Momentum• Momentum is a measure of how hard

it is to stop or turn a moving object.• What characteristics of an object

would make it hard to stop or turn?– Mass– Velocity

Momentum• ρ=mv• ρ – momentum (greek letter rho)• m – mass (kg)• v – velocity (m/s)• Momentum is a vector• The units are kg m/s OR Ns

Example• Calculate the momentum of a 65-kg

sprinter running east at 10 m/s.

Example• Calculate the momentum of a system composed

of a 65-kg sprinter running east at 10 m/s and a 75-kg sprinter running north at 9.5 m/s.

Change in momentum• Like any change, change in

momentum is calculated by looking at final and initial momentums.

• Dρ = ρf – ρi– Dρ: change in momentum– ρf: final momentum– ρi: initial momentum

Example• A 0.50 kg water balloon is thrown against

a wall at 32 m/s. It bursts when it hits the wall. What is its change in momentum?

• Now a 0.05 kg bouncy ball is thrown against a wall at 32 m/s and it bounces back with the same speed. What is its change in momentum?

Impulse (J)• Impulse is the product of an

external force and time, which results in a change in momentum of a particle or system.

• J = F t and J = Dρ• Units: N s or kg m/s (same as

momentum)

Impulse formula from Newton’s 2nd law

• F=ma• F=m Δv/t• Ft=mΔv• Ft = Δρ• This is called the impulse

momentum theorem

Example• A soccer player kicks a 0.45 kg ball at

25 m/s. If the goalie stops it by exerting 215 N of force, how long does it take for the ball to stop?

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

Example• Suppose a 1.5-kg brick is dropped on

a glass table top from a height of 20 cm.a) What is the magnitude and direction of

the impulse necessary to stop the brick?b) If the table top doesn’t shatter, and

stops the brick in 0.01 s, what is the average force it exerts on the brick?

c) What is the average force that the brick exerts on the table top during this period?

Impulse (J) on a graphF(N)

t (ms)0 1 2 3 40

1000

2000

3000

area under curve

Example

• This force acts on a 1.2 kg object moving at 120.0 m/s. The direction of the force is aligned with the velocity. What is the new velocity of the object?

0.20 0.40 0.60 0.80 t(s)

F(N)

1,000

2,000

Real-world connectionCollision time affects the amount of force that an object experiences during a collision. From the impulse equation we can see that force and time are inversely proportional. That means that the longer the amount of time to bring an object to a stop in a collision, the less force is experienced.

Real-world connection (write theorem for each to explain)• Air bags• Wearing pads in sports• Catching water balloons• Bending knees when landing from

jumping• Follow through in sports• (doesn’t change force – what else

could it change in equation?)• “Rebound” in collision result in large

change of momentum so what do car manufacturers do to lessen chance of rebound?