Elastic & Inelastic Collision Calculator

Collision Physics Guide

What do I need to know about Conservation of Momentum?

In all collisions: total momentum is conserved. p_before = p_after. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Momentum is a vector — directions matter. In 1D problems: use positive for one direction, negative for the opposite. Example: 2kg moving at 5 m/s and 3kg moving at −2 m/s. Total momentum = 2×5 + 3×(−2) = 10 − 6 = +4 kg·m/s. After collision, the total must still equal +4. Conservation of momentum follows from Newton's 3rd law — the forces between colliding objects are equal and opposite, so their change

What should I know about Elastic Collisions?

Elastic: kinetic energy is also conserved (collisions of hard balls, gas molecules, billiards approximate). Two equations to solve: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (momentum). ½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂² (KE). Simplification — relative velocity reverses: u₁ − u₂ = −(v₁ − v₂). Special cases: equal masses, one stationary: m₁ stops, m₂ moves with u₁. Mass m₁ hits much heavier m₂: m₁ bounces back at nearly u₁; m₂ barely moves (like a ball off a wall). Tiny mass hits stationary heavy mass: the tiny mass rebounds at close to its original speed while the heavy mass barely moves at all, just like a ball bouncing off a wall.

What's the key thing to understand about Inelastic Collisions?

Inelastic: kinetic energy is NOT conserved — some converts to heat, sound, deformation. Momentum is still conserved. Perfectly inelastic: objects stick together. Common in: car crashes (real cars do not bounce off each other elastically). Lump of clay hitting another lump. Bullet embedding in a wooden block. Formula for perfectly inelastic: v = (m₁u₁ + m₂u₂) / (m₁ + m₂). Both objects end with the same final velocity. Example: 2kg at 10 m/s hits stationary 3kg. v = (2×10 + 0)/(2+3) = 4 m/s. Kinetic energy before the collision is greater than kinetic energy after, since the difference is converted into heat, sound, and deformation of the objects.

What do I need to know about Coefficient of Restitution?

Coefficient of restitution (e) measures how much energy is preserved: e = (v₂ − v₁) / (u₁ − u₂). For elastic: e = 1. For perfectly inelastic: e = 0. For real collisions: 0 < e < 1. Examples: superball: e ≈ 0.9. Basketball off wood floor: e ≈ 0.75. Steel ball off steel anvil: e ≈ 0.6. Tennis ball on tennis racket: e ≈ 0.45-0.55. Cricket ball off bat: e ≈ 0.5. Higher e: more bounce, less energy lost. Sports engineering: balls and bats have regulated e values. ICC regulations require a cricket ball to have a coefficient of restitution within a specific tested range, ensuring consistent bounce behaviour across matches.