Impulse changes momentum
A force acting over a short time delivers an impulse, and that impulse is exactly the momentum change it produces.
Impulse
Impulse is force times the time it acts, and it equals the momentum change it produces: J = F_avg * delta-t = delta-p. The average force during a brief collision is usually huge, because squeezing a fixed momentum change into a short contact time demands a large force. Car crumple zones work by stretching delta-t so F_avg drops.
J = F_{\text{avg}} \, \Delta t = \Delta p = mv_f - mv_iMomentum is a vector
Momentum p = mv points along the velocity, so a rebound reverses its sign. The change is final minus initial with signs carried through — a ball bouncing off a wall can have nearly the same speed before and after yet a large momentum change. Forgetting the sign flip is the most common impulse mistake.
\Delta p = mv_f - mv_i \quad (\text{signs included})Worked example
A 0.50 kg ball arrives at a wall moving right at 8.0 m/s and rebounds left at 6.0 m/s. Take right as positive: momentum goes from (0.50)(8.0) = +4.0 kg m/s to (0.50)(-6.0) = -3.0 kg m/s, a change of -7.0 kg m/s. If contact lasts 0.025 s, the average force is -7.0/0.025 = -280 N: 280 N pushing left, roughly 57 times the ball's 4.9 N weight.
F_{\text{avg}} = \frac{(-3.0) - (+4.0)}{0.025} = -280\ \text{N}Flashcard
Impulse is force times duration
Check your understanding
A 0.20 kg ball strikes a wall head-on at 15 m/s and rebounds at 10 m/s. What is the magnitude of the impulse the wall delivers to the ball?