Chapter 7

Momentum

Chapter Warm Up

1. What is a non physics definition of momentum? Give an example.

2. What is the physics definition of momentum? Give an example.

3. How can the momentum of an object be changed?

4. What is impulse?

5. What does it mean when a quantity is

conserved?

6. How are elastic and inelastic collisions the

same?

7. How are elastic and inelastic collisions

different?

Section 1: Linear Momentum

Definition:

Inertia in motion

Example:

Symbol:p

Equation:

Momentum = mass x velocity

p=mv

Units:

p= kg m = kgm

s s

Vector quantity

Examples:

1. A 2250 kg pickup truck has a velocity of

25m/s to the east. What is the momentum of

the pickup truck?

5.6 x 104 kgm/s east

2. A car has a mass of 1210 kg. How fast must

it be traveling if its momentum is 2.5 x 103

kgm/s?

2.1 m/s in the direction of travel

3. A child is riding a bike, and is traveling at a

velocity of 4.5 m/s to the northwest. If the

momentum of the bike and the child is 1.2 x

102 kg m/s to the northwest, what is the

combined mass of the bike and the child?

27 kg

How can an object’s momentum be changed?

change mass or velocity

if change velocity – object accelerates– a force is

needed

larger force – larger change in momentum

BUT: TIME FORCE IS APPLIED IS ALSO

IMPORTANT

How about the time the force is applied?

apply force briefly to an object – change in

momentum

apply same amount of force for a longer time–

larger change in momentum

Why????

p = mv, but velocity has a time component– so

the larger the Δt, the larger the Δv, and the

larger the momentum change

So….

A large force over a small time can equal the

same momentum change as a smaller force

over a longer time

FORCE AND TIME ARE BOTH IMPORTANT

This leads to a new quantity: Impulse

Impulse

Definition:

Product of force and time interval during

which the force acts

Causes momentum to change

Equations:

Impulse = FΔt

Impulse = p = mv

But, from NII:

F = ma

and from Chapter 2

a = Δv/Δt

substituting

F = mΔv/Δt

rearranging

FΔt = Δ(mv)

So impulse = Δ momentum

This is the Impulse – Momentum Theory

Section 2: Impulse – Momentum

Theory

Definition:

Any impulse acting on a system changes the system's

momentum. (http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Momentum/ImpulseMomTheorem.html)

Equation:

FΔt = Δ(mv)

usually written as

FΔt = mΔv

Examples:

1. A 1400 kg car moving westward with a

velocity of 15 m/s collides with a utility pole

and is brought to rest in 0.30 s. What force is

exerted on the car during the collision?

7.0 x 104 N east

2. A 0.50 kg football is thrown with a velocity

of 15 m/s to the right. If a stationary receiver

exerts a force of 3.8 x 102 N to the left when

catching the ball, how long did it take the

receiver to catch the ball and bring it to a

halt?

0.020s

3. A man drops from rest off a diving board that

is 3.0 m above the surface of the water and

comes to rest 0.55 s after reaching the water.

If the force on the diver is 1.1 x 103 N

upward, what is the diver’s mass?

79kg

So… How do we change the momentum of an

object?

change any or all

force of impact

time of impact

mass of object

velocity of object

Impulse – Momentum in the Real

World

Hitting a ball

If you want to hit a ball a long way – you

swing harder and follow through. The harder

swing means more force, and the follow

through means more impact time, so v is

larger, and therefore the ball goes farther.

Barrels on the Interstate at bridges

Allow the momentum to decrease over a

longer impact time, thus decreasing the impact

force

Catching a ball

Bringing your hand back as you catch the ball

increases the impact time, thus decreasing the

impact force – hand doesn’t hurt as much,

easier to retain control.

Your own examples

The bottom line:

Impact time and impact force are inversely

proportional for the same change in

momentum

A moving object has a certain amount of

momentum, so if you increase the impact time,

you will decrease the impact force ( which is

what you usually want)

or

If you decrease the impact time, you will

increase the impact force

DON’T CONFUSE IMPULSE, IMPACT, AND

MOMENTUM!!!!

Impact is a force

Impulse is what is applied to an object to

change its momentum

To bring an object to a stop,

impulse applied = change in momentum ( as

momentum goes to zero.)

Check your concepts:

1. Which involves less impulse, a dish falling to

a tile floor, or a dish falling the same distance

to a carpet?Neither– the change in momentum is the same, so the

impulse required is the same. Mass doesn’t change, and

Δv is a free fall issue, depending on the height.

