Elastic Collision Calculator

In short In an elastic collision both momentum and kinetic energy are conserved, and those two conditions are enough to fix the outcome completely. The most striking case is equal masses: they simply EXCHANGE velocities. Two 2 kg objects at +7 and −3 m/s leave at −3 and +7 — which is exactly why the first ball in a Newton's cradle stops dead while the last one swings away, and why a cue ball stops on a full-face hit. This page re-sums the momentum and the kinetic energy from its own answers rather than assuming them, so you can watch both conservation laws hold. It also gives the opposite extreme, a perfectly inelastic collision where the two stick together and leave at a single speed. Momentum is still exactly conserved there — it always is — but kinetic energy is not: the difference goes into heat, sound and deformation. Two objects of equal mass meeting head-on at equal speed end up motionless, having lost all of their kinetic energy while their total momentum was zero the whole time. Every real collision sits somewhere between those two extremes. One property worth memorising: in any elastic collision the relative speed is exactly reversed — the speed of approach equals the speed of separation. That is often the fastest way to solve one by hand, and it is printed here so you can check it.