Elastic and Inelastic Collisions

What elastic and inelastic collisions?

An elastic collision is one in which kinetic energy is conserved and is usually seen on a microscopic, sub-atomic scale. For example, if two objects A and B collide then the kinetic energy will be conserved (Equation 63.5) as well as the momentum (Equation 63.6):

$$\underbrace{\frac{1}{2}m_{A}v_{A}^{2} \ + \ \frac{1}{2}m_{B}... ...v_{A}^{2} \ + \ \frac{1}{2}m_{B}v_{B}^{2}}_{After \ collision}$$ (64.5)

$$\underbrace{m_{A}v_{A} \ + \ m_{B}v_{B}}_{Before \ collision} = \underbrace{m_{A}v_{A} \ + \ m_{B}v_{B}}_{After \ collision}$$ (64.6)

An inelastic collision is one in which kinetic energy is not conserved and is more often seen on a macroscopic scale, e.g. a ballistic test in which a bullet is fired into a tank of water. Energy can be released or added in inelastic collisions and can take a variety of forms, e.g. chemical, thermal, etc.

Note: Although kinetic energy is not conserved, total energy is conserved.

When presented with a problem that deals with an inelastic collision, a common objective will be to calculate the amount of energy that was ``lost.'' To do this, calculate the total kinetic energy before the collision and subtract it from the total kinetic energy after the collision - the difference is the energy that was ``lost'' inelastically:

$$\underbrace{\frac{1}{2}m_{A}v_{A}^{2}}_{Before \ collision} ... ...^{2}}_{After \ collision}= \ Energy \ \lq\lq lost'' \ inelastically$$ (64.7)