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Momentum and collision calculator

Find momentum from mass and velocity, and the outcome of an elastic or perfectly inelastic collision between two bodies.

Total momentum
4 kg·m/s
Elastic: body 1 after-3.4 m/s
Elastic: body 2 after3.6 m/s
Inelastic: combined speed0.8 m/s
Kinetic energy before31 J
Energy lost if they stick29.4 J

Use negative velocities for motion in the opposite direction.

Momentum is mass times velocity, and it is conserved in every collision. Whatever the total was before, it is the same afterwards, provided no outside force acts. This holds whether the bodies bounce apart, stick together, or shatter.

p = m v   m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Elastic versus inelastic

In a perfectly elastic collision, kinetic energy is conserved as well as momentum. Billiard balls and gas molecules come close. In a perfectly inelastic collision the bodies stick together and move as one; momentum is still conserved but energy is not — the difference goes into deformation, heat and sound. Real collisions sit between the two extremes.

Direction is not optional

Momentum is a vector. Two objects of equal mass approaching each other at the same speed have zero total momentum, and if they stick together they stop dead. Getting the signs right is most of the work in these problems: pick a positive direction and stay with it.

A useful special case

In an elastic collision between equal masses where one is at rest, the moving one stops and the stationary one leaves at the original speed. This is the Newton’s cradle result, and it is the only arrangement that satisfies both conservation laws at once.

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