2. Why is basketball played on a wood or

composite floor rather than concrete?

The wooden or composite floor has more “give”,

which increases the impact time, therefore decreasing

the impact force, which means the player feels less

force on the body.

3. Why do athletes get injured on artificial grass

more often than on real grass?

Same as the basketball floor – the grass increases impact

time, so decreases impact force.

Section 3: Conservation of Momentum

What does conserved mean?

The amount of a quantity in a system is not

changed during an interaction

The amount you end with must be the same as

the amount you started with.

Conservation Laws

Energy

Energy cannot be created nor destroyed, it

merely changes form

Matter

Matter cannot be created nor destroyed, it

merely changes form

Momentum

Conservation of Momentum

In a closed system, the total amount of

momentum is conserved(constant)

Momentum can be transferred from one object

to another within the system

To change the amount of momentum of a system,

an outside force or impulse must be applied to

the system

Internal ones are action-reaction pairs and don’t

affect the momentum of the system

sitting in a car and pushing on the

dashboard is internal

pushing on the bumper is external

If there is no net force, there is no net impulse,

so no net change in momentum of the system

This leads to the Law of Conservation of

Momentum

In the absence of an

external force, the

momentum of a

system remains

unchanged

Equation:

m1v1i + m2v2i = m1v1f + m2v2f

m1 = mass of object 1

v1i = initial velocity of object 1

m2 = mass of object 2

v2i = initial velocity of object 2

v1f = final velocity of object 1

v2f = final velocity of object 2

Examples:

1. A 76 kg boater, initially at rest in a stationary

45 kg boat, steps out of the boat and onto the

dock. If the boater moves out of the boat with

a velocity of 2.5 m/s to the right, what is the

final velocity of the boat?

4.2m/s to the left

2. An astronaut is at rest on a space walk when

the tether line to the shuttle breaks. The

astronaut is able to throw a spare 10.0 kg

oxygen tank in a direction away from the

shuttle with a speed of 12.0 m/s, propelling

the astronaut back to the shuttle with a speed

of 1.90 m/s. What is the astronaut’s mass?

63.2kg

Section 4: CollisionsWhat is a collision?

A collision occurs when 2 objects try to

occupy the same space at the same time

IN COLLISIONS, MOMENTUM IS

CONSERVED

Net momentum before collision = net momentum after collision

2 Types of collisions:

Elastic collisions

Inelastic collisions

Elastic collisions

2 objects collide and fly apart

momentum is transferred from one object to the other

Example

Billiard balls

one moving towards the other when collide and bounce apart

momentum is transferred from the one with more initial momentum to the one with less initial momentum

Equation:

m1v1i + m2v2i = m1v1f + m2v2f (look familiar?)

Examples:

1. A 16.0 kg canoe moving to the left at 12.5

m/s makes an elastic head-on collision with a

14.0 kg raft moving to the right at 16.0 m/s.

After the collision, the raft moves to the left

at 14.4 m/s. Find the velocity of the canoe

after the collision. Disregard any effects of

the water.

14.1 m/s to the right

2. A 25.0 kg bumper car moving to the right at

5.00 m/s overtakes and collides elastically with

a 35.0 kg bumper car moving to the right.

After the collision, the 25.0 kg bumper car

slows to 1.50 m/s to the right, and the 35.0 kg

car moves at 4.50 m/s to the right. What is the

velocity of the 35 kg bumper car before the

collision?

2.0m/s to the right

Inelastic collisions

2 objects collide and stick together ( 2 objects become 1 object)

Example

A person catching a ball

When the person catches the ball, two objects, a ball and a person, become 1 object a ball-person

Equation:

m1v1i + m2v2i = (m1 + m2)vf

Examples:

1. An 1850 kg luxury sedan stopped at a traffic

light is struck from the rear by a compact car

with a mass of 975 kg. The two cars become

entangled as a result of the collision. If the

compact car was moving at a velocity of 22.0

m/s to the north before the collision, what is

the velocity of the entangled mass after the

collision?

7.58 m/s north

2. A dry cleaner throws a 22 kg bag of laundry

onto a stationary 9.0 kg cart. The cart and the

laundry bag begin moving at 3.0 m/s to the

right. What was the velocity of the laundry bag

before the collision?

4.2 m/s to the right

3. A 47.4 kg student runs down the sidewalk

and jumps with a horizontal speed of 4.20 m/s

onto a stationary skateboard. The student and

the skateboard move down the sidewalk with a

speed of 3.95 m/s. What was the mass of the

skateboard?

3.0 kg