Verify relative-velocity reversal and a fixed center of mass
Three steps, the way the exam actually works: work through the lab, write down your own measurements, then answer a 10-point free response. What you recorded goes to the grader with your writing, so a conclusion that does not follow from your own numbers will cost you the point — exactly as it would with a real reader.
Predict before you look
- Momentum is conserved in every collision; kinetic energy is conserved only in an elastic one. Write down which of the two you expect to be able to check by watching a single readout.
- The center-of-mass velocity is total momentum divided by total mass. Predict, before running anything, what a collision does to it.
Nothing to submit here — these are to think through, so the prediction below is an informed one rather than a guess.
Commit to an answer now. It is not graded and being wrong costs nothing — the point is to have something specific to reconcile against once you have the data.
Answer every prediction to unlock the lab. A sentence is enough.
Run the investigation
Predictions first
The procedure and the simulation unlock once you have committed above. Observing before predicting is how a wrong intuition survives a lab intact.
Record what you measured
These are your numbers, not ours. The grader sees them, so your conclusions have to follow from what you actually recorded.
| Total momentum before the collision | kg·m/s |
|---|---|
| Kinetic energy before | J |
| Final velocity of cart 1, elastic | m/s |
| Final velocity of cart 2, elastic | m/s |
| Kinetic energy after, elastic | J |
| Approach speed u₁ − u₂ | m/s |
| Separation speed v₂′ − v₁′ | m/s |
| Common final velocity, perfectly inelastic | m/s |
| Kinetic energy after, perfectly inelastic | J |
Answer the free response
Using your recorded data: (a) State the total momentum before and after each collision and explain why it is the same in both modes even though the kinetic energies differ enormously. (b) Compare your approach and separation speeds for the elastic collision, state the general rule this demonstrates, and explain how it relates to the coefficient of restitution. (c) Compute the center-of-mass velocity from your data and show that the perfectly inelastic final velocity equals it. Explain why that had to be so. (d) State how much kinetic energy was lost in each mode and explain why the perfectly inelastic collision does not lose all of it.
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