Inelastic Collision Calculator

In a perfectly inelastic collision, two objects collide and stick together. Momentum is conserved but kinetic energy is not — some energy converts to heat, sound, and deformation.

Conservation of momentum:

m₁v₁ + m₂v₂ = (m₁ + m₂) × vf

Solving for final velocity:

vf = (m₁v₁ + m₂v₂) / (m₁ + m₂)

The kinetic energy before and after:

KE_before = (1/2)m₁v₁² + (1/2)m₂v₂² KE_after = (1/2)(m₁ + m₂)vf² Energy lost = KE_before − KE_after

Sign convention matters: velocities moving right are positive, velocities moving left are negative. If object 2 is stationary (v₂ = 0), it simplifies to vf = m₁v₁ / (m₁ + m₂) — the final speed is always less than the initial speed, and the more massive the combined object, the slower it moves.

The fraction of energy lost equals 1 − m₁/(m₁ + m₂) when v₂ = 0. A car crash where the two cars interlock is the classic example. A 1,500 kg car at 20 m/s hitting a stationary 1,000 kg car: vf = (1,500 × 20) / 2,500 = 12 m/s. KE lost = 0.5 × 1,500 × 400 − 0.5 × 2,500 × 144 = 300,000 − 180,000 = 120,000 J. That 120 kJ went into crushing metal.

This is why airbags and crumple zones work: they extend the collision time, but they also ensure a larger fraction of energy dissipates in controlled deformation rather than in the occupants.