This week, we will use the concepts of momentum and energy
to examine an application of great importance-- collisions.
A collision is an event where two or more objects exert
forces on each other over a short time interval,
and where the interaction forces dominate
over any external forces.
Common examples are collisions involving projectiles,
collisions of motor vehicles, collisions in sports,
and collisions between atomic or subatomic particles.
It is worth noting that the colliding objects need not
actually touch each other in the collision,
as long as the interaction force does not require a contact.
For example, two positively charged
protons shot towards each other will repel each other due
to the Coulomb electric force.
Their interaction can be treated as a collision
even if they never actually touch.
We will see that momentum is always conserved in a collision
as long as external forces can be entirely neglected.
However, energy is not necessarily conserved.
This leads to the distinction between elastic collisions,
where energy is conserved, and inelastic collisions,
where energy is not conserved.
We will also derive a simple, but powerful principle
in the case of elastic collisions in one dimension,
that the relative velocity of one particle with respect
to the other is simply reversed by the collision.