Collisions in one dimension: what is conserved, and what is not

Year 11 Physics · positive is to the right, so every velocity below is a signed number and a rebound shows up as a change of sign · total momentum p = m₁v₁ + m₂v₂ · restitution v₂ − v₁ = e (u₁ − u₂)

Set the two bodies

A negative velocity means moving left

Mass m₁ 2.0 kg

Velocity u₁ +3.0 m/s

Mass m₂ 4.0 kg

Velocity u₂ 0.0 m/s

Coefficient of restitution e 0.00 · perfectly inelastic

0 · they stick 0.5 · part bouncy 1 · perfectly elastic

Before the collision

Arrow length is speed · arrow direction is the sign

Press Run collision to send them at each other.

The ledger — read both rows

Body 1 plus body 2, added together

	Before	After	Change
Total momentum kg·m/s	+6.00	—	not run yet
Total kinetic energy J	9.00	—	not run yet

Momentum has nowhere to go: nothing outside the pair pushes on it. Kinetic energy does have somewhere to go — deformation, sound, heat — so it survives only when nothing is deformed, which is what e = 1 means.

Body 1 final velocity

—

Not run yet

Body 2 final velocity

—

Not run yet

Energy lost to the collision

—

Zero only when e = 1

Predict first

These two are about to collide and stick together. The pair will clearly be moving more slowly afterwards. Will the total momentum after the collision be less than it was before?