Read · 2 min
In Inelastic collisions the total kinetic energy of the masses taking part in the collision is NOT conserved. That means that after the collision some part of the initial kinetic energy is released in the enviroment as heat.
We should note that energy is always conserved. During an inelastic collision no energy is lost. (it is just transformed from one form to another).
A special case of an inelastic collision is a "plastic collision". In plastic collisions the maximum possible amount of kinetic energy is lost. But why is there a "maximum possible amount of kinetic energy" that can be released as heat?
In most collisions, the impulses of the internal forces ( the forces the masses experience as they collide) are far greater than the impulses of external forces. (eg weight) So, as a consequence of Newton's second law, the total momentum of the system containing the colliding masses has to be conserved. Nature's priority is first to make sure momentum is conserved. Then, depending on the properties of the masses the kinetic energy might or might not be conserved. To answer our previous question: The kinetic energy loss has a maximum limit. Beyond that limit, it would be impossible to conserve momentum. This limit occurs in plastic collisions where the masses stick together.
Finding out what happens after a 1D inelastic collision:
(in all examples we assume that we know the masses of the bodies colliding)
- In inelastic collisions where the masses do NOT stick together it is not possible to determine the velocities of the bodies after the collision UNLESS we know some information about the velocities after the collision.
For example, when two bodies collide, we can find countless combinations for the two final velocities, satifying conservation of momentum. So, which one would we pick? To answer that question we have to know the velocity of one of the two bodies after the collision.
- In plastic collisions however, (where the bodies stick together), knowing the velocities of the bodies before the collision is enough. Our only unknown will be the final velocity of the two stuck masses (in contrast to case 1) , in plastic collisions we do not have 2 different final velocities but only one, since the bodies stick together and move with the same velocity). So, applying conservation of momentum will give us the final velocity.
In general in 1D collision problems we work the following way:
a) Define the increasing direciton of position.
b) Let the signs of the velocities take care of the vector directions.
c) Apply conservation of linear momentum respecting the signs of velocities.
d) Solve the Conservation of Momentum equation for the unknown we wish to find.
Then we can calculate the amount of kinetic energy that was lost during the collision.