Newton's Cradle: Momentum and Energy Transfer

1 · Predict

If you pull back the first ball to a release height h and let it swing into the row, what determines how fast the last ball flies out?

• The far ball leaves with about the same speed the first ball had at impact.
• The far ball leaves slower, since the middle balls absorb some of the motion.
• The far ball leaves faster than the first ball's impact speed.

2 · Set Up

1. Open the Newton's Cradle preset in the sandbox.
2. Drag the leftmost ball outward and up to set a release height, then read off how high it sits above its resting point.
3. Release the ball and let it swing down into the row of touching balls. Watch which ball(s) fly out on the far side, and how high they swing.

3 · Collect Data

Plot the far ball's exit speed (y-axis) against release height (x-axis) for your three trials. Is the relationship a straight line?

4 · Analyze

1. For each row, compute the release PE (mgh) and the impact KE the first ball should have just before it reaches the bottom of its swing (½mv², using your measured farSpeed for v). How do the two energies compare?
2. Using conservation of momentum and kinetic energy for a chain of equal masses, explain why the far ball leaves with (approximately) the first ball's impact speed, while the balls in between barely move at all.

5 · Extend

1. Why do the middle balls barely move, even though the impulse from the collision passes through every one of them?
2. In the sandbox, does the far ball ever swing exactly as high as your release height? What does the gap (if any) tell you about how elastic the collisions really are?

The Physics Behind This Experiment

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