Please explain derivation of this momentum formula?

Question

anonymous · Answer

I'm trying to understand how the 2nd formula is derived from the first one, but can't really figure it out entirely. I'm missing the big picture sense of this. Can someone please explain in steps where everything in equation 2 comes from in equation 1?

irishboy123 · Answer

this seems to assume that the colliding masses stick together, ie collision is inelastic.

the first clue is that final momentum is combined mass times a final velocity.

anonymous · Answer

This is for elastic collisions for which kinetic energy is conserved

irishboy123 · Answer

crumbs.

if that is the case, then the standard derivation for elastic collisions involves combining conservation of momentum (always true) with conservation of energy (true if elastic).

so, (1/2)m v^2 is calculated for ALL particles before the collision, and after the collision; and the 2 are equal.