Suppose a large mass $M$ travelling at $v$ impacts a small stationary mass $m$, then following through the elastic collisions from high school, we get that the smaller mass can exit the collision FASTER than $v$.

In the limit of huge $M$, we can change reference frame and make $M$ basically stationary, and $m$ simply bounces off, thereby having a velocity change of $2v$.

How can I visualise this from a microscopic level? If the normal force between objects only exists while they are in contact, the moment contact was lost between two objects they no longer act on each other. So as soon as the target balls speed reaches the tiniest amount above the impact ball speed, the balls should separate and no longer interact. This would lead to all collisions being "sticky" and completely inelastic.

So why are not all collisions sticky? How do collisions work that apparently allow acceleration past the point where contact is lost? And if this is something to do with Coulomb interaction, is there any historical commentary on how Newton and peers felt about this prior to the understanding of electrodynamics?


1 Answer 1


To understand elastic collisions, you don't have to look at microscopic levels. It is enough to treat the collision as a continuous process instead of an instant event.

Every collision starts the same: one object hits another, and both get deformed according to material properties. The deformation is caused by the relative kinetic energy of the objects. One could say, the kinetic energy is transformed into deformation energy.

An inelastic collision is over as soon as all the transformation is complete, and the deformed objects stay deformed until the end of time (or until another collision deforms them further).

At the point where both objects have the same velocity, the elastic collision is only halfway over. The deformation energy is now re-transformed into kinetic energy, because the objects assume their previous shapes. They will touch as long as the "reformation" takes. And only then, when the original shapes are restored, and the objects have a non-zero relative velocity, will the objects part.

  • $\begingroup$ I think I understand - so you could presumably model this as the contact being between ideal springs? Initially the springs compress, and then the energy is re-released slowing down the impacting ball and accelerating further the target ball. $\endgroup$
    – Corvus
    Jun 18, 2014 at 8:22

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