A ball with a mass of #2 kg# is rolling at #2 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?
The 2-kg ball recoils backwards at
This is a lengthy problem to work out!!
The two missing final velocities mean we have two unknowns to determine. This will require two independent equations that include these velocities.
Prior to collision, the total momentum is p = mv = 4 kg m/s
and the total KE is
For convenience, I will use u for the final velocity of the 2-kg ball, and v for that of the 4-kg ball.
Cons. of momentum tells us:
initial momentum = final momentum
which I will write as
Cons of KE tells us:
initial KE = final KE
which we write as
We now must solve these two equations in two unknowns
Rewrite the momentum equation as
4 = (4 -
4 = 4 -
So, u =