Newton's Cradle.A Newton's cradle is composed of row metal balls, each hung from a string attached to a horizontal rod, so that when they are rest, they are nearly touching each other (and form a neat line). Explain and prove (mathematically!) why, releasing balls causes the same number of balls on the other side of the cradle to be ejected?

Question

03-08-2019
Physics

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Newton's Cradle.A Newton's cradle is composed of row metal balls, each hung from a string attached to a horizontal rod, so that when they are rest, they are nearly touching each other (and form a neat line). Explain and prove (mathematically!) why, releasing balls causes the same number of balls on the other side of the cradle to be ejected?

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Answer:

In Newton's Cradle there are N number of balls are suspended from the thread such that they all touch each other.

Now when we pull one ball apart and released then after the collision one ball on the other side moves up

Then in next time if we pull two balls from one side then after collision it will pull upwards exactly two balls on the other side after collision.

So here the number of balls on the other side is exactly same every time we pull the balls.

This is due to the conservation of momentum principle

As we know that all the balls are identical here then when we pull any number of balls on one side and then release them then after collision the momentum of the balls is transferred to same amount of the balls on the other side

Since there is no external force on this system so we can say that that this momentum conservation will exist for all cases and all number.