During a collision the objects involved generally apply equal-and-opposite forces on one another. There are usually no external forces, so the momentum of the system of objects is conserved.

Generally, momentum is conserved in all types of collisions.

There are four classes of collisions based on what happens during the collision and, in particular, what happens to the total kinetic energy of the system.

1. Super-elastic: Kinetic energy is larger after the collision (e.g., an explosion).
   
   
2. Elastic: Kinetic energy is conserved.
   
   
3. Inelastic: Kinetic energy is smaller after the collision.
   
   
4. Completely inelastic: Kinetic energy is smaller, and the objects stick together, after the collision.

In one dimension, the fact that momentum is a vector can be dealt with using appropriate signs. In other words, choose a positive direction.

For every collision you can write out a conservation of momentum equation (i.e., set the momentum before the collision equal to the momentum afterwards). Elastic collisions and completely inelastic collisions are often easier to analyze than other types of collisions because there is more information to work with.

In an elastic collision kinetic energy is conserved, so you can write out an equation setting the kinetic energy before the collision equal to the kinetic energy afterwards. Combine this with your momentum equation to solve the problem.

In a completely inelastic collision there is only one final velocity, because the objects move together. If there is just one unknown you can use your one momentum equation to solve.

The sliders in the simulation set the mass and initial velocity of the two carts, as well as the elasticity of the collision.

The elasticity k is defined as the ratio of the relative velocities of the two colliding objects after and before the collision:

k = (v_2f - v_1f) / (v_1i - v_2i)

The elasticity is related to the type of collision as follows:

Type of Collision	Elasticity
Super-elastic	k > 1
Elastic	k = 1
Inelastic	k < 1
Completely inelastic	k = 0

Here are some things to think about when using the simulation:

• The total momentum before and after a collision should always be the same.
• The total kinetic energy before and after a collision is only the same for an elastic collision.