy an average home in the United States is about 8.1 ¥ 10'" J (as of 2016). How many days could 4 dead (;II;\u)s at rest) hamster supply energy for an average home in the US, assuming you can extract 100% of the energy contained in the hamster? # doys LAY A % ) X 101 ) [day \___— 5. (iii) Why can’t we just use dead hamsters to fulfill our energy needs? W B T B £ we cronge Moss )‘“’ (W"CSX b would B \X . ) e ‘ ) C('h+ b‘{ C(T’\(X)Ye(’ ‘\O O*‘/‘Q(ﬂefig%&uﬂefi »)(’(‘f;u}? Yy e Toc 5. (iv) A meteoroid with rest mass equal to the average hamster’s mass (125 grams) is traveling MG // towards Earth at constant speed. If the total relativistic energy of this meteoroid is 100 times what you calculated in (i) for the hamster, how fast is it m;ving? ‘ \ \JL \E&Jjge, of pretecil ‘ \\

w 3. Simultancity The idea of simultaneity was introduced in the reading and lecture usin presidents of Forwardland and Backwardland signing a peace treaty on a the example of the treaty signing as discussed in lecture. Recall that in th sets of observers, those on the train, and those on the platform 3A. (i) Suppose two people on the platform (Frannie from Forwardland and Bob fr Backwardland) were not so interested in peace between their countries. Frannie and B toss rotten tomatoes at one another; people on the platform report that the two tomatoc thrown simultaneously and, remarkably, collided midair with one another just as the Presid train was passing the platform. What would people on the train report? Explain your ansv choice in 1-2 sentences. ~&. They report that the tomatoes were thrown simultaneously, and collided. “h¢ They report that the tomatoes were thrown simultaneously, but did not collide They report that the tomatoes were thrown at different times, but did collide. ~&~ They report that the tomatoes were thrown at different times, and did not collide Tre Vea 1S Aral he (YopL? on He a0 hove o Oiffere tom the plaform 3 WS S cecase dte dwo Cbsenves are re\dive malian 3A. (ii) Suppose that, after the upset from the initial Peace Signing Treaty, the Presidents of Forwardland and Backwardland decide to repeat the peace treaty signing described in lecture, but from the train platform instead of from a train. Due to safety restrictions at the train station, some people viewed this historic event from a train passing by the platform at a constant velocity. Viewers on the platform report that the two presidents now signed the treaty at the exactly the same moment. Which of the following choices best describes what viewers on the train would report? Explain your answer choice in 1-2 sentences. . They report that the train platform was moving and the presidents signed the treaty at the same time. 7».4 They report that the train platform was stationary and the presidents signed the treaty at @ the same time. ) They report that the train platform was moving and the presidents signed the treaty at _ different times. /cf‘ They report that the train platform was stationary and the presidents signed the treaty at different times. \fi =mS The viewers are ot est so Gom reir perspectie £ e o 'T} Moron (n the ctrer side ,) s TT‘&‘)\'W‘?. e &

Vanessa Cueva

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