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Momentum Energy and relativity question

  1. Jun 2, 2017 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m is moving along the positive x direction with momentum p and energy E

    It collides with a particle of the same mass at rest to form a new particle of mass M.

    Show that

    M^2 = 2m/c^2 * (E + mc^2)


    2. Relevant equations

    E^2= p^2c^2 + m^2c^4


    3. The attempt at a solution
    I know the momentum of M will be equal to that of m before the collision hence it will be p.

    I tried looking at conservation of energy but the answer does not seem to fall out nicely I must be overlooking something any help would be appreciated.
     
  2. jcsd
  3. Jun 2, 2017 #2

    strangerep

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    Science Advisor

    You should probably have shown your attempted "looking at conservation of energy" in sect 3 of your OP. Without that, it's impossible to know what you did wrong. So I'll just sketch the general method...

    Write out the invariant mass formulas for both particles separately. (Start by calling their respective energies and 3-momenta ##E1,p1## and ##E_2,p_2##, then replace with known values where possible from the problem statement.)

    Write out the total energy and 3-momentum (calling them ##E_{tot}, P_{tot}##). You then have 3 equations to work with.

    Write out the invariant mass formula for the composite system, calling the total mass ##M##. You can then rearrange it to get the answer by substituting various values from the previous 3 equations.
     
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