# Motion of two objects in a perfectly inelastic collision

Imagine two small metal spheres of equal mass and size moving at the same speed in opposite direction collide with each other. Logically (without doing the math) it seems that both spheres will collide and just stop "dead" (because of equal mass and speed). I don't know whether I made a fundamental oversight in not actually calculating the results but I have a problem with the phenomenon I state above.

If the spheres collide and stop, then they would have stopped in no distance at all... that is and infinitely large deceleration. That would require an infinite force.. We know an infinitely large force is not generated in this instance so obviously the spheres wouldn't just stop instantly.. they would decelerate over a small (perhaps tiny) distance...
Where does this distance "come from"? they don't pass into each other so one would be lead to assume that the spheres were deformed... can deformation account for this discrepancy? and if so.. just out of curiosity... what if the spheres were made out of a very hard substance like diamond? (  )

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In a perfectly inelastic collision the initial kinetic energy is transformed into heat or potential energy of deformation. In the latter case the deformation displacement delta_x is determined with the initial kinetic energy and the coefficient of elasticity. Also, deceleration takes time. The harder material is, the smaller the displacement.

If you consider elastic collisions, then, after deformation the potential energy of deformation transforms into kinetic energy and two ball fly apart.

rock.freak667
Homework Helper
well from the momentum equation

mu-mu=2mvf → vf=0

But in an perfectly inelastic collision, the objects coalesce or stick together. So they'd have to deform really. If they could not deform for some reason then the final momentum would also be zero but the objects could move off with a velocities v1 and v2.

Like an example is a car crash, both can be going at the same velocity in opposite directions but when they crash (perfectly inelastically) they'd crumple up and stick together.

in other words.. what I said in my first post just won't happen..