The effect of very small ball gaps in Newton’s cradle

Abstract

A Newton’s cradle with three steel balls was filmed with a slow motion video camera to examine the collision dynamics. The initial collision with two stationary balls in contact was as expected, with the incident ball bouncing backwards slowly, the middle ball moving forwards slowly and the ball at the far end emerging at a speed slightly less than the incident ball. A short time later, a different outcome was observed when one ball collided with two balls visually in contact. In that case the incident ball came to rest and remained in contact with the middle ball, as if the two balls in contact were actually separated before the collision. The second observation can be explained if the impact force has the form F = kx n where n is larger than the n = 1.5 exponent usually used to describe collisions between solid spheres. Alternatively, the result can be explained with an n = 1.5 exponent if there is a very small gap between the balls, not visible on video film. The latter explanation was confirmed by measuring electrical contact between the balls.