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Inelastic collision for equal masses

  1. Nov 11, 2015 #1
    Assume that we have two equal masses that collide horizontally, where one is initially at rest. From the conservation of linear momentum, we have
    ##P_0 = P##
    ##mv_{10} = mv_{1} + mv_{2}##
    ##v_{10} = v_{1} + v_{2}##

    Assuming we have an initial velocity, it would seem as though the final velocity of mass 1 could add with the final velocity of mass 2 in order to equal the initial velocity. However, this is not the case because collisions don't act randomly like that. Therefore, what am I missing? I know that in elastic collisions, ##v_{10} = v_{2}## because of the additional constraint posed by the conservation of mechanical energy, but I claimed that this was an inelastic collision. Is there some constraint that I am missing?
  2. jcsd
  3. Nov 11, 2015 #2


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    Equivocating on the variable ##m## ?
  4. Nov 11, 2015 #3
    You might need to elaborate...
  5. Nov 11, 2015 #4
    The problem is not fully specified. There are two unknowns, v1 and v2, and only one equation. One more condition comes from either stating that it is a completely inelastic collision,or stating the percentage of kinetic energy lost. Either one will give the necessary second condition.
  6. Nov 11, 2015 #5
    That answers my question. Thanks.
  7. Nov 12, 2015 #6


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    In a completely inelastic collision, the objects "stick together", which means that their velocities are equal after the collision.
  8. Nov 12, 2015 #7


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    One way to get a clear picture is to change coordinates to a center of mass system. In that case, after collision, neither object will be moving when the collision is completely inelastic.
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