Question

Mass m = 0.1 kg moves to the right with speed v = 0.54 m/s and collides with an equal mass initially at rest. After this inelastic collision the system retains a fraction = 0.9 of its original kinetic energy. If the masses remain in contact for 0.01 secs while colliding, what is the average force in N between the masses during the collision? Hints: All motion is in 1D. Ignore friction between the masses and the horizontal surface. You will probably need to use the quadratic formula to solve the resulting equations. VR must be greater than VL since the masses can't pass through each other!

Answer 1

Let and be the speed of the left and the right ball after the collision. Before the collision the velocity of the left ball was and the right ball was at rest.

Momentum of the two masses before the collision

Momentum of the two masses after the collision

By conservation of momentum

Kinetic energy of the system before the collision

Kinetic energy of the system after the collision

Given that

This is quadratic equation in , in general the roots of a quadratic equation are

We get

Substituting value

We get and

Now, we will calculate the force experienced by the mass on the right:

Momentum of mass on the right before the collision as it was initially at rest.

Momentum of the mass on the right after the collision is

The change in momentum of the mass on the right is

The change takes place in time

The average force acted on the mass on the right is

Similarly you can check that the average force on the left ball is . and are action/reaction pairs.