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Special Relativity Question

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data

    A particle has a rest energy of 1672MeV and a lifetime of 8.2x10^-11 s. It creates a .024m long track in a lab detector. What is the total energy of the particle

    2. Relevant equations



    3. The attempt at a solution

    Total Energy = mc^2 + mc^2(1 - A) where A is defined as the Gamma Factor...basically i need to calculate the velocity of the particle and I realize that the lifetime give is the proper time (life of the particle in its frame) and the distance is in the lab frame. So I need to distance/time and I want to convert the proper time to the time interval in the lab frame but how do i do time dilation without the velocity? Thanks
     
  2. jcsd
  3. Feb 23, 2013 #2

    Simon Bridge

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    You'll have to find a bunch of relations that have to hold simultaniously - so that you can cancel out v.
     
  4. Feb 23, 2013 #3
    soo...what relations? I'm still stuck
     
  5. Feb 23, 2013 #4

    Simon Bridge

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    1. total energy
    2. time dilation
    3. length contraction (related to 2)
    4. relationship between distance and time in one reference frame
     
  6. Feb 23, 2013 #5
    got it..thanks
     
  7. Feb 23, 2013 #6

    Simon Bridge

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    No worries :)
     
  8. Feb 24, 2013 #7
    Ugh nevermind lol I don't have it.... and it's driving me crazy.

    V= L/T = L'/T' and I know L and T'.

    Time dilation says T=T'sqrt(1-A^2) where A is V/c

    so i plug in V=L/(T'sqrt(1-A^2)) and solve for V but I get (V^2)(T')^2 - ((V^4)(T')^2)/c^2 = c^2

    ahhhhhh
     
  9. Feb 24, 2013 #8

    Simon Bridge

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    [edit] didn't read all the way ...

    Well done.
    Sometimes explaining why you have a problem produces the solution.

    The particle travels distance L in the lab, in the particle's proper time T, then ##L=v\gamma T##
    Since the total energy is ##E=\gamma E_0## I have two equations and two unknowns.

    When I saw your problem, actually did it via length contraction ... to put everything in the particle's frame.
    In that frame, the detector moves a distance ##L/\gamma## in time T - and you get the same equation out.

    Notice how I constructed the relations from the physics rather than trying to find the "right" equation to manipulate?
     
    Last edited: Feb 24, 2013
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