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B How to measure rest length while moving

  1. Nov 7, 2016 #1
    I don't remember seeing this solution to the question.

    Imagine an object of length d with a reflector on the far end (x=4).
    A moves past the object at speed a, emitting a signal at the origin in the positive x direction. A makes one pass in the +x direction, reverses and makes one pass in the -x direction.
    Relative to U, with c=1, a=.4:
    time out is the same for both passes, t0=d/c.
    return time-pass 1, t1=t0(1-a)/(1+a)
    return time-pass 2, t2=t0(1+a)/(1-a)
    with time dilation for A;
    total time-pass 1, T1=2t0*sqrt ((1-a)/(1+a))
    total time-pass 2, T2=2t0*sqrt ((1+a)/(1-a))
    t0=.5sqrt(T1*T2)
    Example:
    d=.5sqrt(5.24*12.16) = 4.0

    measuring rest length.gif
     
  2. jcsd
  3. Nov 7, 2016 #2

    Ibix

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    Science Advisor

    Looks right, but the methodology seems overly complex to me. I am required to decelerate from +a to -a. Why not just stop at zero and measure in the rest frame? Or just use the Lorentz transforms, given that I need to know the velocity precisely enough to sign flip it?
     
  4. Nov 8, 2016 #3
    I agree with simplicity. Was just making calculations for doppler effects, and thought this would work, but needed another opinion.
    Thanks.
     
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