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When the conservation of linear momentum is violated

  1. Oct 21, 2014 #1
    Hello Forum,

    The conservation of linear momentum is applicable when the net external force is zero or negligible compared to the internal forces. This principles is applicable to perfectly elastic, partially elastic and totally inelastic collisions.
    But only for perfectly elastic collisions the mechanical energy (KE+PE) is conserved.

    That said, what happens when two cars collide in a crash in an inelastic collision and the system does not move, i.e. total final momentum is zero? There is clearly a violation of the conservation of momentum, correct? All the mechanical energy is dissipated into crushing the cars. That said, I thought that the conservation principle applied to inelastic collision without problem, regardless of the deformation and loss of mechanical energy involved....

  2. jcsd
  3. Oct 21, 2014 #2


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    Staff: Mentor

    In that case, before the collision, the two cars must have momenta that are equal in magnitude and opposite in direction. The vector sum of the two initial momenta is zero.

    (This ignores effects from friction between the cars and the road, of course.)
  4. Oct 21, 2014 #3
    Thank you.

    So, total momentum before the collision is equal to total momentum after the collision (as long as the external forces don't eat up too much of the momentum). That is why, in laboratory experiments, it is important to calculate the total momentum right before the collision and right after the collision. Otherwise the total momentum will start changing, due to the presence of friction (external force acting for a long enough time).

    Inelastic collisions imply sticking between the objects involved in the collision, deformation, loss of mechanical energy. The deformation requires energy (hence the loss of mechanical energy). But the conservation of total momentum should still be valid (if the net external force is zero).

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