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Two spheres collide and assume that the collision is perfectly elastic

  1. Aug 31, 2004 #1
    Two spheres collide and assume that the collision is perfectly elastic. Also --only linear momentum.

    I have the relationship:

    (va' - vb') dot N = -(va - vb) dot N

    Where N is the normal vector at the point of collision. va and vb are initial velocities of object A and B, respectively. And va' and vb' are the final velocities of object A and B respectively.

    I want to know how this relationship is derived.

    This is what I try:

    Relative to object B, object A has velocity v_ab. Relative to object B,
    object B has velocity 0.

    m_a*v_a + m_b*v_b = m_a*v_a' + m_b*v_b'

    Relative to B:

    m_a*v_ab + 0= m_a*v_ab' + 0

    v_ab = v_ab'

    That would give me this: (va' - vb') dot N = (va - vb) dot N

    But I am missing the negative sign, because they should be opposite. Please
    advise. Thanks in advance.
     
  2. jcsd
  3. Aug 31, 2004 #2
    As I'm sure you're aware, in an elastic collision, both kinetic energy and momentum are conserved. If you write both sets of equations and solve them simultaneously, you'll get (va' - vb') = - (va - vb)
     
  4. Aug 31, 2004 #3
    Yeah (needed KE), I've solved it now. I solved it in the center of mass frame, which seemed easier.
     
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