# How does ball A come to rest and Ball B remain stationary?

• Richie Smash
Momentum and kinetic energy are conserved in an elastic collision, but momentum may not be conserved if friction makes it stop.f

## Homework Statement

In a collision between three identical steel balls A B C

A comes to rest and B remains stationary, while C rolls off.

In terms of the Forces acting, explain how Ball A came to rest and why Ball B remained stationary.

## The Attempt at a Solution

Well what I know here is that Ball A experiences the downward pull of gravity and also friction upon collision? Maybe that is why it stops.

I know that momentum is conseved and transfers through ball B but I can't think of the ''Forces acting here''

I do have the general idea of what's going on and that this collision is a good representation of an elastic collision where momentum and kinetic energy are conserved.

How can I represent this answer in a concise way without getting too complicated? Just the fundamental reasons

Give ball A some velocity and mass.
Ball B and ball C have the same mass but zero velocity.
Assume an elastic collision.
Conserving kinetic energy gives something like:
##\left(v^2_A m_A + v^2_Bm_B+v^2_Cm_C\right)_{pre}=\left(v^2_A m_A + v^2_Bm_B+v^2_Cm_C\right)_{post} ##
Since all the balls are the same weight, you can factor them out of the equation.
##\left(v^2_A + v^2_B+v^2_C\right)_{pre}=\left(v^2_A + v^2_B+v^2_C\right)_{post} ##
Also, you can use conservation of momentum to get:
##\left(v_A + v_B+v_C\right)_{pre}=\left(v_A + v_B+v_C\right)_{post} ##
It's not very clean to solve all three together, so imagine a tiny gap between balls B and C...work out the relation from A to B (ignoring ball C), then the new B to C.
https://en.wikipedia.org/wiki/Elastic_collision

Richie Smash
also friction upon collision? Maybe that is why it stops.
kinetic energy are conserved.
You can't have it both ways. If friction makes it stop then KE will not be conserved.