💥 Collision Lab

How collisions work

A collision is any brief, forceful interaction between objects, and one quantity always survives it: momentum. Momentum is mass times velocity, and in any collision — however violent — the total momentum of the objects just before equals the total just after, as long as no outside force intervenes. This is conservation of momentum, and it follows directly from Newton's third law: the two objects push on each other with equal and opposite forces, so whatever momentum one gains, the other loses.

Kinetic energy, however, is not always conserved, and that difference separates the two main kinds of collision. An elastic collision conserves both momentum and kinetic energy; an inelastic collision conserves momentum but turns some kinetic energy into heat, sound, or deformation. This simulator tracks total momentum on a live graph, so you can watch it stay flat through every impact.

Experiments to try in this simulation

1. Momentum is always conserved: run any preset and watch the yellow total-momentum line. Through every collision it stays flat, even as the blue and red individual momenta trade back and forth.

2. Elastic versus inelastic: switch collision type and compare. Elastic collisions send the balls apart with the same total kinetic energy; a perfectly inelastic one leaves them stuck together with far less kinetic energy — though momentum still holds.

3. Newton's cradle: load the cradle preset. One ball in, one ball out — a striking demonstration that both momentum and energy are conserved in an elastic chain.

4. Restitution: in elastic mode, lower the coefficient of restitution from 1 toward 0 and watch the bounces grow less lively as more energy is lost each hit.

Key equations

Conservation of momentum for two bodies is m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, where u are the velocities before and v after. For a perfectly elastic collision, kinetic energy is also conserved: ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂². The coefficient of restitution e measures how elastic a collision is — the ratio of relative speed after to relative speed before — running from e = 1 (perfectly elastic) to e = 0 (perfectly inelastic, objects stick).

Those two conservation laws are enough to predict the exact outcome of any one-dimensional collision, which is why the simulator can show the post-impact velocities with no fudge factors.

Real-world applications

Collision physics is the science behind car-crash safety: crumple zones are engineered to make a crash more inelastic on purpose, absorbing kinetic energy over a longer time so less force reaches the passengers. The same conservation laws govern billiards and pool, rocket propulsion (a rocket and its exhaust conserve momentum together), the particle-physics experiments that smash particles to probe their structure, and the gravitational slingshot manoeuvres that fling spacecraft across the solar system.