Walkthrough
Collisions, step by step
Momentum is conserved in every isolated collision. Kinetic energy is conserved only in the elastic ones. Walk the five steps, then drag the carts.
01
Choose the system
Put both carts inside the system. Their pushes on each other are then internal and cancel. Momentum of that system is conserved if the net external force is negligible during the hit.
02
Write total momentum before the hit
p = m v, signed. Add the two carts. That sum is the number the after picture has to match, elastic or not.
03
Name the collision type
Elastic means total kinetic energy comes out equal. Inelastic means it falls. Perfectly inelastic means the carts stick and share one velocity. Momentum does not care which of those you picked.
04
Solve, then audit energy
Use momentum first. Only use a second energy equation if the collision is elastic, or if they stick. Then compare KE before and after. The missing kinetic energy became thermal energy, sound, and deformation. Total energy did not vanish.
05
Drag the lab until the bars agree
The momentum bars should add to the same total before and after. The kinetic energy bars stay level only when e = 1. If they collapse, you are looking at an inelastic hit, which is the usual case.
Momentum, kg·m/s
Kinetic energy, J
e = 1 is elastic, e = 0 is perfectly inelastic (the carts stick together). Anything between is an ordinary inelastic collision.
| Quantity | Before | After |
|---|---|---|
| Cart 1 velocity | 3.00 m/s | 1.00 m/s |
| Cart 2 velocity | 0.00 m/s | 4.00 m/s |
| Total momentum | 6.00 kg·m/s | 6.00 kg·m/s |
| Total kinetic energy | 9.00 J | 9.00 J |
| Kinetic energy lost | n/a | 0.00 J |
Drag anything and watch the two momentum bars trade size while the total bar holds still. That is conservation of momentum, and it holds at every value of e. The kinetic energy total only holds still at e = 1.
Full comparison: what is conserved in a collision. Calculator: momentum collision calculator. Physics 1 cram sheet: units and weights.