# Momentum and Collisions

# 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:

[math]p=mv[/math], 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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