Question

A novelty collision device known as the executive toy consists of five identical metal balls. When one ball swings in, after multiple collisions, one ball swings out at the other end of the row of balls. When two balls swing in, two swing out; when three swing in, three swing out, and so on-always the same number out as in. Suppose that one ball, with mass m, swing in and collide with the next ball with a velocity v. Why don’t two ball swing out at the other end with a velocity of v/2? Clearly establish the reasoning and physical principles to receive full credit.

Answer 1

The stated phenomena happen to ensure the conservation of momentum as well as the conservation of energy.

Now let us calculate energy and momentum in the case given in the question

The momentum just before the collision is

The energy just before the collision is

Now let us take the case of two balls coming out with half the velocity

The momentum now is

Hence conservation of momentum is followed but

The energy now is

Hence conservation of energy is not followed.

But in case of one ball coming out with the same velocity both the laws are followed.