Unit 05 — Energy & Momentum

Momentum

This page covers the core ideas now; worked examples and practice problems will keep expanding.

1. Momentum & Impulse

p momentum (kg·m/s) — a vector, mass times velocity.
J impulse (N·s) — the change in momentum, caused by a force acting over time.

p = mv

J = FΔt = Δp

Impulse is why a longer collision time (an airbag, bending your knees on landing) reduces the force you feel — the same Δp is achieved with a smaller force when Δt is larger.

2. Conservation of Momentum

In any system free of external forces (or where external forces are negligible during a short collision), total momentum before equals total momentum after.

m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f

Misconception

"Momentum and kinetic energy are conserved in every collision." False — momentum is conserved in all collisions (given no external forces), but kinetic energy is only conserved in elastic collisions. Most real-world collisions are inelastic: momentum is conserved, KE is not.

3. Collisions

Elastic: objects bounce apart, kinetic energy is conserved.
Perfectly inelastic: objects stick together and move as one mass afterward, kinetic energy is not conserved, momentum still is.

m₁v₁ᵢ + m₂v₂ᵢ = (m₁ + m₂)v_f (perfectly inelastic)

4. Simulator

5. Practice Problems

1. A 3 kg cart moving at 4 m/s collides and sticks to a stationary 1 kg cart. Find the final velocity.

(3)(4) + (1)(0) = (4)v_f → v_f = 3 m/s.