How to use it
- Choose the type of collision, and for partly elastic enter e between 0 and 1.
- Enter both masses and pick the unit.
- Enter both velocities before the collision, with a minus for motion to the left.
- Read the velocities after, the total momentum and the kinetic energy before and after.
Formulas
With coefficient of restitution e (1 elastic, 0 perfectly inelastic):
- v₁ = (m₁u₁ + m₂u₂ + m₂e(u₂ − u₁)) ÷ (m₁ + m₂)
- v₂ = (m₁u₁ + m₂u₂ + m₁e(u₁ − u₂)) ÷ (m₁ + m₂)
Momentum m₁u₁ + m₂u₂ is the same before and after; kinetic energy is ½mv² summed over both objects.
Worked example
A 2 kg ball at 3 m/s hits a 1 kg ball at rest, elastically: v₁ = (6 + 1 × (0 − 3)) ÷ 3 = 1 m/s and v₂ = (6 + 2 × 3) ÷ 3 = 4 m/s. Kinetic energy stays 9 J (1 J + 8 J).
Two cars stick together: 1000 kg at 20 m/s hits 1500 kg at rest. Both move on at 20,000 ÷ 2500 = 8 m/s; kinetic energy drops from 200,000 J to 80,000 J, so 60% is lost.
Tips
- Equal masses, elastic: the objects swap velocities, like Newton’s cradle.
- A heavy object hitting a light one barely slows down, while the light one flies off at almost twice the speed.
- Only head-on (1D) collisions are covered; glancing collisions need vectors.