Newton's cradle

A Newton's Cradle (also ball pendulum, Newton pendulum or Newton's cradle ) is a set of (typically five) identical balls ( usually of metal) which are suspended from two in all spheres of equal length threads in a row and at the same height. The balls thus form single pendulum with the same mass and length of the pendulum, whose freedom of movement is restricted by the trapezoidal suspension in the same vertical plane. The distance between the suspension points in the frame corresponds exactly to the diameter of the balls so that they hang vertically at rest and just touching.

If now one side of the outer balls with stretched filaments raises and lets fall back against the line of other balls, one ball is exactly repelled at the opposite end; originally moving ball " remains ," all the other balls remain at rest. When the ball repelled then oscillates back and in turn impacts, it abuts the outermost sphere on the other side - the system maintains " swinging ".

Particularly noteworthy is the behavior of more than a moving ball: If you can commute two or more balls, getting as many balls are on the other side repelled with just the speed as on the opposite side at this speed are bounced, and not only one ball at a higher rate, as one might expect intuitively.

A Newton's Cradle is therefore a device for demonstration of the momentum and energy conservation law.

The device goes back to the French physicist Edme Mariotte ( 1676 ). It was popular in the 1960s as a small, decorative toy.

Operation

The in the picture leftmost, resting ball takes the pulse of the bouncing ball and passes it off to the right adjacent ball, and then the next to the right and so on. The ball rightmost can however pass on no pulse and is repelled.

It is elastic collisions remain with preservation of the kinetic energy and momentum. Since no external forces act in the direction of movement during the collision, has the momentum of the balls of the mass, which meet at the speed of the left on the dormant balls, be equal to the momentum of the triggered balls of mass. Assuming further that the initiated balls move collectively with the speed to the right, stating the conservation of momentum

Furthermore, the energy has to match before and after the collision, in which one neglects the energy that goes into vibrations of the balls,

If we write this as

And considering the first equation, then, as it is not zero, the velocities equal, then the first equation says it fly as many balls away as strike.

Here it was assumed that the initiated balls all move away at the same speed and rest the rest. That they do, but you can not infer from the energy and momentum conservation for more than two balls.

Because when push in the center- balls from the left with speed balls with speed, with the proviso that is compatible with energy and momentum conservation, that after the collision balls continue to run at speed to the right and balls with speed to the left. But balls with inverted speed and balls with speed are possible.

To explain the behavior of the ball chain one must consider in more detail how a shock wave passes through the chain.