Practice
Momentum, impulse and collisions
Momentum, impulse and average force, then explosions and one-dimensional collisions that stick or bounce.
The skill
Momentum, , carries a sign, so pick a positive direction and keep it. Choose the system so that the forces during the collision or explosion are internal; then the total momentum just before equals the total just after. If an outside force acts for a time, its impulse equals the change in momentum. Kinetic energy is a separate question: it is conserved only in an elastic collision, and objects that stick together always lose some. The mistake to watch for is dropping the minus sign on an object moving the other way.
A worked example
A 3.9 kg cart moving at 2.2 m/s on a level, frictionless track collides with a 2.3 kg cart at rest, and the carts stick together.
How much kinetic energy does the system lose in the collision, in joules? Give your answer to three significant figures.
Solution
- Momentum is conserved: v = (3.9)(2.2) ÷ 6.2 ≈ 1.3839 m/s after the collision, or 1.38 m/s to three figures. Keep the extra places for the next step.
- Kinetic energy before: 1/2 (3.9)(2.2)² = 9.438 J. After: 1/2 (6.2)(1.3839)² ≈ 5.937 J.
- Lost: 3.50 J, transformed by nonconservative forces into other forms such as thermal energy and sound.
Answer: 3.5