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Angle of particles after elastic collision

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle of mass M1 collides elastically with a particle of mass M2 at rest. Show that if M1>M2 then the angle of M1 after the collision cannot exceed the value arcsin(M2/M1).


    2. Relevant equations
    conservation of momentum: M1v1=M1v1`+M2v2`
    conservation of kinetic energy: (1/2)M1v12=(1/2)M1v1`2+(1/2)M2v2`2


    3. The attempt at a solution
    I've figured out that the velocities after collision are:
    v1`=v1*[(M1-M2)/(M1+M2)]
    and
    v2`=v1*[(2M1)/(M1+M2)]
    but I don't know how to find the maximum angle of M1 after collision. Please help
     
  2. jcsd
  3. Apr 1, 2009 #2

    Pythagorean

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    Gold Member

    what's the critical point between when M1 > M2 is true, and when it's no longer true?

    what will M1 - M2 be at that point?

    to get angle into your equation, think projection.
     
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