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Chapter 9
Momentum
Topics:
• Impulse
• Momentum
• The impulse-momentum
theorem
• Conservation of momentum
• Inelastic collisions
Sample question:
Male rams butt heads at high speeds in a ritual to assert their
dominance. How can the force of this collision be minimized so as
to avoid damage to their brains?
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 9-1
Momentum
Momentum is the product of an object’s mass and its velocity:


p = mv
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Slide 9-10
Reading Quiz
1. Impulse is
A. a force that is applied at a random time.
B. a force that is applied very suddenly.
C. the area under the force curve in a
force-versus-time graph.
D. the interval of time that a force lasts.
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Slide 9-2
Answer
1. Impulse is
C. the area under the force curve in a
force-versus-time graph.
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Slide 9-3
Impulse
The force of the foot
on the ball is an
impulsive force.
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Slide 9-8
Graphical Interpretation of Impulse
J = Impulse = area under
the force curve  Favg t
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Slide 9-9
The Impulse-Momentum Theorem
Impulse causes a change in momentum:




J =pf - pi = ∆p
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Slide 9-11
Impulses and Forces in car
1.
Consider a car going at highway speeds colliding in a front-end
crashes
collision with a brick wall. Compare the impulse needed to bring
the passenger in the front seat to a stop if they are stopped by:
• Their seatbelt
• The dashboard
• An airbag
2. Rank the force being applied for each case.
(You will need to think about Delta t. Hint: the longer the distance
travelled while the force is being applied, the longer Delta t.)
A.
B.
C.
D.
E.
Dashboard = Seatbelt = Airbag
Dashboard > Seatbelt > Airbag
Airbag > Seatbelt > Dashboard
Dashboard > Airbag > Seatbelt
Seatbelt > Dashboard > Airbag
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Slide 9-12
Impulse graphs for dashboard, seatbelt, and airbag
on crash-test dummy
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Slide 9-10
Shut the Door
Imagine that you are sitting on your bed in your dorm room, and
suddenly you hear the voice of your ex coming down the hall. You
really want to avoid any contact (you broke things off a week ago),
and so you want to shut the door. But you don't have time to get up
and shut it and act like it wasn't on purpose. You need something
fast. Sitting beside you, you happen to have a superball (super
bouncy rubber ball) and a ball of clay that you fidget with when
you're studying on your bed.
What do you do? (Hint: Draw the momentum vectors before and
after.)
A.
B.
C.
D.
Throw the superball
Throw the clay ball
Throw either ball, it doesn’t matter
Not enough information to tell
Explain your answer and show why you chose one and not the
other.
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Slide 9-12
Momentum Diagrams/graphs for Shut the Door
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Slide 9-10
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Slide 9-15
Example
A 0.5 kg hockey puck slides to the right at 10 m/s. It is hit with
a hockey stick that exerts the force shown. What is its
approximate final speed?
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Slide 9-12
Checking Understanding
Two 1-kg stationary cue balls are struck by cue sticks. The cues
exert the forces shown. Which ball has the greater final speed?
A. Ball 1
B. Ball 2
C. Both balls have the same final speed
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Slide 9-13
Answer
Two 1-kg stationary cue balls are struck by cue sticks. The cues
exert the forces shown. Which ball has the greater final speed?
C. Both balls have the same final speed
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Slide 9-14
Reading Quiz
2. The total momentum of a system is conserved
A.
B.
C.
D.
always.
if no external forces act on the system.
if no internal forces act on the system.
never; momentum is only approximately
conserved.
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Slide 9-7
Answer
2. The total momentum of a system is conserved
A.
B.
C.
D.
always.
if no external forces act on the system.
if no internal forces act on the system.
never; momentum is only approximately
conserved.
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Slide 9-8
Forces During a Collision
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Slide 9-20
Impulse-Momentum Theorem and Conservation of Energy
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Slide 9-10
The Law of Conservation of Momentum
In terms of the initial and final total momenta:
r
 p f   pi
In terms of components:
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Slide 9-18
Start with this
Key Equation in
component form
r
 p f   pi
p
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f ,x
  pi, x
Slide 9-19
Example
A curling stone, with a mass of 20.0 kg, slides across the ice
at 1.50 m/s. It collides head on with a stationary 0.160-kg
hockey puck. After the collision, the puck’s speed is 2.50
m/s. What is the stone’s final velocity?
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Slide 9-20
Inelastic Collisions
For now, we’ll consider perfectly inelastic collisions:
A perfectly inelastic collision results whenever the two objects
move off at a common final velocity.
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Slide 9-21
Example
Jack stands at rest on a skateboard. The mass of Jack and
the skateboard together is 75 kg. Ryan throws a 3.0 kg ball
horizontally to the right at 4.0 m/s to Jack, who catches it.
What is the final speed of Jack and the skateboard?
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Slide 9-22
Example
A 10 g bullet is fired into a 1.0 kg wood block, where it
lodges. Subsequently, the block slides 4.0 m across a floor
(µk = 0.20 for wood on wood). What was the bullet’s speed?
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Slide 9-23
Forms of Energy
Mechanical Energy
 Favg t
Ug
K
Thermal
Energy
Us
Other forms include
E th
Echem
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Enuclear
Slide 10-10
Energy Question
2. What do we mean by conservation of energy?
(2-minute brainstorm)
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Slide 10-7
A “Natural Money” Called Energy
Income
System
Liquid
Asset:
Cash
Saved
Asset:
Stocks
Transfers
into and
out of
system
Transformations
within system
Key concepts:
Expenses
• Definition of the system.
• Transformations within the system.
• Transfers between the system and the environment.
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Slide 10-9
The Basic Energy Model
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Slide 10-11
Checking Understanding
A skier is moving down a slope at a constant speed. What energy
transformation is taking place?
A. K  Ug
B. Ug  Eth
C. Us  Ug
D. Ug  K
E. K  E th
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Slide 10-12
Answer
A skier is moving down a slope at a constant speed. What energy
transformation is taking place?
B. Ug  Eth
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Slide 10-13
Starting and Stopping
A car with a mass of 1 metric ton (1 metric ton = 1000 kg) speeds
up to highway speed from rest on a strait section of Central Blvd. A
little while later, the car comes to a stop as it approaches a red
light.
Left Side - Determine the net impulse and average net force on
the car as it goes from rest to highway speed.
Right Side - Determine the net impulse and average net force
on the car as it goes from highway speed to a complete stop.
Note: you will need to estimate the time each motion takes to find
the average net force. Think of your own experience with driving.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 9-12
Impulses in car crashes
1. Consider a car going at highway speeds colliding in a front-end
collision with a brick wall. Rank the impulses needed to bring the
passenger in the front seat to a stop if they are stopped
separately by:
• Their seatbelt
• The dashboard
• An airbag
A.
B.
C.
D.
E.
Dashboard = Seatbelt = Airbag
Dashboard > Seatbelt > Airbag
Airbag > Seatbelt > Dashboard
Dashboard > Airbag > Seatbelt
Seatbelt > Dashboard > Airbag
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Slide 9-12
Reading Quiz
3. In an inelastic collision, we make use of the fact that
A. impulse is conserved.
B. momentum is conserved.
C. force is conserved.
D. energy is conserved.
E. elasticity is conserved.
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Slide 9-6
Answer
3. In an inelastic collision, we make use of the fact that
B. momentum is conserved.
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Slide 9-7