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Help with Energy at inelastic collision

  1. Jun 19, 2011 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m1 and momentum p1 collides with a particle of mass m2 at rest. A reaction occurs, as a result giving two new particles, with masses m3 and m4, that are emitted at angles
    [itex]\theta_3[/itex] and [itex]\theta_4[/itex], in relation to the original direction of m1. Determine the energy Q that has been produced on the reaction in terms of the masses, the angles and p1.

    2. Relevant equations

    [tex]Q = T_f - T_i[/tex]
    [tex]T = \frac{p^2}{2 m}[/tex]

    3. The attempt at a solution

    [tex]p_1 = p_3 cos(\theta_3) + p_4 cos(\theta_4)[/tex]
    [tex]p_2 = 0 = p_3 sin(\theta_3) - p_4 sin(\theta_3)[/tex]
    [tex]Q = T_3 + T_4 - T_1[/tex]
    [tex]Q = \frac{{p_3}^2}{2m_3} + \frac{{p_4}^2}{2m_4} - \frac{{p_1}^2}{2m_1}[/tex]

    I'm stuck here.
    I suppose I have to, obviously, express both [itex]p_3[/itex] and [itex]p_4[/itex] in terms of [itex]p_1[/itex], but I'm not exactly sure of how to do it. Or maybe I just need some algebraic manipulation to get rid of both [itex]p_3[/itex] and [itex]p_4[/itex].

    Any help appreciated.
     
  2. jcsd
  3. Jun 19, 2011 #2

    ojs

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    That absolutely correct, you need algebraic manipulation to express [itex]p_3[/itex] and [itex]p_4[/itex] in terms of [itex]p_1[/itex], [itex]\theta_3[/itex] and [itex]\theta_4[/itex].
     
  4. Jun 19, 2011 #3

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    ... and these are the equations you need to manipulate:
     
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