Impulse and Force-Time Graphs

In the previous lesson, we used conservation of momentum to analyse collisions and explosions. But we often want to know more: how large were the forces involved? How long did the collision last? What is the relationship between force, time, and the change in momentum? These questions are answered by the concept of impulse.

---

Impulse

Impulse is defined as the product of force and the time for which it acts:

Impulse = F delta t

The unit of impulse is the newton-second (N s), which is equivalent to kg m/s (the same unit as momentum).

More importantly, impulse equals the change in momentum:

Impulse = F delta t = delta(mv) = mv - mu

This is actually Newton's second law in its most general form. Newton originally stated his second law as "the rate of change of momentum is proportional to the applied force," which gives:

F = delta(mv) / delta t

Rearranging: F delta t = delta(mv), which is the impulse-momentum theorem.

Worked Example 1

A 0.40 kg ball hits a wall at 10 m/s and bounces back at 8.0 m/s. What is the impulse on the ball?