Momentum

Momentum is an expression of how hard it is to change the motion of an object. It has to do with the object's mass and velocity and is an indication of how hard you would have to push, and for how long, in order to bring the object to a stop.

Objects with a large amount of momentum are difficult to stop. (Ex. an American football player running at full speed)

Objects with a small amount of momentum are easy to stop. (Ex. a one-year-old child waddling along)

Any moving object has momentum, which depends on its:

1.Velocity

2.Mass

Where: ρ = momentum

m = mass

v = velocity

ρ = mv

• Momentum is a vector quantity, meaning it has both magnitude AND direction.

- Right and Up are +

- Left and Down are -

• The units are kg·m/s

• The units can also be written as N·s

Ex:

Calculate the momentum of a 6.2 kg pumpkin traveling at a velocity of 5.0 m/s west.

ρ = mv = 6.2 (5.0) = 31 kg·m/s

Ex:

A baseball of mass 0.14 kg is moving at 35.0 m/s.

a. Find the momentum of the baseball.

ρ = mv = 0.14 (35.0) = 4.9·kg m/s

b. Find the velocity at which a bowling ball, mass 7.6 kg, would have the same momentum as the baseball.

ρ = mv → 4.9 = 7.6 v → v = 1.55 m/s

Remember:

Change = Final - Initial

Ex:

a) A 0.50 kg water balloon is thrown against a wall at 32 m/s coming to a stop. What was its change in momentum?

Δρ = ρf – ρi = mvf – mvi = 0.5(0) – 0.5(32) = -16 kg·m/s

Remember:

Change = Final - Initial

Ex:

b) A 0.50 kg bouncy ball is thrown at 32 m/s, bouncing back with the same speed. How does its change in momentum compare to that of the water balloon?

Δρ = ρf – ρi = mvf – mvi = 0.5(-32) – 0.5(32) = -32 kg·m/s

Its change in momentum is double that of the water balloon.

Impulse

Momentum: mass times velocity, ρ =mv

Impulse: The change in momentum (Δ ρ).

We define the change in momentum from Newton’s 2nd Law:

Fnet = ma

Fnet = mΔv

t

Δ ρ=mΔ v=F net t

Ex.Luigi is sick of taking orders. He swings a 9.0 kg hammer at 16 m/s when Mario’s mustache brings it to a stop in 0.25 s. What is the net force exerted on Mario’s mustache?

Ex.

A soccer player kicks a 0.850 kg ball at 25.0 m/s east. If the goalie stops the ball in 0.0525 s, how much force does he exert on the ball?

If the goalie stops the 6.5 kg bowling ball traveling at the same velocity in the same amount of time, how much force is required?

ExampleA student jumps off a desk. When they land they bend their knees on impact. Why does this help prevent some serious damage to their knees?

ExampleCoaches for many sports such as baseball, tennis and golf can often be heard telling their athletes to “follow through” with their swing. How does this help a weaker player hit a ball farther than a stronger player?

ExampleUsing the principle of impulse explain why an airbag can help people sustain less damage during a collision.