Intermediate · 12 min
Momentum and impulse
Calculate momentum changes and use conservation of momentum in simple collisions.
Changing momentum
Momentum is mass multiplied by velocity: p = m × v. It has direction and is measured in kg·m/s. Impulse is the change in momentum. For a constant net force, impulse equals force multiplied by time: Δp = F × Δt. The same momentum change over a longer time needs a smaller average force. This helps explain why cushioning can reduce the force during a stop.
Worked example
A 2 kg cart changes velocity from 1 to 4 m/s. Change in momentum = 2 × (4 − 1) = 6 kg·m/s
Momentum in a collision
Total momentum stays constant when the net external impulse on a system is zero or negligible. In a one-dimensional collision, choose one positive direction and include signs. If two objects stick together, their final momentum is their combined mass multiplied by their shared velocity. Kinetic energy need not be conserved: some can become internal energy or sound.
Worked example
A 2 kg cart at 3 m/s sticks to a stationary 1 kg cart. Initial momentum = 6 kg·m/s Shared velocity = 6 ÷ (2 + 1) = 2 m/s
Compare stopping forces
- Calculate the average force magnitude needed to stop a 1 kg cart moving at 4 m/s in 0.5 s.
- Repeat for a stopping time of 2 s. Compare the forces while keeping the momentum change the same.