Types of Collisions
When one body hits another, their velocities change. However, the total momentum remains the same, so the final and initial velocities are related by this equation for conservation of momentum:
where
m1 = mass of body 1
u1 = initial velocity of body 1
v1 = final velocity of body 1
m2 = mass of body 2
u2 = initial velocity of body 2
v2 = final velocity of body 2
If we only know the initial velocities, it is not possible to find the final velocities, because there are two unknowns but only one equation. (We assume that the masses are given.)
To understand this better, consider an example. Suppose a ball is thrown at a book. The ball could bounce back, and the book would move forward. If it is a tennis ball, it is very bouncy and will bounce back quickly. If it is a paper ball, it would hardly bounce. If it is a plasticine ball, it could get stuck to the book and move together with it.
In this example, we see that even with the same initial velocities, the final velocities could be quite different. They would depend on the materials of the bodies, whether they are hard, soft, elastic, or sticky. However, regardless of the nature of the bodies, the total momentum before and after collision would remain the same. That is to say, the principle conservation of momentum is always true.
We know that the momentum conservation equation alone cannot tell us the final velocities because there are two unknowns. We also see that the final velocities can be different for bodies of different materials. There is another quantity apart from momentum that also depends on velocity. This is the kinetic energy.
We know that energy is conserved. However, when two bodies collide, some kinetic energy can change to heat energy. So kinetic energy need not be conserved. The reason why the velocities after collision can be different for different bodies is related to how much of their kinetic energy is changed to heat. A tennis ball that is very bouncy would produce little heat after collision. A plasticine ball that gets stuck to the book would lose most of its kinetic energy to heat.
Copyright 2011 by Kai Hock. All rights reserved.
Last updated: 11 March 2011