Collision lab

Why the total bar never moves

The carts push on each other, and by Newton's third law those two pushes are equal in size and opposite in direction at every instant. They act for exactly the same length of time, so the impulses they deliver are also equal and opposite. Whatever momentum one cart gains, the other loses. Add the two together and the change cancels exactly.

That argument never mentions how bouncy the collision is, which is why the elasticity slider cannot touch the momentum total. It does need the net external force on the pair to be zero, which is what the frictionless track buys you. Slide the elasticity anywhere from 0 to 1 and watch: the two momentum bars redistribute, the total holds.

Why kinetic energy is different

Kinetic energy is not a separately conserved quantity. It is one category of energy, and a collision is free to move energy out of it into deformation, heating and sound. Total energy is still conserved; the kinetic share is not.

• e = 1, elastic. Nothing leaves the kinetic category. Both totals hold still. Try equal masses with one cart at rest: they swap velocities exactly, which is what a Newton's cradle demonstrates.
• 0 < e < 1, inelastic. The carts separate, but at a reduced relative speed, and some kinetic energy is gone.
• e = 0, perfectly inelastic. The carts move off together. This loses the most kinetic energy the collision can, but almost never all of it: the combined object usually keeps moving, and anything moving has kinetic energy.

What to try

1. Make a perfectly inelastic collision lose everything. Set e = 0, then hunt for the one case where the kinetic energy after is zero. It happens exactly when the total momentum is zero, because the stuck-together mass has nowhere to go. Equal masses at equal and opposite speeds is the easy version.
2. Bounce a light cart off a heavy one. Set e = 1, cart 1 to 0.2 kg, cart 2 to 5 kg at rest. The light cart rebounds at nearly its original speed while the heavy one barely moves, the way a ball bounces off a wall.
3. Watch an elastic collision redistribute energy. At e = 1 the energy total is fixed, but the individual bars are not. Elastic means the total is preserved, not that each cart keeps what it brought.

For the full problem-solving routine, read conservation of momentum and the impulse-momentum theorem. The AP course content behind this sits in Topic 4.3 and Topic 4.4. To get numbers for a specific setup, use the momentum collision calculator.