Elastic and Inelastic Collisions

Momentum is conserved in any collision. However, there are different types of collisions depending on how much kinetic energy is conserved.

Elastic Collisions

Elastic collisions resemble collisions between balls in a game of pool, where the objects involved in the collision remain unchanged after the collision occurs. In elastic collisions, the total kinetic energy will be conserved as well as the total momentum of the system. As a result, the objects will bounce off of one another with no kinetic energy lost.

Few collisions are truly perfectly elastic, most often some kinetic energy is transformed into other forms of energy, like heat, but we can approximate many collisions as being elastic, such as collisions between atoms and molecules or collisions between billiard balls.

Figure 1: The figure represents an elastic collision between a bowling ball and a volley ball. Before the collision, the two balls move in opposite directions and towards each other, with velocity v₁ and v₂, respectively. After the collision, because of the conservation of momentum, both balls proceed in the same direction.

Inelastic Collisions

Car crashes can be an example of inelastic collisions. In these collisions, the total momentum is conserved but the total kinetic energy is not conserved. Much of the kinetic energy is converted into other forms of energy like the energy of sound (which we hear as the sound of the crash), the internal potential energy of the cars (if their bodywork is deformed), or heat.

In reality, very few collisions are perfectly elastic or perfectly inelastic collisions where all possible kinetic energy is lost. Almost all collisions are somewhere in between, and we can simply label them as inelastic, implying that some kinetic energy is lost due to the collision. The amount of kinetic energy lost during an inelastic collision depends on a variety of factors, including the shape and material of the colliding bodies.

A particular kind of inelastic collision where all the possible kinetic energy is transformed into other kinds of energy is called a perfectly inelastic collision.

Figure 2: The figure represents a perfectly inelastic collision. In this case, the colliding bodies stick together proceeding with the same velocity, and some of the kinetic energy is lost by bonding the two bodies together.