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Calculating mass of particle given total energy and momentum

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle, observed in a particular reference frame, has a total energy of 10GeV and a momentum of 6GeV. What is its mass in units of GeV/c^2?


    2. Relevant equations
    I used [tex]p=\gamma mv[/tex]
    and
    [tex]E=\gamma mc^2[/tex]


    3. The attempt at a solution
    So I divided the above equation for P by the equation for E to get

    [tex]\frac{P}{E} = \frac{v}{c^2} \Rightarrow v=\frac{P}{E}c^2[/tex]

    and then substituting back into the quation for E:

    [tex]m = \frac{E}{\gamma c^2} = \frac{\sqrt{1-\frac{P^2}{E^2}}E}{c^2}[/tex]

    But this doesn't give the correct answer - any ideas?

    With very, very many thanks,

    Froskoy.
     
  2. jcsd
  3. Mar 10, 2012 #2

    tiny-tim

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    Homework Helper

    Hi Froskoy! :smile:

    (try using the X2 button just above the Reply box :wink:)
    It's not clear what they mean by "total energy". :redface:

    Maybe they mean the kinetic energy, (γ - 1)mc2

    try that :smile:
     
  4. Mar 10, 2012 #3

    phyzguy

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    You dropped a factor of c^2, in your final equation, which should read:
    [tex] m = \frac{E \sqrt{1-\frac{p^2 c^2}{E^2}}}{c^2}[/tex]
    which is consistent with the well-known relation E^2 = p^2 c^2 + m^2 c^4. However, this shouldn't matter, since when using units of GeV and GeV/c^2, c=1 anyway. Why doesn't this give the right answer? If E= 10Gev, and p = 6GeV/c^2, m = 8Gev/c^2, which is what your equation gives.
     
  5. Mar 10, 2012 #4
    Hi!

    Thanks very much for confirming what I had is correct - it turned out to be a calculation error.

    With very many thanks again,

    Froskoy.
     
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