Warm-up

A mosquito collides head-on with

a car traveling 60 mph. How do

you think the size of the force that

car exerts on the mosquito

compares to the size of the force

that mosquito exerts on car?

12.1 Momentum

Momentum is a property of moving matter.

Momentum describes the tendency of objects

to keep going in the same direction with the

same speed.

Changes in momentum result from forces or

create forces.

12.1 Momentum

The momentum of a ball depends on its mass

and velocity.

Ball B has more momentum than ball A.

12.1 Momentum and Inertia

Inertia is another property of mass that resists

changes in velocity; however, inertia depends

only on mass.

Inertia is a scalar quantity.

Momentum is a property of moving mass that

resists changes in a moving object’s velocity.

Momentum is a vector quantity.

12.1 Momentum

Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec.

A 1 N force is applied to deflect the motion of each ball.

What happens?

Does the force deflect both balls equally?

Ball B deflects much

less than ball A

when the same force

is applied because

ball B had a greater

initial momentum.

12.1 Calculating Momentum

The momentum of a moving object is its

mass multiplied by its velocity.

That means momentum increases with both

mass and velocity.

Velocity (m/sec)Mass (kg)

Momentum

(kg m/sec)p = m v

1. You are asked for momentum.

2. You are given masses and velocities.

3. Use: p = m v

4. Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s

5. Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s

The car has more momentum even though it is going much slower.

Comparing momentumA car is traveling at a velocity of 13.5 m/sec

(30 mph) north on a straight road. The

mass of the car is 1,300 kg. A motorcycle

passes the car at a speed of 30 m/sec (67

mph). The motorcycle (with rider) has a

mass of 350 kg. Calculate and compare

the momentum of the car and motorcycle.

Warm up:

Cars A, B, C, and D,

have twice the

mass of the cars E,

F, G, and H. Rank

the cards in order

from smallest to

biggest

momentum.

A

B

E

F

C

H

G

D

12.2 Force is the Rate of Change of

Momentum

Momentum changes when

a net force is applied.

The inverse is also true:

If momentum changes,

forces are created.

If momentum changes

quickly, large forces are

involved.

12.2 Force and Momentum Change

The relationship between force and motion

follows directly from Newton's second law.

Change in momentum

(kg m/sec)

Change in time (sec)

Force (N) F = D p

D t

1. You are asked for force exerted on rocket.

2. You are given rate of fuel ejection and speed of rocket

3. Use F = Δp ÷Δt = Δ(mv) ÷Δt = (Δm÷Δt) v =

4. Solve: F= (100 kg/s) (-2,500 m/s) = - 250,000 kg m/s2

The fuel exerts and equal and opposite force on rocket of +250,000 N.

Calculating force

Starting at rest, an 1,800 kg rocket takes off,

ejecting 100 kg of fuel per second out of its

nozzle at a speed of 2,500 m/sec. Calculate

the force on the rocket from the change in

momentum of the fuel.

12.2 Impulse

The product of a force and

the time the force acts is

called the impulse.

Impulse is a way to

measure a change in

momentum because it is

not always possible to

calculate force and time

individually since

collisions happen so fast.

12.2 Force and Momentum Change

To find the impulse, you rearrange the

momentum form of the second law.

Change in

momentum

(kg•m/sec)

Impulse (N•sec) F D t = D p

Impulse can be expressed in kg•m/sec

(momentum units) or in N•sec.

Warm up

You want to close an open door

by throwing either a 400-g lump

of clay or a 400-g rubber ball

toward it. You can throw either

object with the same speed, but

they are different in that the

rubber ball bounces off the

door while the clay just sticks

to the door. Which projectile

will apply the larger impulse to

the door and be more likely to

close it?

12.1 Conservation of Momentum

The law of conservation of momentum states

when a system of interacting objects is not

influenced by outside forces (like friction), the

total momentum of the system cannot change.

If you throw a rock forward from a

skateboard, you will move

backward in response.

12.1 Conservation of Momentum

12.1 Collisions in One Dimension

A collision occurs when two or more objects hit

each other.

During a collision, momentum is transferred

from one object to another.

Collisions can be elastic or inelastic.

12.1 Collisions

Elastic collisions

Two 0.165 kg billiard balls roll toward each other and collide

head-on. Initially, the 10-ball has a velocity of 0.5 m/s. The 5-

ball has an initial velocity of -0.7 m/s. The collision is elastic and

the 5-ball rebounds with a velocity of 0.4 m/s, reversing its

direction.

What is the velocity of the 10-ball after the collision? Did it

rebounded?

Inelastic collisions

A train car moving to the right at 10 m/s

collides with a parked train car.

They stick together and roll along the

track.

If the moving car has a mass of 8,000 kg

and the parked car has a mass of 2,000

kg, what is their combined velocity after

the collision?