Chapter+4+-+COLLISIONS

Chapter 4 - COLLISIONS

**__Basics of Collisions__**
Collisions are when two freely moving bodies directly come together or when a freely moving object directly hits a fixed object. In general as a result of the collision the two bodies bounce away from each other, but in the case of a fixed object the fixed object doesn’t move. Examples of these are when two snooker balls collide they come together and then bounce apart this could be in opposite directions or continue to travel in the same direction but with different velocities. Another type of collision is when a ball is falling towards the ground and collides with the ground then travels in the opposite direction. When modeling these collisions we assume that the particle recovers its shape and causes them to rebound and is called elastic collision. this happens because the two objects recive an impluse from each other. Impluse is just a force in newtons with a direction. As shown in diagram 1. But becasue not every collision is elastic some energy is lost and this is the coefficient of restitution, we use this Newton's expermimental law of restitution.

If e=0 then the impact is inelastic so no rebound occurs. If e=1 then the impact is perfectly elastic so no energy is lost. Using both of these equations we know we can now substitute in values we know to find the value we have to find the unknown values by having two simultaneous equations with the same unknowns. Here is an example to show you how to answer a basic collision question like this. Example 1 A particle of mass 3kg moving at 6ms¯¹ collides directly with stationary particle of mass 5kg. The coefficient of restitution between the particles is 0.4. Find their velocities after the impact.

This can also be used to calculate collisions between a ball/particle hitting a wall.