A ball with a mass of # 3 kg# is rolling at #4 ms^-1# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?
In an elastic collision, both momentum and kinetic energy are conserved. The velocity of the
Momentum is conserved in all collisions. Kinetic energy is conserved in elastic collisions but not in inelastic or partially elastic collisions.
The initial momentum of the whole system is
The total momentum after the collision will be the same after the collision. If we call the
The total kinetic energy before the collision will be
Since kinetic energy is conserved, the final kinetic energy will be the same, and will be given by:
Multiply both sides by 2 to make it tidier:
We now have two equations and two unknowns, so we can solve them as simultaneous equations. Rearranging Equation 1 to express
Substituting this into Equation 2:
I'll leave the algebra as an exercise for the reader, but this solves to give
Substituting these values should confirm that both momentum and kinetic energy were conserved.