The Physics Philes, lesson 34: Worlds Collide
In which billiard balls bounce, cars crash, and kinetic energy is (sometimes) conserved.
Over the past few weeks we’ve been discussing momentum and the principle of conservation of momentum. This week we’ll continue on that trajectory and talk about how momentum affects collisions of particles!
I know! Exciting, right?
Before we jump in, we should probably figure out what we mean when we say “collision.” Let’s define it broadly as any strong interaction between bodies that lasts a relatively short time. Like a fender bender, for example.
Remember from previous posts that we can neglect external forces if those forces are much smaller than the internal forces and treat the bodies as an isolated system. This is the usual case with collisions.
Now, there are three general types of collisions: elastic, inelastic, and completely inelastic.
Elastic collisions are collisions in the forces between the bodies are conservative (as well as the momentum). In other words, if the total kinetic energy of the system is the same before and after the collision, then the collision is elastic. As we saw last week, we can’t conflate kinetic energy and momentum. They are not the same thing. A good example of an elastic collision are billiard balls:
See? They bounce apart and potential energy is converted back into kinetic energy.
An inelastic collisions is when there is less kinetic energy after the collision than before. A car crash is an example of an inelastic collision. This makes sense. In a car crash, some of the kinetic energy is lost. It’s pretty intuitive, actually. A car crash looks a lot different from breaking billiard balls.
I can’t mention a car crash without a little gratuitous Mythbusters, can I?
The third type of collision can be thought of as a subcategory of inelastic collisions. They are completely inelastic collisions. This is when colliding bodies stick together and move as one body after the collision takes place. For example, if you were to drop some clay or Silly Putty on a hard floor, it would make a splat. The clay or putty wouldn’t bounce up at all. The two bodies – the clay/putty and the floor – merge and travel at the same speed (in this case, a speed of v = 0).
The basic rule is this: In any collision in which the external forces can be neglected, momentum is conserved and the total momentum is the same before and after the collision. Only in elastic collisions is the total kinetic energy equal before the collision as after.However, there are some examples where the kinetic energy is actually greater after the collision than before, like a rifle recoil.
Those are the three basic types of collisions. Next week we’ll dig into elastic collisions a little more. Until then, please leave any corrections or clarifications in the comments!