In a crash test, two cars crumple together. Metal bends, the bang is loud, and the wreck slides on slowly. Kinetic energy was clearly transformed. Did the crash destroy the system's momentum too?
No. The two quantities follow different rules in a collision, and this lesson separates them. Recall the law: the total momentum of a system stays constant when the net external force on the system is zero.
Here is a test on a track with almost no friction, taking rightward as positive. A 2 kg cart moving right at 3 m/s hits a parked 4 kg cart. The system's total momentum before is 2 × 3 = 6 kg·m/s.
Run one uses springy steel bumpers. The carts bounce apart: the 2 kg cart rebounds left at 1 m/s and the 4 kg cart rolls right at 2 m/s. The total momentum after is 4 × 2 + 2 × (−1) = 8 − 2 = 6 kg·m/s. Measurements show the total kinetic energy is also unchanged: the collision is elastic.
Run two uses couplers. The carts stick and move off together at 1 m/s. The total momentum after is 6 × 1 = 6 kg·m/s again. But the clack and the jolt transformed some kinetic energy into heat and sound: the collision is inelastic.
Both runs keep the same total momentum, and the reason does not care whether the carts bounce or stick: momentum is conserved because Newton's third law makes the forces the two objects exert on each other equal in size and opposite in direction, and they act for the same time, so the impulses are equal and opposite and the momentum changes cancel.
Margit says: 'The crumpling crash destroyed some of the system's momentum along with the kinetic energy.' Is she correct?
Kinetic energy is the quantity that tells the runs apart. In the elastic run, the total kinetic energy is unchanged. In the inelastic run, some of it became heat, sound, and deformation.
This topic tracks kinetic energy only as kept or transformed. Putting numbers on kinetic energy comes in a later topic.
Two football players collide and fall together in a heap. The hit is loud and both slow sharply. Which total is still conserved, and which is not?
The players stick together, and the sound and the jolt show kinetic energy being transformed, so the collision is inelastic.
Total momentum is conserved in both elastic and inelastic collisions.
Total kinetic energy is conserved only in elastic collisions, and this collision is not elastic.
The system's total momentum is conserved; the system's total kinetic energy is not.
Two steel ball bearings collide and bounce apart, and measurements show the total kinetic energy is unchanged. Which totals are conserved?
Unchanged total kinetic energy with the objects bouncing apart makes the collision elastic.
Total momentum is conserved in every collision, and total kinetic energy is conserved in elastic ones.
Both totals are conserved: the total momentum and the total kinetic energy.
In which collisions is a system's total momentum conserved, when the net external force is zero?
Piet says: 'Two carts collide and bounce apart with a bang, and one bumper bends. The system's total momentum just after the hit equals the total just before.' Is he correct?
Which pairing is correct?
Two hockey players collide and bounce apart. The thud is loud and one helmet dents. Which statement is correct?
Two pickup trucks crumple together in a parking-lot crash. Which quantity can you still set equal before and after the crash?