PHY2061 R. D. Field Solutions Relativity Page 1 of 6 Relativity SolutionsProblem 1: A rod whose length at rest is 10 metersis moving to the right along the positive x-axis of the O-framewith velocity V = 0.8c. An observer riding on the rod (i.e.in the O'-frame) sets off two explosions simultaneously – so he says. If the rod is parallel to the x-axis how far apart are the two explosions (in meters) in the O-frame? Is this length the same as the length of the rod as measured in the O-frame? If your answer is no, then what is the length of the rod (in meters) as measured in the O-frame? Answers: 16.67, no, 6 Solution:The two explosions occur simultaneously in the O'-framewhich implies that ∆t' = 0and thus mmLtcxx67.16)10)(667.1()(0===′∆+′∆=∆γβγwhere I used ∆x' = L0. This is notthe same as the length of the rod as measured in the O-frame. The length of the rod as measured in the O-framecorresponds to marking both ends of the rod simultaneously in the O-frame(i.e.∆t = 0) as follows: LtcxLxγβγ=∆−∆==′∆)(0and mmLL6667.1100===γ. Problem 2: In the previous problem, what is the time interval (in seconds) between the two explosions as measured in the O-frame?Which explosion occurred first in the O-frame, the one at the left or right end of the rod? Answers: 4.44x10-8, left one first Solution:The two explosions occur simultaneously in the O'-framewhich implies that ∆t' = 0and thus mmLxtctc3.13)10)(33.1()(0===′∆+′∆=∆γββγwhere I used ∆x' = L0. This, yxzy’z’x’V=0.8cO'OExplosionssimultaneously inthe O'-frameL0
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