1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

  9. Feb 24, 2013 #8

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    [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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted