HomeTextbookMechanics 7: Conservation of Momentum and Collisions

Mechanics 7: Conservation of Momentum and Collisions — 2 Comments

1. Momentum Question on said:

Hello Doc. This is a timely entry, thanks!

We are teaching momentum right now, and ran into something interesting. In the case of a ball hitting a stationary wall (one-dimensional, perfectly elastic collision), the conservation of momentum equation ALONE does not work. One needs to add conservation of energy, in order for things to make sense. But the kid is not there yet: we have not talked about kinetic energy formula — we proceeded directly to momentum because we had covered m and v, touched upon vectors, so we were ready to mesh them together and introduce momentum, p.

So we are here:

m1v1 (initial) + m2v2 (initial) = m1v1 (final) + m2v2 (final)

But the wall (2) is always stationary, so its v2 = 0, both in the initial and final states.
It follows that
m1v1 (initial) = m1v1 (final)
Which only works in the scalar sense, as the velocity vector has changed direction.

Yes, yes: Conservation of energy makes sense of it. But the child is not there yet, and we are looking for a way to make sense of momentum WITHOUT introducing energy into the picture. Is there a way to explain what happens in this perfectly elastic, one-dimensional, collision of a ball vs. stationary wall, so that it makes intuitive sense to the kid while demonstrating the conservation of momentum?

Thanks,
Syd

• Doc on said:

Syd — thanks for the comment. Glad you are finding my material useful.