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Length Contraction

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data

    A rod of rest length L0 = 10.4 m moves with a speed v = 0.42c along the x axis. The rod makes an angle of q0 = 66.1° with respect to the x' axis (primed frame is moving with the rod). What is the length of the rod as measured by a stationary observer?

    2. Relevant equations

    L=L1*(1/gamma)


    3. The attempt at a solution
    I have tried this several times, but can't seem to get it right.
    L0=L1=10.4
    gamma=(1-.422)-.5
    Just solved for L..but didn't work.
     
  2. jcsd
  3. Dec 5, 2008 #2

    Doc Al

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    Staff: Mentor

    Careful. Only the component parallel to the direction of motion contracts.
     
  4. Dec 5, 2008 #3
    So only the x component...is contracted. so L*cos(66.1)=L(x)?
     
  5. Dec 5, 2008 #4

    Doc Al

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    Staff: Mentor

    Right. (That's L0, of course.)
     
  6. Dec 5, 2008 #5
    now I multiply that by 1/gamma or (1-Beta2).5
    and beta = .42...

    so L=3.8238
     
  7. Dec 5, 2008 #6

    Doc Al

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    Staff: Mentor

    OK so far, but realize that this is just the x-component, Lx not the full L. What's the y-component? Then calculate the measured length of the rod.
     
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