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Homework Help: Elastic collisions formula help

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data

    After some messey algebra it can be said that

    V_B = (2 m_A V_o_A)/(m_A + m_B)

    V_A = ( (M_A - M_B ) V_o_A )/(M_A + M_B)

    were did this come from???

    2. Relevant equations

    momentum

    3. The attempt at a solution

    I don't even know were to start
     
  2. jcsd
  3. Jan 18, 2010 #2
    Re: Momentum

    were _B indicates a quantity realtive to B
    and _A indicates a quantity realitve to A

    and V_o is the intial velocity
     
  4. Jan 18, 2010 #3

    ideasrule

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    Homework Helper

    Re: Momentum

    That's for elastic collisions. It comes from solving the conservation of momentum and conservation of energy equations simultaneously.
     
  5. Jan 18, 2010 #4
    Re: Momentum

    ummm... hmm

    ok... um so there is just kinetic energy??? no potential and you had to solve for the velocities becasue these are the only terms the same in momentum and kinetic energy so... lets see.. um..
     
  6. Jan 18, 2010 #5
    Re: Momentum

    ok then

    m_A V_o_A + m_B V_o_B = m_A V_A + m_B V_B

    .5 m_A V_o_A^2 + .5 m_B V_o_B^2 = .5 m_A V_A^2 + .5 m_B V_B^2
     
    Last edited: Jan 18, 2010
  7. Jan 18, 2010 #6

    ideasrule

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    Homework Helper

    Re: Momentum

    Yes. Now bring the terms that start with "m_A" to the left in both equations, bring the terms that start with "m_B" to the right in both equations, and see what you get.
     
  8. Jan 18, 2010 #7
    Re: Momentum

    oh ok hold up
     
  9. Jan 18, 2010 #8
    Re: Momentum

    m_A V_o_A + m_B V_o_B = m_A V_A + m_B V_B
    m_A V_o_A - m_A V_A = m_B V_B - m_B V_o_B
    m_A(V_o_A - V_A) = m_B (V_B - V_o_B )


    .5 m_A V_o_A^2 + .5 m_B V_o_B^2 = .5 m_A V_A^2 + .5 m_B V_B^2
    .5 m_A V_o_A^2 - .5 m_A V_A^2 = .5 m_B V_B^2 - .5 m_B V_o_B^2
    .5 m_A (V_o_A^2 - V_A^2) = .5 m_B (V_B^2 - V_o_B^2)
     
  10. Jan 18, 2010 #9
    Re: Momentum

    i'm not really sure were this problem is going
     
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