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Homework Help: Special relativity, delay of a clock in a plane

  1. Aug 15, 2010 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    A plane is moving at 600m/s with respect to the ground. According to clocks on the ground, how much time would it take so that the plane's clock is delayed by 2 microseconds?


    2. Relevant equations
    Lorentz transformations.


    3. The attempt at a solution
    Let O be a reference frame on the ground and O' be a reference frame on the plane.
    v=600m/s. If I'm not wrong, they ask me [tex]t_B-t_A[/tex] such that [tex](t_B-t_A)-(t_A'-t_B')=2 \times 10 ^{-6}s[/tex]. (*)
    What I've done so far is [tex]t_B'-t_A'=\gamma \left [ t_B-t_A +\frac{v}{c^2}(x_A-x_B) \right ][/tex], replacing [tex]x_A-x_B[/tex] by [tex]v(t_A-t_B)[/tex], then solving for [tex]t_B-t_A[/tex] in (*), I reach that it's worth exactly [tex]1000000s[/tex]. Or 11 days, 13 hours, 46 minutes and 40 s. It seems too big for me. Do you get a different answer?
     
  2. jcsd
  3. Aug 16, 2010 #2

    collinsmark

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    Your final answer is about the same as mine.
     
  4. Aug 16, 2010 #3

    fluidistic

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    Oh ok. Thanks a lot for the confirmation.
     
  5. Aug 16, 2010 #4

    collinsmark

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    Be careful of your precision though. The speed of light isn't exactly 3.000000 x 108 m/s. So I don't think you should be calculating the time down to the very second with that. But something around 1.0 x 106 seconds is the answer that I got, is what I meant.
     
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