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Basic Special Relativity (Time Dilation)

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data

    The Concorde traveled 8000km between two places with an average speed of 375 m/s. What is the time difference between two atomic clocks, one on the train and one at rest with respect to the train?

    2. Relevant equations

    T=AT' where A is the Lorentz gamma factor

    3. The attempt at a solution

    Seemed simple enough the distance divided by time would yield the T (the time taken from the rest frame) so (8x10^6 m/s)/(375) and then solve for T' (proper time which would be the time of a clock on the train correct?) but the speed of 375 m/s is so miniscule in comparison to the speed of light the lorentz factor comes out to be 1 (which isn't surprising) but in the back of the book it says the answer is 16.7 microseconds...what am I doing wrong? Thanks
     
  2. jcsd
  3. Feb 10, 2013 #2

    TSny

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    To a good approximation for your problem, you can approximate [1-(v/c)2]1/2 using the binomial approximation (1-x)a≈1-ax for x<<1.
     
  4. Feb 10, 2013 #3

    cepheid

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    Not using a calculator with enough precision?
     
  5. Feb 10, 2013 #4

    How does this help though? that just makes 1-ax = 1 - (7.8125e-13) which still is very close to 1. Where/how do you produce the 16.7 nanoseconds?
     
    Last edited: Feb 10, 2013
  6. Feb 10, 2013 #5

    TSny

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    Use the binomial approximation in the equation T = AT' without plugging any numbers in yet. Then see if you can rearrange for the quantity T-T'. Then plug in numbers.
     
  7. Feb 10, 2013 #6
    I don't think you can )easily) solve for T-T' with the expansion... T=T'/1-ax ==> T-Tax=T'...unless im missing some simply algebra i don't see how to manipulate to solve for T-T'
     
  8. Feb 10, 2013 #7

    TSny

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    Rearrange your last equation as T - T' = Tax

    As you said in your original post, you know how to get T for the right hand side.
     
  9. Feb 10, 2013 #8
    ahhh finally got it.. Thanks a bunch!
     
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