Before you read this, I suggest that you read posts 16.13 and 16.21.
If I drop a tennis ball on a hard, flat, smooth surface, it bounces back to almost the height it was dropped from. As it drops, it converts potential energy into kinetic energy; after it has bounced, it converts kinetic energy into potential energy (post 16.21). When it bounces back to almost its original height, its potential energy is almost the same as its initial potential energy. So, when the ball bounces, there is a collision with the ground in which most of its mechanical energy has been conserved.
When an object collides with something without losing mechanical energy we say that it has undergone an elastic collision.
If I drop an egg on the floor, it does not bounce back. It breaks and sticks to the floor. So, no mechanical energy is conserved in the collision of the egg with the floor. What happened to the kinetic energy that the egg had when it hit the floor? It is used to do work (post 16.20) to separate the eggshell into pieces.
When an object collides with something and loses all its mechanical energy we say that it has undergone an inelastic collision.
Most real collisions aren’t completely elastic or inelastic. But physicists and engineers use these ideas to model the behaviour of systems in the real world that closely resemble one or the other (see post 16.43).
Now let’s think of games in which a ball, moving on a smooth flat surface, hits a stationary ball. Bowls, billiards and snooker are examples of games like this.
At the time of the collision, we are interested in the behaviour of the two balls and nothing else. We don’t care why the first ball is moving, only that it is. So, when we think about the collision, we isolate a system, that consists of the two balls resting on a surface. We can isolate the system in this way because nothing else now affects the behaviour of the balls at the time of the collision.
At the time of the collision, there is no external force acting on the system that affects the movement of the balls. The force that one ball exerts on the other, at the time of the collision, is internal to the system. Since there is no external force acting on the system, there can be no change in its momentum – since, force is rate of change of momentum (post 16.13). The previous statement (that when there is no external force acting on a system, it conserves its momentum) is called the principle of conservation of momentum.
When two or more objects collide, we can define a system in this way so that there is no external force acting on it and momentum is conserved. Remember that momentum is simply the mass of an object multiplied by its velocity – since velocity is a vector (post 17.4), so is momentum. We can think of this another way; force is a vector (post 16.50) – so momentum must be a vector because force is the rate of change of momentum (post 16.13).
And we can define any system of colliding objects so that momentum is conserved; this is equally true of elastic collisions (at one extreme) and inelastic collisions (at the other extreme).
16.13 Changes in movement