Momentum and collision calculator.

Momentum and collision formulas

Momentum is mass times velocity, p = mv, and in a collision between two objects with no outside force the total momentum stays the same. HyperPhysics defines momentum as a vector in kg·m/s. Kinetic energy is conserved only in a perfectly elastic collision; in an inelastic collision some becomes other forms of energy, and in the extreme case the objects stick together (OpenStax).

The calculator uses the coefficient of restitution e, the ratio of separation speed to approach speed (1 for elastic, 0 for objects that coalesce): v₁′ = (m₁v₁ + m₂v₂ + m₂e(v₂ − v₁)) ÷ (m₁ + m₂) and v₂′ = (m₁v₁ + m₂v₂ + m₁e(v₁ − v₂)) ÷ (m₁ + m₂).

Worked example. A 2 kg cart at 3 m/s hits a 1 kg cart at rest. Total momentum is 6 kg·m/s. Elastic: final speeds 1 m/s and 4 m/s, kinetic energy stays 9 J. Sticking together: both move at 2 m/s and 3 J of the 9 J is lost.

This is a one-dimensional point-mass model. Real collisions also involve rotation, friction and deformation, so use it for coursework rather than crash analysis or safety work.