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Special R

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Two trains, A and B, are moving towards each other with relative speed 0.8c. The
    passing of the two trains (from when their fronts align to when their backs align) takes 20%
    longer as observed from train A as is does as observed from train B. What is the ratio of the
    length of A to the length of B?

    2. Relevant equations

    I am guessing:
    T'=Tsqrt(1-(v/c)^2)
    L'=Lsqrt(1-(v/c)^2)

    3. The attempt at a solution

    I am confused, I feel like there is missing information?

    I am trying to relate these two equations! but im really not sure how to go about solving this one!! please help. just so i know where to start....
     
    Last edited by a moderator: Sep 19, 2013
  2. jcsd
  3. Sep 18, 2013 #2
    Let LA represent the length of train A in its own rest frame, and let LB represent the length of train B in its own rest frame. Let v be the relative velocity.

    The observers on train A focus on 3 sequential events:
    1. The front of train B aligns with the front of train A.
    2. The front of train B aligns with the rear of train A.
    3. The rear of train B aligns with the rear of train A.

    Draw diagrams of these three events.

    Knowing the rest length of train A and the relative velocity of the trains, what is the time interval between events 1 and 2 (as reckoned by the observers on train A)?
    What is the length of train B as reckoned by the observers on train A, knowing the rest length of train B and the relative velocity of the trains?
    Knowing the length of train B as reckoned by the observers on train A and the relative velocity of the trains, what is the time interval between events 2 and 3 (as reckoned by the observers on train A)?
    As reckoned by the observers on train A, what is the time interval between events 1 and 3?
    Now, do the same analysis for the observers on train B. As reckoned by the observers on train B, what is the time interval between events 1 and 3?
     
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