User:Inconspicuum/Physics (A Level)/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:

$$F = ma$$

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:

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

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

$$I = \Delta p = mv - mu = F\Delta t$$

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:

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

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