Physics Chapter 6

Impulse and Momentum

Momentum• Momentum depends on…

– Mass– Velocity– Momentum = Mass x Velocity

• The property of momentum…– Variable: p– Unit:

– Scalar or Vector?

– Equation: p = mv

kg m

s

Example #1

Which has more momentum, a 1-ton car moving at 100 km/h or a 2-ton truck moving at 50 km/h?

Example #2

How fast would a 18 kg kid on a tricycle have to go in order to have the same momentum as a 55 kg car traveling at 25 m/s?

Impulse• Momentum can change. Most often, the

mass of an object remains the same, while the velocity changes.

• p = mv• v acceleration a = v/t v=at• p = mv becomes p = m x a x t• p = Force x time = Ft• This is called Impulse

– I = Ft

F

Example #3If a baseball bat applies a 22-N force to a baseball for 0.13 s, what is the impulse experienced by the ball?

Impulse & Momentum

• Impulse equals a change in momentum

• I = p

• VariationsFt = mv

Ft = mvf – mvi

I = mv

I = mvf – mvi

Ft = p

Example #4

What is the impulse needed to stop a 10-kg bowling ball moving at 6 m/s?

Example #5A car crashes into a wall at 25 m/s and is brought to a rest in 0.1 s. Calculate the average force exerted on a 75-kg test dummy by the seat belt.

Impulse & MomentumIncreasing Momentum

mv = FtIncrease the time to increase the velocity

• Examples:– Follow through in sports

• Basketball shoot• Baseball hit• Soccer kick• Golf swing

– Long-range cannons have long barrels

Impulse & MomentumDecreasing Force

mv = FtIncrease the time to decrease the Force

• Examples:– Catching

• Egg toss• Water balloon• Football

– Cars: Crumple Zones & Air Bags– Roll with the punches– Mighty Ducks– Jumping and landing (sprung floors)– Running Shoes– Any padding– Bungee Jumping

Problems

• Review Questions1-11, 13

• Exercises1-4, 6, 9, 10

• Problems1, 2, 5

Conservation of Momentum• Newton’s Second Law…

– If we want an object to accelerate, we must apply a force.

• Impulse and Momentum…– If we want a change in momentum, we must

apply an impulse.

• In both cases, the force or impulse must be exerted on the object or any system of objects by something external.

Conservation of Momentum

• If we define the system to include all the objects we want to study…

all forces become internal; there can be no impulse; no impulse means no change in momentum!

• When a physical quantity remains unchanged during a process, that quantity is said to be…

CONSERVED.

Collisions• Momentum is conserved

Momentum before = Momentum after

• Three types of collisions…– Elastic objects rebound off each

other without lasting deformation.– Inelastic objects are deformed by

the collision; think car crashes.– Perfectly inelastic both objects

stick together

Example #1aThe blue car is moving at 10 m/s, with a mass m. The orange car, also mass m, is at rest. If the freight cars are coupled together by the collision, what is their combined velocity?

v = 0

v = 10 m/s v = ?

Example #1bIf the freight cars in the previous example do not couple and experience an elastic collision, what is the velocity of the orange car?

v = 0

v = 10 m/s v = ?

v = 0

Example #2Two trucks with equal masses, m, experience a head on collision. After collision, the coupled wreck remains at the point of impact with zero momentum. If the green truck was moving at 10 m/s, how fast was the red truck moving?

v = ?v = 10 m/s v = 0

Example #3A 3 kg object traveling at 5 m/sec collides head-on with a 2 kg object that is traveling at 2 m/sec in the opposite direction. What is the velocity of the second object after the collision if the first object is moving at 1 m/sec?

Problems

• Review Questions18-23

• Exercises13, 21

• Problems6-10