Elastic Collisions in One Dimension

ELASTIC COLLISIONS IN ONE DIMENSION

The conservation of momentum is useful when looking at two-object collisions. Remember that this concept works only when there is a net zero external force on a system (only internal forces). It is most helpful to look at collisions in one dimension. An elastic collision is a collision that also conserves internal kinetic energy, which is the sum of all the kinetic energies of a system.

What’s true is that completely elastic collisions can only happen with subatomic particles like electrons and neutrons. Macroscopic collisions can closely resemble elastic systems; however, in reality, kinetic energy is always converted into other forms of energy, such as heat or friction and sound. Things like icy surfaces, air tracks, and firm objects that do not deform are examples of kinetic energy being nearly conserved.

Go back and remember what internal kinetic energy is. This is the sum of all the kinetic energies of the objects within a given system. When two things collide on a frictionless system, both things are included as part of the system. There will be momentum before they collide and momentum after they collide. Because of conservation of momentum, there will be the same momentum before the collision as there is after the collision.

There are equations for the conservation of momentum as well as those for the conservation of internal kinetic energy that need to be included as part of the problemsolving in these situations. Figure 40 shows these Equations:

Figure 40.