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Newton’s cradle is a common desk toy consisting of a number of identical pendulums with steel balls as bobs. These pendulums are arranged in a row in such a way that, when at rest, each ball is tangent to the next and the cords are all vertical. Assume that the COR for the impact of a ball with the next is e = 1. Explain why if you release the ball to the far left from a certain angle, the ball in question comes to a stop after impact while all the other balls do not seem to move except for the ball to the far right, which swings upward and achieves a maximum swing angle equal to the initial release angle of the ball to the far left.

Step-by-step

Treat each impact as only involving two balls. Because the COR e = 1 and the masses are identical we see from the solution to Problem 5.47 that ball 1 will come to a complete stop after impacting with ball 2. We also see that ball 2 will have a post impact velocity identical to the pre impact velocity of ball 1. Each ball in the train is tangent to the next so it will not appear to move at all during its impact with the next ball. Ball 4 impacts ball 5 which is free to move. Ball 5 will have a post impact velocity equal to the pre impact velocity of ball 1. The work-energy principle tells us that ball 5 will stop moving when it has reached the initial height ball 1 was released from. Finally, since the lengths of the pendulums are identical the maximum swing angle of ball 5 is equal to the initial release angle of ball 1.

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