7.2 Collisions
In a collision:
- Two or more objects strike each other
- The total external force is either zero or negligible, and therefore momentum is conserved
Collisions are categorized by what happens to the total kinetic energy of the system. In an inelastic collision, the total kinetic energy is different before and after the collision. In an elastic collision, the total kinetic energy is the same before and after the collision.
On the scale of macroscopic objects, all collisions are inelastic. However, some are very close to elastic. For example, a collision between two pool balls is very nearly elastic. On the atomic and subatomic scale, collisions that are truly elastic occur regularly.
7.2.1 Inelastic collisions
Collisions in which objects permanently change shape (deform) are very common examples of inelastic collisions. Energy is required for deformation—this energy is provided by the kinetic energy the objects had before the collision.
Momentum is conserved (as in all collisions):
pi = pf
but kinetic energy is different before and after:
Ki ≠ Kf
As a special case of this, consider two objects that stick together after a collision. For two objects to stick together, there is generally some sort of deformation involved. When two objects stick together, it is often called a perfectly or completely inelastic collision.
However, objects do not need to stick together for the collision to be classified as inelastic. For example, a rock flying through and shattering a class window would be an inelastic collision: when the glass shatters, chemical bonds are broken, which requires energy. The energy required to break the glass comes from the kinetic energy of the rock.
Example
Note: in the previous example, the velocity of the truck should be negative. For example, if the problem says the truck “is moving at 5.3 m/s in the opposite direction,” then the solution should have “vt = -5.3 m/s.”
Example
7.2.2 Elastic collisions
As with all collisions, momentum is conserved in elastic collisions:
pi = pf
Additionally, the total kinetic energy of a system is the same before and after an elastic collision:
Ki = Kf
Most collisions that you will encounter in daily life will be inelastic collisions, though some (such as collisions between pool balls) are very good approximations of elastic collisions.
Elastic collisions are very common on the atomic and sub-atomic scales. For example, if you’ve had chemistry you’re probably familiar with the Ideal Gas Law. This is a very accurate description of the interactions between certain atoms, and one of the primary assumptions that the ideal gas law is built on is that the collisions between atoms are elastic.