# Momentum

## Momentum

Momentum is a measure of the amount of impetus a moving object has. It is a way of quantifying how hard it is to make an object slow down or change directions.

Image someone gently passes you a tennis ball, it is light and moving slowly. When you catch it, it is easy for you to stop it. If that same ball was hit from a racket by a professional at 120 mph it would be much harder to stop, and probably hurt a lot too. This is because it has a higher velocity and so has more momentum.

Now image someone gentle throws a cricket ball at you, it is still probably OK to stop, it has more mass, but its velocity is not very high, so not much momentum. Catching that same ball as a wicketkeeper when it is moving fast is not so easy, the ball has more velocity and so has more momentum. This is why you wear protection in cricket. Momentum is something we all know about, you don’t have to understand the maths to know you don’t try to stop a train with your bare hands, not unless you are superman that is.

Momentum is a product of the mass of the object and the velocity of the object.

Momentum = mass x velocity

p =m v mass is measured in kg, velocity in m/s. Momentum is measured in kgm/s

Example:

What is the momentum of an 85 kg girl running at 4 m/s?

p = mv

p = _85 x 4 = 340 _kgm/s

What would be the momentum of a 4 kg cannon ball travelling at 85 m/s (190 mph)?

p = _4 x 85 = 340 _kgm/s Exactly the same.

Small, fast-moving objects have the same momentum as larger slower moving objects.

## Collisions

A collision is a situation where two objects hit each other and interact. During a collision, the momentum is conserved as long as there are no outside forces acting upon the objects. When the cue ball collides with the 8 ball the momentum is conserved, as they are the same mass the 8 ball moves off at the same velocity as the cue ball had before the collision.

What if the two balls are both moving, but heading towards each other?

The total momentum before the collision = The total momentum after the collision.

Example 1: Both balls have a mass of 100 g ( 0.1 kg) and are moving at 2 m/s towards each other.

Ball A - Momentum = mass x velocity =0.1 x 2 = 0.2 kgm/s

Ball B - Momentum = mass x velocity =0.1 x -0.2 = - 0.2 kg m/s (The negative sign indicates the ball is travelling in the opposite direction to Ball B)

Total momentum = 0.2 + - 0.2 = 0 kgm/s

After the collision, the momentum will be zero too. Newton’s third law tells us that on impact they interact with equal but opposite forces. This reduces the velocity of both balls to zero.

Momentum is zero both before and after.

Example 2: What if one of the balls, (Ball A) is twice the mass other, (Ball B)?

Before the collision

Ball A’s momentum = 0.2 x 2 = 0.4 kgm/s

Ball B’s momentum = 0.1 x -2 = - 0.2 kgm/s

Total momentum before =0.4 + -0.2 = 0.2 kgm/s

After the collision

Total momentum still equals 0.2 kgm/s, so the combined balls are moving in the direction of Ball A, but now they have a combined mass of 0.3 kg.

Momentum = mass x velocity so velocity = Momentum / mass =0.2 / 0.3 = 0.67 m/s

The balls collide and move off together at 0.67 m/s in the direction Ball A was originally moving.

Forces involved in a Collision

Force = Change in Momentum / time

F = (mv - mu) / t where v = final velocity u = initial velocity

From example 2 above, if the change in velocity and movement happened in 0.2 s then:

Force on Ball A

F= mv - mu /t =(0.2 x 0.67) - (0.2 x 2) / 0.2 = -1.33 NThe force is negative as it is in the opposite direction to the velocity of the ball to slow it down.

Force on Ball B

F = mv - mu /t = (0.1 x 0.67) - (0.1 x -2) / 0.2 = 1.33 N.

Notice that the two forces are equal but opposite, just as stated in Newton’s Third Law of Motion.

What is the momentum of a 50Kg person moving at 2 m/s?