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 velocityp=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 momentumapply 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 IMPORTANTThis leads to a new quantity: Impulse

ImpulseDefinition:

Product of force and time interval during which the force actsCauses momentum to change

Equation: Impulse = FΔt

But, from NII:F = ma

and from Chapter 2a = Δv/Δt

substitutingF = mΔv/Δt

rearranging FΔt = Δ(mv)So impulse = Δ momentumThis 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 allforce of impacttime of impactmass of objectvelocity of object

Impulse – Momentum in the Real World

Hitting a ball

Barrels on the Interstate at bridges

Catching a ball

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)

orIf you decrease the impact time, you will

increase the impact force

DON’T CONFUSE IMPULSE, IMPACT, AND MOMENTUM!!!!Impact is a forceImpulse is what is applied to an object to change it’s momentumTo 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 interactionThe amount you end with must be the same as the amount you started with.

Conservation LawsEnergy

Energy cannot be created nor destroyed, it merely changes formMatter

Matter cannot be created nor destroyed, it merely changes formMomentum

Conservation of MomentumIn 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 1v1i = initial velocity of object 1m2 = mass of object 2v2i = initial velocity of object 2v1f = final velocity of object 1v2f = 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 collisions2 objects collide and fly apartmomentum is transferred from one object to the otherExampleBilliard ballsone moving towards the other when collide and bounce apartmomentum 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 collisions2 objects collide and stick together ( 2 objects become 1 object)

ExampleA person catching a ballWhen 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