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Apparent paradox

  1. Nov 25, 2005 #1
    Consider collision of two bodies of mass m1 and m2. m2 is at rest whicle m1 moves with velocity v1.
    When they collide they sitck together. The question is what is the final velocity V of the two bodies combined.
    This apparently simple problem if solved naively leads to an apparent paradox if we solve the problem by
    1. conservation of momentum
    2. conservation of energy


    By conservation of momemtum
    since v2=0 we get the final velocity V of the two bodies combined as



    By conservation of energy
    (m1v1^2)/2 + (m2v2^2)/2 = ((m1+m2)V^2)/2
    here again by substituting v2=0 we get

    V= sqrt(m1/(m1+m2))v1

    so if we go by two different routes we arrive at two different answers, whereas we should be arriving at the same answer.
    So which one is correct?
    I know I have applied the concepts very naively, if I am wrong at any point of these derivatiosn please point me.
  2. jcsd
  3. Nov 25, 2005 #2


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    There is no paradox. When there is a 'stick', this is always an inelastic collision. KE is not conserved.

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