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# Momentum and Collisions

Introduction: For a moment, consider a collision, like what is shown on the left. The physics behind these collisions explains what happens during a car accident, should two cars have a head-on collision with each other. When two objects collide, they do so with a certain momentum, or a measure of the product of mass and velocity. The equation for momentum is shown below:

$p=mv$, where m=mass, p=momentum, and v=velocity

Momentum is a vector quantity, since it has both a direction and a magnitude associated with it. Momentum, being the product of mass and velocity, is measured using the SI units kilogram•meters/second, where "kilogram" is used to measure mass and "meters/second" is used to measure velocity. Based on the idea that momentum is a vector quantity, there must also be a direction associated with this measurement in kilogram•meters per second.

Momentum is incredibly important, because it describes what happens in the head-on collision between the two cars described before, both before and after the collision. The two cars described before will collide and, in the system that results from their collision, create a total momentum that is equivalent to the product of their combined mass and the vector sum of their velocities. In any case that involves a collision, the total momentum before the collision and the total momentum after collision must always be the same - a law known as the Law of the Conservation of Momentum.

How the momenta before and after the collision are expressed depends on the type of collision that is involved. In elastic collisions, kinetic energy is also conserved. In inelastic collisions, kinetic energy is not conserved. In completely inelastic collisions, kinetic energy is not conserved, and the objects also lock and move together after the collision.

It is also important to note that the change in momentum (∆p) is equivalent to what is known as the impulse, a quantity that can be defined as the quantity Force•time. This equation for momentum is summarized as follows:

J=F•t=m•∆v=∆p, where J=impulse, F=force, t=time, m=mass, ∆v=change in velocity, and ∆p=change in momentum

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