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Help with collision equations

  1. Feb 5, 2004 #1
    Can anyone help show me the process of solving the equations
    (m1*v1)+(M2+V2)=(m1+v1')+(M2+V2')
    (.5m1*v1^2)+(.5M2*V2^2)=(.5m1*v1')+(.5M2*V2')

    to get the equations

    ----m1+M2 2M2v
    v1' ----- v1 + ----- V2
    ----m1+M2 m1+M2


    -----2m1 M2-m1
    V2' ----- v1 + ----- V2
    ----m1+M2 m1+M2


    i need the algebra used or at least how i should start i know you solve one and plug it into the other, but im not sure if i should start by factoring, expanding or what any help would be greatly appreciated. I started by factoring but just need a shove in the right direction.
     
  2. jcsd
  3. Feb 6, 2004 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    One thing you need is practice in copying the problem correctly:
    in some places you have + where you should have * and you are missing "squares" in the second equation.

    I take it you are given v1 and V2 and need to solve for v1' and V2'.

    It's actually a lot easier to solve specific problems (with actual numbers for m1, m2, v1, and V2) than to solve the general formulas.

    I would recommend that you solve the first equation for v1':
    m1*v1'= m1v1+m2V2-m2v2' so v1'= (m1v1+m2V2-m2v2')/m1

    and substitute that into the second equation so that you have an equation for V2' only (involving v1 and V2, of course). Solve that for V2' then substitute back into v1'= (m1v1+m2V2-m2v2')/m1 for v1'.

    (One obvious simplification is to multiply that second (kinetic energy) equation by 2!)
     
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