Answer to Question #151383 in Classical Mechanics for Isurini Sirisena

Question

A student is using a ‘Newton’s Cradle’. This consists of a set of identical solid metal balls hanging by threads from a frame so that they are in contact with each other.

He initially pulls one ball to the side. He releases the ball, it collides with the nearest stationary ball and stops. The ball furthest to the right immediately moves away. The middle three balls remain stationary.

(a) Explain what measurements the student would take and describe how he would use them to investigate whether momentum had been conserved in this event. [4]

(b) The student makes the following observations:

• the ball on the right returns and collides with a similar

result; this repeats itself a number of times

• after a while, the middle balls are also moving

• shortly afterwards, the balls all come to rest.

Discuss these observations in terms of energy

Answer 1

(a) The student should measure mass of the balls, length of the treads, and height between the point where the student released the ball and the line passing thru centers of the resting balls.

Using energy conservation, he would calculate the speed of the left ball and then measuring the height of rise of the right ball he would calculate the speed of the right ball. Next, he would check whether mass times speed is the same or not.

(b) Potential energy of the left ball turns into kinetic energy. This kinetic energy passes from one ball to another until it reaches the right one. It can be transferred thru balls because there are very small gaps between them and the middle balls have certain degree of freedom.

After s while, the balls in the middle start swinging too because they are not perfectly round and/or not perfectly centered, so the collision is not absolutely central.