Momentum & Collision Lab

In any closed system, momentum is always conserved because of Newton's third law: the force Cart 1 exerts on Cart 2 is equal and opposite to the force Cart 2 exerts on Cart 1. Kinetic energy, however, is only conserved in perfectly elastic collisions (e = 1). In real-world macroscopic collisions, energy is always dissipated into thermal energy, sound, and material deformation (e < 1). On the subatomic scale, collisions between gas molecules are perfectly elastic, which is why gases don't eventually settle to the floor as cold puddles of static matter.

The coefficient of restitution e is this tool's master dial. It is simply the separation speed divided by the approach speed: e = 1 is a perfect rebound (a superball), while e = 0 means the carts stick together like wet clay. You can measure it at home — drop a ball and divide bounce height by drop height, which equals e². A basketball that returns to about 64% of its drop height has e ≈ 0.8.

A spacecraft gravity assist obeys these exact rules with nothing ever touching. In the planet's reference frame the flyby is perfectly elastic (e = 1): the probe leaves at the same speed it arrived, merely redirected. But in the Sun's frame it can pick up almost twice the planet's orbital speed. Voyager 2 gained roughly 10 km/s at Jupiter this way — borrowed from the planet's orbital motion, which slowed by an utterly negligible amount in return.