# Momentum and Collisions

Momentum and Collisions

Generally Speaking…

In January so far, we have been looking at momentum and how momentum is always conserved in all types of collisions.  This means that for a system of objects, the momentum of all objects in that system before a collision is the same as the momentum of all the objects after a collision.

The Formula for Momentum…

In order to calculate the momentum of an object, we must know the object’s mass, m and the object’s velocity, v.  Using these two quantities, we can calculate momentum, p, as p = m v

Types of Collisions…

There are two major types of collisions - Elastic Collisions & Inelastic Collisions.

Elastic Collisions are characterized by colliding objects that have the same Kinetic Energy before the collision as after the collision.  This means that the Kinetic Energy of Elastic Collisions is conserved.  The objects in elastic collisions ALWAYS bounce off each other.

Elastic Collision (objects bounce off each other after collision)

Inelastic Collisions are characterized by colliding objects that do NOT have the same Kinetic Energy before the collision as after the collision.   This means that the Kinetic energy of Inelastic Collisions is NOT conserved.  Inelastic collisions are either labeled as “Inelastic” or “Perfectly Inelastic”.  If a collision is “Perfectly Inelastic”, the objects stick together.  Otherwise, the objects bounce off each other (but are still in an Inelastic Collision!).

Perfectly Inelastic Collision (objects stick together after collision)

Here are two examples of student work:

1.

This example uses the Conservation of Momentum to find the final velocity, vf of an object in an
Elastic Collision (Kinetic Energy is also conserved).

1.

This example uses the Conservation of Momentum to find the final velocity, vf of
an object in an Inelastic Collision.

1.

This example uses the Conservation of Kinetic Energy to find the final velocity, vf
of an object in an Elastic Collision when Kinetic Energy is conserved.

Ian Joseph
ijoseph@isps.edu.tt