# A-level Physics (Advancing Physics)/Forces and Impulse in Collisions

You should already know that the force exerted on an object is proportional to its acceleration. The constant of proportionality is known as the mass of the object:

${\displaystyle F=ma}$

In the case of a collision, for one of the particles in the collision, the acceleration is simply the difference between its velocity before the collision (u) and its velocity after the collision (v) per unit. time:

${\displaystyle F={\frac {m(v-u)}{\Delta t}}={\frac {mv-mu}{\Delta t}}}$

So, force is the rate of change of momentum. The quantity on top is known as the impulse of the collision, measured in Ns; Δ t is the length of time it took for the collision to take place. So, the impulse I is given by:

${\displaystyle I=\Delta p=mv-mu=F\Delta t}$

In a collision where a certain change in momentum (impulse) occurs, a force is exerted. If the collision time is small, a larger force is exerted. If the collision time is long, a smaller force is exerted. If you have a graph of force against time, impulse is the area under the graph, since:

${\displaystyle I=\int {F\;dt}}$

The impulse on one particle in a simple collision is the negative impulse on the other particle.

## Questions

1. Escape velocity from the Earth is 11.2kms-1. How much impulse must be exerted on a 47000kg payload to get it to travel away from the Earth?

2. Two billiard balls, of mass 10g, collide. One is moving at 5ms-1, and the other at 2ms-1. After the collision, the first billiard ball is moving backwards at 4ms-1. The collision takes 1 ms. What force was exerted on this ball?

3. What impulse and force were exerted on the second ball?

4. A 60kg spacewalker uses a jet of gas to exert an impulse of 10Ns. How many times would he have to do this to reach a speed of 1 ms-1 from stationary?

5. A 5kg bowling ball collides with a stationary tennis ball of mass 0.1kg at 3ms-1, slowing to 2.5ms-1. It exerts a force of 100N on the ball. How long did the collision take?

Worked Solutions