Question: Observe the behavior of Newton's Cradle. Momentum conservation is satisfied when one ball is pulled back and released, resulting in a collision such that one ball on the other end moves away at the same speed. Suppose each ball has mass, m, and the velocity of each released ball just before the collision is v. By determining the total momentum and kinetic energy before and after the collision, show that momentum and kinetic energy are conserved in this case (consider the instances in time just before and just after the collision, and neglect and collisions occurring between the stationary balls.) Momentum would also be conserved if 2 balls moved away at half the initial pre-collision speed. Show that this would be true by determining the total momentum before and after the collision. Would the kinetic energy be conserved in this second scenario? Determine the initial and final kinetic energy to find out.

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Asked Mar 28, 2019
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Question: Observe the behavior of Newton's Cradle. Momentum conservation is satisfied when one ball is pulled back and released, resulting in a collision such that one ball on the other end moves away at the same speed. Suppose each ball has mass, m, and the velocity of each released ball just before the collision is v. By determining the total momentum and kinetic energy before and after the collision, show that momentum and kinetic energy are conserved in this case (consider the instances in time just before and just after the collision, and neglect and collisions occurring between the stationary balls.) Momentum would also be conserved if 2 balls moved away at half the initial pre-collision speed. Show that this would be true by determining the total momentum before and after the collision. Would the kinetic energy be conserved in this second scenario? Determine the initial and final kinetic energy to find out.

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Expert Answer

Step 1

Newton’s cradle demonstrates the principle of conservation of momentum. When the first ball of the Newton’s cradle collides with the second the first ball stops but its momentum isn’t lost. It is transferred to the second ball, then to the third then fourth until it reaches the very last ball.

Step 2

The conservation of momentum is satisfied because the number of balls moving before the collision is equal to the number of ball after collision.

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Step 3

Since each ball has equal mass, the mass of the moving balls remains constant from collision to collision. The moving balls after the collision will never surpass the starting height of the balls on the pre collision side so t...

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