Collision calculator (momentum)

Formula

How it works

Momentum (mass × velocity) is conserved in every collision. In an elastic collision kinetic energy is also conserved, which gives two equations that solve for both final velocities. In a perfectly inelastic collision the objects stick together afterwards and move with one shared velocity, found from momentum alone; kinetic energy is not conserved in that case.

Worked example

The same calculation with the default values:

• Collision type Elastic
• Mass 1 2
• Velocity 1 (before) 5
• Mass 2 3
• Velocity 2 (before) -2

1. v₁′ = ((2 − 3) × 5 + 2 × 3 × -2) ÷ (2 + 3) = -3.4 m/s
2. v₂′ = ((3 − 2) × -2 + 2 × 2 × 5) ÷ (2 + 3) = 3.6 m/s
3. kinetic energy before = 0.5×2×5² + 0.5×3×-2² = 31 J
4. kinetic energy after = 0.5×2×-3.4² + 0.5×3×3.6² = 31 J (conserved - this is what makes the collision elastic)

Result: Velocity 1 (after): -3.4 m/s · Velocity 2 (after): 3.6 m/s · Total momentum: 4 kg·m/s

Common mistakes

• Choosing "elastic" for a real-world collision (like two cars) when almost all everyday collisions are at least partly inelastic - kinetic energy is only exactly conserved in idealized cases.
• Forgetting that velocity is signed: two objects moving toward each other have opposite-sign velocities, not two positive numbers.
• Comparing kinetic energy before and after an inelastic collision and being surprised it dropped - that lost energy became heat, sound and deformation, which is expected, not an error.