BART does a serious upgrade to their trains such that they now have a speed of 0

Question

BART does a serious upgrade to their trains such that they now have a speed of 0.85c. measured relative to the (racks. During testing one of the trains moves though the Balboa train station at 0.85c without slowing down. A observer O on the train platform notes that front and back of the train line up simultaneously with the with the ends of the train platform, which has a length of D0 = 115 m. What is the rest length of the train? According to an observer O on the train, what is the length of the train platform? According to O', how long does it take the train to pass observer O standing on the platform?

Explanation / Answer

according to o the length of the train L matches the length D_0 of the platform (a) length of the train    L_0 = L / sqrt ( 1 - ( u /c)^2 ) here u = 0.85 c and  L =  115 m L0   = (115 m)/( 0.5267)   = 218.34 m (b)   length of the train platform D = D_0*sqrt ( 1 - ( u /c)^2 )    = (115 m) (0.5267) = 60.5705 m (C) For o to pass the entire length of the train , concludes that o must move a distance equal to it's rest length 218.34 m Time t'   =   218.34m / 0.85c   = 0.856 *10^-6 sec (C) For o to pass the entire length of the train , concludes that o must move a distance equal to it's rest length 218.34 m Time t'   =   218.34m / 0.85c   = 0.856 *10^-6 sec

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