quiz1 solution(revised).pdf - Physics 2D Quiz1...

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Physics 2D Quiz1 solution(revised) Siyang Wang April 12, 2016 prob 1 If light propagated in the ether and the speed of light was equal to c in the frame of the ether(in contra- diction to Special Relativity), the Michelson-Morley experiment with armsof equal length L parallel and perpendicular to the earth’s motion through the ether should have transit times with: The total time of the travel for the round trip in parallel direction is: t 1 = L c - v + L c + v = 2 L c 1 - v 2 c 2 - 1 in perpendicular direction: t 2 = 2 L ( c 2 - v 2 ) 1 / 2 = 2 L c 1 - v 2 c 2 - 1 / 2 So the transit times are greater than 2L/c in both arms(text book p7-8) prob 2 A pion(mass 139MeV/ c 2 ) is produces with energy 10000MeV in the lab frame. In pion’s rest frame, it decays 26ns after it is produced. How far does the pion travel in the lab frame? γ = E m 0 c 2 71 . 94 and we can get its speed from: γ = 1 q 1 - v 2 c 2 the speed v is very close to c(0.9999c). The decay time in lab frame is dialated by a factor γ . So in lab frame it travels: d lab = 26 nm × γ × v 561 m
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