Two objects meet. What happens next is governed by one of the most reliable rules in physics — and one of the most commonly misunderstood.
Collisions and Momentum
Change masses, velocities and restitutionThe rule that never breaks: momentum
Momentum is mass times velocity (p = mv). In any collision where nothing external interferes, total momentum is always conserved. Always. It does not matter whether the objects bounce, stick, crumple or explode.
Watch the momentum readout while you drag the restitution slider from 1 down to 0: the number before the collision and the number after stay identical every single time.
The rule that sometimes breaks: kinetic energy
Kinetic energy (½mv²) is a different story. It is only conserved in a perfectly elastic collision, where the restitution coefficient e = 1. Set e to 1 and the “KE lost” readout stays at 0%.
Now pull e down. Energy starts disappearing. At e = 0 — a perfectly inelastic collision — the two blocks move together afterwards and the loss is at its maximum. The energy has not vanished from the universe; it has become heat, sound and permanent deformation of the objects.
The velocities after impact come from combining these two ideas:
- v₁′ = [ (m₁ − e·m₂)v₁ + (1 + e)m₂v₂ ] / (m₁ + m₂)
- v₂′ = [ (m₂ − e·m₁)v₂ + (1 + e)m₁v₁ ] / (m₁ + m₂)
Try this
- Give block A a huge mass and block B a small one, with B stationary. A barely slows down and B shoots away — like a bowling ball hitting a pin.
- Do the reverse: a light, fast block hitting a heavy stationary one. The light block bounces back.
- Set e = 0 and both masses equal. The two blocks leave together at half the original speed.
Why it matters
Momentum conservation is why car crumple zones work (spread the change over more time), why rockets move (throw mass backwards, go forwards), and how investigators reconstruct accidents from skid marks. Understanding that momentum is conserved while energy is not is the difference between a student who can quote a formula and one who understands collisions.