Question

Problem 5: One day the hyper-express train Albert Einstein is parked at the platform of Sirius Station, the engineer on the train and the stationmaster on the platform compare their measurements of the lengths of the train and the platform. They agree that both are exactly 100.0 m long. On a different day, the train passes Sirius Station without stopping, keeping a constant speed of 0.998 c. (a) How long is the train, as measured by the stationmaster on the platform? [Hint: Answer first which observer is in the rest frame.] (Opts.) (b) How long is the platform, as measured by the engineer on the train? [Hint: which observer is now in the rest frame?] 74pts.)

Answer 1

1-v2 C2 b = speed of the klatform with respect to the train Solution 7 length of train (le) = 2oom speed of the of the train (w) = 0.998c the stationmaster. is in. the rest frame, so station master will observe. contracted length because the train is moving with the speed comparable to the to the speed of light so, the contracted length is given by PART(A) L = Lo L La (0.99812 t joo 1- 0.99.6004 L 6.32 meter Aus. PART (6) Now the engineer ů in the rest frame train and for the engineer the platform moring back of speed r=0.9986 respect the train. Again use the formula for leigth contraction Le =) length of the platform in rest frame of length of the platform in rest frame of the train Loo 0.00 3996 Loo x 0.06 32 14 of the ů with L- Lo 02 c2 the platform and Lo=foom too fiato:998) Too FT-0.996004 An. L 180x0.0632 L=6.32 meter