Newtons cradle is a toy that consists of several metal balls

Newton\'s cradle is a toy that consists of several metal balls touching each other and suspended on strings (Figure P6.82). When you pull one ball to the side and let it strike the next ball, only one ball swings out on the other side. When you use two balls to hit the others, two balls swing out. Can you account for this effect using your knowledge about elastic collisions?

Solution

When a ball is pulled and then released, the ball hits the other ball with a momentum equal to p. Since, in any collision conservation of momentum holds good, this momentum is directly transferred to adjacent metal ball. As the collision is elastic and balls have equal masses, the 1st ball comes to rest by completely transferring its energy to the adjacent ball. Now the second ball do the same as the 1st one and so on. Thus, only the last ball gains all the momentum of the 1st ball and moves.

If two balls are pulled and then released, the momentum this time is twice. So, this momentum is enough to move two balls which are at the other end.