# hw11_solutions - Physics 325 - Homework Solutions f,11 1)...

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Physics 325 - Homework Solutions f,11 1) An observer is standing on the station platform when a modern, high-speed train passes through at v:0.80c. The observer, who measures the platform to be 60m long, notices that the front and back of the train line up exactly with the ends of the platform. a) How long does the ground-based dbserver measure for the train to pass a fixed point on the platform? . Solutionz We call the observer on the platform S and the observer on the train S'. As observed by S, we have: I l<-F60m# platform S v:0.8c To see the entire train pass a fixed point on the platform, in reference frame S, the observer will see the train travel at a velocity y:0.8c over a distance F60m, so we have D = vt :+ t D/v 60ml(o.sx 3xr)smts) =z.sxr0-7s 0.25ps (r.r) b) What is the proper length of the train? Solution: In reference frame S', the person on the tlain observes the proper length of the train. we will label this proper length /', since it is observed in frame s, . The lenglh / measured in frame S was lengthcontracted, so we have: =l'\rc + t'=ly =60mtf,tr =lolm (1.2) c) what is the length of the platform, according to an observer on the train? Solution: The observer in frame ^S'must observe length of the platform to be contracted: t', I rJ;t4l 6or\m 36m where /" is the proper length of the platform and l', is the length observed in frame ,S'. d) How long will it take for a point on the platform to pass the full length of the train, according solution: From our solution to part b), we know length of the train. we can again use oru distance : velocity x time relation io find:

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t' : l' I v :l00ml(O.Sx: xl08m t s)= +.Zx l0-7s = 0.42ws Note that this time is longer than the time calculated in part a), indicating that observer S' measures a time that is dilated relative to observer S. We can also
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## This note was uploaded on 02/23/2009 for the course PHYS 325 taught by Professor Lamb during the Fall '09 term at University of Illinois at Urbana–Champaign.

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hw11_solutions - Physics 325 - Homework Solutions f,11 1)...

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