Elastic Collision Calculator (1D)
Compute the final velocities of two objects after a one-dimensional elastic collision, where both momentum and kinetic energy are conserved.
How it works
v1′ = ((m1−m2)·u1 + 2·m2·u2) ÷ (m1+m2) · v2′ = ((m2−m1)·u2 + 2·m1·u1) ÷ (m1+m2)
A perfectly elastic collision conserves both momentum and kinetic energy. In one dimension these two conservation laws give a unique pair of final velocities. Two useful special cases: equal masses simply swap velocities, and a light object bouncing off a very heavy stationary one rebounds with nearly its original speed reversed. Use a signed axis — a velocity to the left is negative.
Worked example
A 2 kg object at +5 m/s meets a 3 kg object at −2 m/s. v1′ = ((2−3)·5 + 2·3·(−2)) ÷ 5 = (−5 − 12) ÷ 5 = −3.4 m/s; v2′ = ((3−2)·(−2) + 2·2·5) ÷ 5 = (−2 + 20) ÷ 5 = 3.6 m/s. Kinetic energy is 31 J before and after.
Sources: Elastic collision — Wikipedia
Frequently asked questions
What makes a collision elastic?
In an elastic collision the total kinetic energy after equals the total before — no energy is lost to heat, sound or deformation. Collisions of hard steel balls or gas molecules are close to elastic; a car crash is highly inelastic.
What happens when the two masses are equal?
For equal masses in one dimension the objects exchange velocities. If one is initially at rest, the moving object stops dead and the struck object leaves with the incoming speed — the classic Newton’s cradle result.
How is this different from an inelastic collision?
An inelastic collision conserves momentum but not kinetic energy; a perfectly inelastic one has the objects stick together and move as one. This calculator assumes the elastic case, so kinetic energy is conserved.
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This calculator is for educational purposes. Double-check important results before acting on them.