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Chapter 7
Energy
Topics:
•
•
•
•
•
Important forms of energy
How energy can be
transformed and transferred
Definition of work
Concepts of kinetic, potential,
and thermal energy
The law of conservation of
energy
Sample question:
When flexible poles became available for pole vaulting, athletes
were able to clear much higher bars. How can we explain this using
energy concepts?
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Slide 10-1
First, finishing up momentum
Example Problem 1. 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
Jack and the Skateboard -- Example 2
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
Bullet and Block -- Example 3
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
Professor on Ice -- Explosion Example
A professor of physics is going ice skating for the first time. He has
gotten himself into the middle of an ice rink and cannot figure out
how to make the skates work. Every motion he makes simply slips
on the ice and leaves him in the same place he started. He
decides that he can get off the ice by throwing his gloves in the
opposite direction.
(a) Suppose he has a mass M and his gloves have a mass m. If he
throws them as hard as he can away from him, and they leave his
hand with a velocity v. Explain whether or not he will move. If he
does move, calculate his velocity, V.
(b) Discuss his motion from the point of view of the forces acting on
him.
(c) If the ice rink is 10 m in diameter and the skater starts in the
center, estimate how long it will take him to reach the edge,
assuming there is no friction at all
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Slide 9-5
Finishing up momentum
•
Recoil
•
Elastic Collisions and Supernova
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Slide 10-3
Getting Started
From this class:
•
We will solve conservation of energy problems much like
conservation of momentum problems, looking at a system
before and after an interaction or change.
• Understanding energy will draw on your understanding of
motion and rotational motion.
Basics:
•
•
Energy comes in different forms.
•
Energy can be changed from one
form to another.
Energy can’t be created or
destroyed.
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Slide 10-8
Class Energy Question 1:
1. In your groups, summarize the reading on money. Use your
whiteboards.
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Slide 10-3
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
Class Energy Question 2:
2. What forms of energy do you know of?
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Slide 10-3
Forms of Energy
Mechanical Energy
Ug
K
Thermal
Energy
Us
Other forms include
E th
Echem
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Enuclear
Slide 10-10
Clicker Question 1
1. If a system is isolated, the total energy of the system
A. increases constantly.
B. decreases constantly.
C. is constant.
D. depends on work into the system.
E. depends on work out of the system.
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Slide 10-2
Answer
1. If a system is isolated, the total energy of the system
C. is constant.
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Slide 10-3
Class Energy Question 3
2. What do we mean by conservation of energy?
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Slide 10-3
The Basic Energy Model
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Slide 10-11
Types of Energy in a system
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Kinetic Energy => KE = 1/2 mv2
•
Gravitational Potential Energy => PEg = mgh
•
Spring Potential Energy => PEs = 1/2 k(L)2
(k is the stiffness of the spring and L is the change in length)
•
Thermal Energy => Eth
(measure of how hot something is => related to speed of atoms)
•
Chemical Energy => Echem
(Stored in chemical bonds - released in chemical reactions)
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Slide 10-4
Transferring Energy into of out of a system
•
Heat => Q
•
Work => W = F|| x
Energy that changes form within the system is said to be
transformed from one form to another
Energy that enters or leaves the system is transferred from the
system to the environment or vice versa.
Need to distinguish what is the system and what is the environment.
Forces from the environment can act on the system or objects in the
system (external forces) -- Can also add heat from the
environment
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Slide 10-4
Conservation of Energy
•
Full form
KE + PEg + PEs + Eth + Echem + … = Wext + Q
•
If there is no heat transferred in or out of the System and we are
limited to mechanical energy
KE + PEg + PEs + Eth = Wext
•
This becomes
KEi + Sum PEi + Wext = KEf + Sum PEf + Eth
•
Note thatEth can come from friction, drag, collisions, etc. as well
as Q
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Slide 10-4
Reading Quiz
2. Which of the following is an energy transfer?
A. Kinetic energy
B. Heat
C. Potential energy
D. Chemical energy
E. Thermal energy
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Slide 10-4
Reading Quiz
2. Which of the following is an energy transfer?
A. Kinetic energy
B. Heat
C. Potential energy
D. Chemical energy
E. Thermal energy
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Slide 10-4
Answer
2. Which of the following is an energy transfer?
B. Heat
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Slide 10-5
Reading Quiz
3. If you raise an object to a greater height, you are increasing
A. kinetic energy.
B. heat.
C. potential energy.
D. chemical energy.
E. thermal energy.
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Slide 10-6
Answer
3. If you raise an object to a greater height, you are increasing
C. potential energy.
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Slide 10-7
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
Checking Understanding
A child is on a playground swing, motionless at the highest point
of his arc. As he swings back down to the lowest point of his
motion, 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 10-14
Answer
A child is on a playground swing, motionless at the highest point
of his arc. As he swings back down to the lowest point of his
motion, what energy transformation is taking place?
D. Ug  K
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Slide 10-15
How can we check to see if the
Sum of KE + PE is conserved?
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Slide 10-13
Choosing the System
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Slide 10-16
Conceptual Example
A car sits at rest at the top of a hill. A small push sends it
rolling down a hill. After its height has dropped by 5.0 m, it is
moving at a good clip. Write down the equation for
conservation of energy, noting the choice of system, the
initial and final states, and what energy transformation has
taken place.
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Slide 10-17
Checking Understanding
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force.
Which box experiences the largest change in kinetic energy?
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Slide 10-18
Answer
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force.
Which box experiences the largest change in kinetic energy?
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Slide 10-19
Checking Understanding
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force.
Which box experiences the smallest change in kinetic
energy?
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Slide 10-20
Answer
Each of the boxes, with masses noted, is pulled for
10 m across a level, frictionless floor by the noted force.
Which box experiences the smallest change in kinetic
energy?
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Slide 10-21
Additional Clicker Questions
Trucks with the noted masses moving at the noted speeds crash
into barriers that bring them to rest with a constant force. Which
truck compresses the barrier by the largest distance?
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Slide 10-37
Answer
Trucks with the noted masses moving at the noted speeds crash
into barriers that bring them to rest with a constant force. Which
truck compresses the barrier by the largest distance?
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Slide 10-38
Solving Problems
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Slide 10-22
Example
A 200 g block on a frictionless surface is pushed against a
spring with spring constant 500 N/m, compressing the spring
by 2.0 cm. When the block is released, at what speed does it
shoot away from the spring?
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Slide 10-23
Example
A 2.0 g desert locust can achieve a takeoff
speed of 3.6 m/s (comparable to the best
human jumpers) by using energy stored in an
internal “spring” near the knee joint.
A. When the locust jumps, what energy
transformation takes place?
B. What is the minimum amount of energy
stored in the internal spring?
C. If the locust were to make a vertical leap,
how high could it jump? Ignore air
resistance and use conservation of energy
concepts to solve this problem.
D. If 50% of the initial kinetic energy is
transformed to thermal energy because of
air resistance, how high will the locust
jump?
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Slide 10-24