A ball of clay with a mass of 55 g and a speed of 1.5 m/s collides with a 55 g ball of clay that is at rest. By what percent has the kinetic energy decreased after the inelastic collision?

The kinetic energy decreased 50 % after the inelastic collision.

Explanation:

Since both ball collide and experiments an inelastic collision, the final velocity of the system is found by means of the Principle of Linear Momentum:

(1)

Where:

, - Masses of the balls of clay, measured in kilograms.

, - Speeds of the balls of clay before collision, measured in meters per second.

- Speed of the system after collision, measured in meters per second.

If we know that , and , then the speed of the system after collision is:

The initial () and final kinetic energies of the system (), measured in joules, are now described by the following equations:

(2)

(3)

And the percentage of lost energy due to inelastic collision is:

(4)

If we know that , , and , then the percentage of lost energy due to inelastic collision is:

The kinetic energy decreased 50 % after the inelastic collision.

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