Elastic and Inelastic Collisions

In every collision, total momentum is conserved — this follows from conservation of momentum in one dimension. What separates the two types of collision is kinetic energy: whether the total kinetic energy after the collision equals the total before.

In an elastic collision, both momentum and kinetic energy are conserved. The objects bounce apart with no energy lost to heat, sound, or deformation. Colliding steel balls and interactions between atoms are close to perfectly elastic. With two conservation equations, you can solve for both final velocities.

In an inelastic collision, momentum is still conserved but kinetic energy is not — some is converted to heat, sound, and deformation. In a perfectly inelastic collision the objects stick together and move as one, which loses the most kinetic energy possible while still conserving momentum. Linking momentum to force over time is covered in momentum and impulse, and the two-dimensional case in conservation of momentum in two dimensions.

A 2 kg cart at 3 m/s strikes a stationary 1 kg cart and they stick together (perfectly inelastic). Momentum before is 2 × 3 = 6 kg·m/s, so the combined 3 kg moves at 6 ÷ 3 = 2 m/s. Kinetic energy drops from 9 J to 6 J — the missing 3 J became heat and sound.

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