## Momentum

Linear Momentum – units kg m/s - is defined as the product of mass and velocity. It is a vector, and is of fundamental importance because in any collision or any isolated system it is conserved as a consequence of Newton's third law.

We can write this conversation law for two massesandwith initial velocitiesand and final velocitiesandrespectively as

This can be rearranged as

or

The impulse given to a body as a result of an interaction of some sort with another is written asso we can see from the last expression above that the impulses that bodies exert on each each other are equal and opposite. This is an expression of Newton's third law.

We can write the force exerted on a body asIntegration of this with respect to givesIfis constant thenso we may consider an impulse as due to a forceapplied for a time

Example: A jet of water leaves a hose at the rate ofper second at a speed of 20 m/s. It hits a wall and is brought to rest. Find the force exerted by the jet on the wall.

The force exerted on the wall equals the rate of change of momentum of the water. In one second a mass of water equal to density*volume=1000*0.005=5 kg hits the wall. This water has momentum equal to 5*20=100 kg m/s. Since this water is brought to rest every second, the force exerted on the wall is 100 N.

Example: A toy truck of mass 0.5 kg moving at a speed of 3 m/s collides with a stationary truck of mass 1 kg. The trucks stick together during the collision and afterwards move as one. Find their common velocity after the collision.

Initial momentum
Hence final momentum

${}=1.5=(0.5+1) \times v \rightarrow v=\frac{1.5}{1.5}=1m/s$