Newton’s Cradle
This modern ‘executive’ toy owes nothing to Sir Isaac Newton, other than its ability to demonstrate one of his “laws”.
It is frequently used in Physics lessons to demonstrate conservation of momentum.
If one draws back and then releases a ball from one end of the chain, a single ball flies off from the other end. This swings back, pendulum-like, only for the process to be repeated. Thus the motion passes to and fro giving the characteristic click-click which initially is fascinating but can soon become irritating!
The standard demonstration is then to draw back two balls on one side and predict what will happen subsequently. Conservation of momentum would be satisfied by either two balls being ejected from the far end at the same speed as the incoming balls or one ball being ejected at twice the speed. In fact what happens is that two balls are released. The same thing happens if three or even four balls are used to start the motion. The same number is released from the far end. This can be interpreted, whimsically, as demonstrating that the line of spheres can count! Or see below for an explanation in terms of physics.
The Physics
If one sphere were to move off at twice the speed in response to two arriving, it would violate the law of conservation of energy. But saying that does not explain how it happens. The point is that when two spheres arrive they generate two separate impulses, which travel down the line of spheres exactly one sphere-diameter apart. Thus at the far end, each of the two end spheres receive a single impulse at the same time, so ejecting them from the line.
More Physics
Conservation of energy and momentum require that when a moving sphere strikes a stationary sphere in a perfectly elastic collision along their line of centres the moving one comes to rest and the other moves off with all the momentum. Steel spheres come close enough to being perfectly elastic to demonstrate this behaviour to a first approximation.