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A particle of rest mass m_0 and kinetic energy and sticks to a stationary particle wi

  1. Aug 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle of rest mass [itex]m_0[/itex] and kinetic energy [itex]2m_0c^2[/itex] and sticks to a stationary particle with rest mass [itex]2m_0[/itex]. Find the rest mass of the composite particle.

    2. Relevant equations

    Conservation of momentum and thus energy.

    [itex] E_{bef} = E_r + E_k = E_{aft}[/itex] where Er is energy of rest particle

    3. The attempt at a solution

    [itex]E = m_{01}c^2 + mv\gamma + m_oc^2 = m_{02}c^2[/itex]. The first half of the equation there is a kinetic part and a part at rest, the second half is only at rest.

    I am thinking I am supposed to be substituting the questions given data into this equation and cancelling expressions but i am not sure how to proceed.
     
  2. jcsd
  3. Aug 13, 2012 #2

    vela

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    Re: A particle of rest mass m_0 and kinetic energy and sticks to a stationary particl

    What are ##m_{01}##, ##m_{02}##, ##m_o## (not ##m_0##), and ##m## supposed to represent? None of those quantities appear in the problem statement.

    Your equation doesn't make sense. You're adding energy to momentum ##\gamma mv##. That doesn't work out unit-wise. I take it v is supposed to be the speed of the first particle.

    Think about this: After the two particles collide and stick together, is the composite particle at rest or not?

    It's best if you stick to working with energy E, momentum p, and mass m rather than writing things in terms of ##\gamma## and speed v. It'll simplify the algebra.
     
    Last edited: Aug 13, 2012
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