What Is Elastic Collision?

In an ideal situation, after an object collides, the deformation can be recovered without heat and sound, and there is no loss of kinetic energy. This kind of collision is called elastic collision, also called full elastic collision. True elastic collisions only occur between molecules, atoms, and smaller particles. In life, when a hard wood ball or a steel ball collides, the loss of kinetic energy is small and can be ignored, and their collision can usually be regarded as an elastic collision.

Elastic collision

In general : define the recovery factor

If we only consider the collision with the center, since the relative velocities before and after the collision are opposite to each other in the center of mass system, we have

(1)

Using the definition of the total momentum of the center of mass system as zero and the relative speed, combined with the formula (1), it is easy to deduce the velocity expression after collision in the center of mass system. Finally bring in the expression

Easy to get speed after collision:

Take e = 1 to get the velocity expression after a fully elastic collision. ^[2]

The following properties can be obtained from the above formula:

1. (Limited to heart collision)

: The relative velocity of two objects after collision is equal to that of the opposite direction before collision.

Total momentum

And total energy

Invariant: The vector sum of momentum and the sum of energy are unchanged before and after the collision of two objects.

3. If

Equal size,

And

: If the two objects have the same mass, the speed and direction are interchanged.

There are also types of collisions: inelastic collisions, completely inelastic collisions.