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Length Contraction Problem

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    An electron travels in an accelerator tube at a speed of 0.997 c relative to the Earth. In the frame of the electron, the length of the tube is 1.20 m.
    A. What is the length of the tube relative to Earth?

    B. Relative to Earth, how long does it take for the electron to travel the full length of the tube?

    C. In the frame of reference of the electron, What is the speed of the tube?

    D. In the frame of reference of the electron, how long does it take for the full length of the tube to pass the electron?


    2. Relevant equations
    l = lo √1-v^2/c^2
    t = d/v
    c = speed of light = 3.0 x10^8m/s

    3. The attempt at a solution
    For Part A. I did l = lo √1-v^2/c^2 and plugged it in so 1.2 = lo√1-(0.997)^2 and solved for lo which became to be 15.5m

    For Part B. i used t = d/v and plugged in t = 15.50m/0.997c = 5.18 x 10 ^-8 seconds

    For Part C. I said that the speed is the same and is constant so speed of the tube in frame of reference of the electron = 0.997c

    For Part D. t= d/v = 1.20m/0.997c = 4.012 x 10^-9 seconds.

    Something just doesnt feel right about this, Please check if i did it properly.
     
  2. jcsd
  3. Feb 16, 2012 #2
    Looks okay to me. :)
     
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