# 9709. Mechanics 1. Momentum

Momentum is a vector quantity, with the same direction as the velocity a particle is moving at. It is calculated by multiplying the mass of the particle by its velocity, so Momentum = mv and its units are Newton seconds (Ns) ( because [kg]x[ms-1] =[kg]x[ms-2s]=[kg]x[ms-2]x[s]=[Ns]).

Worked Examples

• Find the momentum of a body of mass 3kg moving at 5ms-1
• A tennis ball of mass 50g hits the ground with speed 10ms-1 and rebounds with speed 6ms-1. Find the change in momentum that occurs in the bounce.

Exercise

Collisions and Conservation of Momentum

There is an impact when two bodies collide, and momentum is transferred between them. We will look only at one dimensional situations.

Momentum is conserved during impact, so the total momentum before the impact is equal to the total momentum after the impact: m1u1 + m2u2 = m1v1 + m2v2

Worked Example

• Two snooker balls are moving directly towards one another. The first snooker ball has mass 200g and is moving at 3ms-1. The second has mass 250g and is moving at 1ms-1. After the collision, the first snooker ball is stationary. What is the speed of the second snooker ball after the collision?

It is possible that after collision the two particles will coalesce, meaning they combine and move off together as a single object. We can then consider them as a single object whose combined mass is the sum of their individual masses.

It is also possible that there will be an explosion, meaning that the two bounce off in opposite directions.

Worked Examples

• A boy is sitting on a sledge. The boy and sledge have combined mass of 50kg. When the boy and sledge are moving at 2ms-1, his sister standing in front of the sledge throws a snowball at the sledge. The snowball has mass 0.2kg and is travelling at 10.55ms-1 when it hits the sledge, head on. The snowball, the boy and the sledge continue together. Assuming that the total momentum is unchanged, find the speed of the sledge.
• A ball of mass 200g moving at 4ms-1 makes a direct collision with a larger ball of mass 500g moving at 1ms-1. On impact the balls coalesce.
• Find the speed of the balls after the collision if the balls were:
• initially moving towards one another;
• initially moving in the same direction.

Exercise and General Exercises