Perfectly Inelastic Collision
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
When two bodies lock together on impact they share one final velocity, and momentum conservation hands it to you directly: the combined momentum divided by the combined mass. A 1000 kg car at 20 m/s rear-ending a stationary 1500 kg van and tangling with it leaves the wreck moving at 20000 ⁄ 2500 = 8 m/s. Kinetic energy, by contrast, is not conserved — here 200 kJ goes in and only 80 kJ comes out, the missing 120 kJ spent deforming metal, which is exactly what crumple zones are designed to do.
The classic application is the ballistic pendulum, devised by Benjamin Robins in 1742: fire a bullet into a hanging block, measure how high the block swings, and work backwards through this equation to get the muzzle velocity — the first accurate method of measuring how fast a bullet flies. Perfectly inelastic collisions dissipate the maximum energy any collision can while still conserving momentum, which is why "sticking together" is the worst case for occupant survival and the best case for a crash-test energy budget.
- = Common final velocity
- = Mass 1
- = Initial velocity 1
- = Mass 2
- = Initial velocity 2
- Common final velocity — Final Velocity (Uniform Acceleration), Velocity-Displacement Relation (v² = v₀² + 2ad)
- Mass 1 — Newton's Second Law, Kinetic Energy
- Initial velocity 1 — Final Velocity (Uniform Acceleration), Displacement (Uniform Acceleration)
- Mass 2 — Newton's Second Law, Kinetic Energy
- Initial velocity 2 — Final Velocity (Uniform Acceleration), Displacement (Uniform Acceleration)