Introduction to Impact Dynamics: the ideal collision when playing pool

While I was playing pool the other day, I remembered a lesson that I learned during my time at the University of Seville as well as at Cranfield University. It is related to the quite complicated subject of Impact Dynamics… But don’t be afraid, today I’ll just cover a simple case as an introduction. In particular, I’m going to write about how the ideal collision between the white ball and the other ball that we are aiming to move.

First of all, we need to differentiate between different types of collisions, depending on the loss of translational kinetic energy or, in other words, the conversion of kinetic energy to rotations, vibrations or heat. For this case, let’s consider two bodies: one in motion (impactor) and another in stationary conditions. Hence, we can distinguish between the following categories:

• Elastic collision: all the energy is transmitted from one body to another, i.e. the impactor stops and the stationary mass starts moving at the same speed as the initial one from the moving mass.
• Completely inelastic collision: the moving mass stops after hitting the stationary body. The stationary mass remains as it was.
• Inelastic collision: the impactor suffers a decrease in speed after the collision, whereas the stationary mass starts moving at a certain speed.
• Superelastic collision: if additional energy is provided to the stationary body during the impact, then it will start moving at a higher speed than the one at which the impactor hit it.