Dave Britten, of Prebbleton, asks :-

How does Newton's cradle work?

Archie Ross, a physicist at the University of Canterbury, responded.

Newton's cradle has five identical steel balls each suspended by two threads and all in contact in a horizontal straight line.

When ball 1 is drawn back and released, gravity and the tension in the threads cause it to return to its original place where it arrives with considerable velocity. On hitting ball 2 it is brought to rest and ball 5 is propelled forward, rising to the same height as ball 1 had initially . Ideally balls 2, 3 and 4 remain at rest. The process then repeats itself in the opposite direction. If two balls are initially displaced then two balls will move off at the other end. Three will give three and four will give four.

The explanation of this behaviour involves two important principles.

Firstly momentum, the product of mass and velocity, is unchanged by the collision. The speed of ball 1 just before it hits ball 2 is the same as that of ball 5 immediately after the collision. The momentum of ball 1 is transferred to ball 5. You might ask "Why don't balls 4 and 5 (twice the mass) move off with half the speed which also would give the same momentum?". The answer involves the second principle thich is that the kinetic energy immediately before and after the collision is unchanged. Since this involves the square of the speed, two balls moving with half the speed have only 2 x 1/2 x 1/2 = 1/2 of the original energy of ball 1. The only way to have both momentum and kinetic energy unchanged is for the same number of balls to fly off one end as were originally displaced at the other.

In practice some energy is transformed into sound and heat and eventually all five balls will swing together. If the balls were made of lead or putty, which are permanently deformed by the collisions, the cradle would behave quite differently.