Important forms of energy

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Chapter 10 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
• Elastic collisions

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?
Slide 10-1
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Looking Back What You Already Know
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 1D motion and rotational motion.

From previous classes

• Energy comes in different forms.
• Energy cant be created or destroyed.
• Energy can be changed from one form to another.

Slide 10-8
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A Natural Money Called Energy
Key concepts

• Definition of the system.
• Transformations within the system.
• Transfers between the system and the environment.

Slide 10-9
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Forms of Energy
Other forms include
Slide 10-10
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The Basic Energy Model
Slide 10-11
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Work and Energy Work is done on a object when a
force acts on the object and moves it.
F
?x
Dragging a box across the floor by a rope.
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Work and Energy Work is done on a object when a
force acts on the object and moves it.
F
?x
Dragging a box across the floor by a rope.
Important Even though a force (F) acts, if the
object doesnt move (if ?x 0) then the work
done by force F is zero. The vectors F and ?x
dont need to be in the same direction.
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Work done by force F WF Fcos(?)?x F ?x
F
?x
?
F
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Work done by force F WF Fcos(?)?x F ?x
F
?x
?
F
When a force does work on an object, the object
gains or loses energy. In general, W ?E
EFinal - EInitial
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Work done by force F can be positive or
negative Positive if F is parallel to
?x Negative if F is anti-parallel to ?x
F ?x
F ?x
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Work can add or take away energy from a system
Work done to the system
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Work can add or take away energy from a system
Work done to the system
Work (a change in energy) can appear in the final
system as a change in kinetic energy (K) and/or a
change in potential energy.
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Definitions Kinetic Energy (the energy of
motion) of a mass M moving at speed V, K ½MV2.
Unit is the Joule (1 kgm2/s2).
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Definitions Kinetic Energy (the energy of
motion) of a mass M moving at speed V, K ½MV2.
Unit is the Joule (1 kgm2/s2). Gravitational
Potential Energy (the energy due to position in a
gravitational field) of a mass M at position
(xi,yi), Ug Mgyi. Joules
y
yi
x
xi
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Example. Increased kinetic energy the force of a
baseball pitchers hand on the ball does work on
the ball, giving it greater speed increased K
V 0
V 90 mph
W ?K
yInitial and yFinal are the same so theres no
change in Ug, just K.
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Example. Increased gravitational potential
energy you slowly lift a book (moving it at a
constant speed)
Work done on the book causes a change (an
increase, in this case) of the books
gravitational potential energy. W ?Ug Mg(yf
yi)
yFinal
Constant speed
M
yInitial
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Example. Decreased gravitational potential
energy you slowly lift a book down (moving it at
a constant speed)
Work done on the book causes a change (a
decrease, in this case) of the books
gravitational potential energy. W ?Ug Mg(yf
yi)
yInitial
Constant speed
M
yFinal
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Picture of Work as the area under a graph
F ( if parallel to ?x)
Positive Work
x
Negative Work
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Picture of Work as the area under a graph
F ( if parallel to ?x)
Positive Work
x
Negative Work
How does this compare to the graphical picture of
Impulse?
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Picture of Work as the area under a graph
F ( if parallel to ?x)
Positive Work
x
Negative Work
F
Impulse
How does this compare to the graphical picture of
Impulse?
t
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Example Problem You (35 kg) are running (2 m/s)
on the playground and fall down and skid to a
stop over 1 m scrapping your knee in the
process. What work does friction do on you
during your skid?
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Example Problem You (35 kg) are running (2 m/s)
on the playground and fall down and skid to a
stop over 1 m scrapping your knee in the
process. What work does friction do on you
during your skid?
Assuming youre running on a level playground,
your vertical position doesnt change, so your
gravitational potential energy is constant ?Ug
0.
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Example Problem You (35 kg) are running (2 m/s)
on the playground and fall down and skid to a
stop over 1 m scrapping your knee in the
process. What work does friction do on you
during your skid?
Assuming youre running on a level playground,
your vertical position doesnt change, so your
gravitational potential energy is constant ?Ug
0. Your Kinetic Energy ( ½Mv2) does change,
however Ki ½(35 kg)(2 m/s)2 and Kf 0 J, so
?K Kf Ki -70 J.
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Example Problem You (35 kg) are running (2 m/s)
on the playground and fall down and skid to a
stop over 1 m scrapping your knee in the
process. What work does friction do on you
during your skid?
Assuming youre running on a level playground,
your vertical position doesnt change, so your
gravitational potential energy is constant ?Ug
0. Your Kinetic Energy ( ½Mv2) does change,
however Ki ½(35 kg)(2 m/s)2 and Kf 0 J, so
?K Kf Ki -70 J. Wfriction ?E ?K -70
J. Friction does negative work on you (and you
slow down as a result). Lets check this
directly
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?x
fk
n 343 N
FBD
Angle betw/ fk and ?x directions
W (35 kg)(9.8 m/s2) 343 N
Wf (fk)(1 m)cos(180) -(µk)(343 N)(1 m)
definitely negative
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?x
fk
n 343 N
FBD
W (35 kg)(9.8 m/s2) 343 N
Wf (fk)(1 m)cos(180) -(µk)(343 N)(1 m)
definitely negative. We could find the
coefficient of kinetic friction since Wf -70 J.
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?x
fk
n 343 N
FBD
W (35 kg)(9.8 m/s2) 343 N
Wf (fk)(1 m)cos(180) -(µk)(343 N)(1 m)
definitely negative. We could find the
coefficient of kinetic friction since Wf -70
J. -70 J -(µk)(343 Nm) so µk (-70 J)/(-343
Nm)
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?x
fk
n 343 N
FBD
W (35 kg)(9.8 m/s2) 343 N
Wf (fk)(1 m)cos(180) -(µk)(343 N)(1 m)
definitely negative. We could find the
coefficient of kinetic friction since Wf -70
J. -70 J -(µk)(343 Nm) so µk (-70 J)/(-343
Nm)
J (for Joule)
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?x
fk
n 343 N
FBD
W (35 kg)(9.8 m/s2) 343 N
Wf (fk)(1 m)cos(180) -(µk)(343 N)(1 m)
definitely negative. We could find the
coefficient of kinetic friction since Wf -70
J. -70 J -(µk)(343 Nm) so µk (-70 J)/(-343
Nm) 0.20 µk
J
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Choosing the System
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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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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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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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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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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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Solving Problems
Slide 10-22
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Power

• Same mass...
• Both reach 60 mph...

Same final kinetic energy, but different times
mean different powers.
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Power is the rate at which work is done (W/?t).
It can also be written as the force necessary to
keep an object moving at constant velocity.
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Power is the rate at which work is done (W/?t).
It can also be written as the force necessary to
keep an object moving at constant velocity.
y
?t
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Power is the rate at which work is done (W/?t).
It can also be written as the force necessary to
keep an object moving at constant velocity.
v
F
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Power is the rate at which work is done (W/?t).
It can also be written as the force necessary to
keep an object moving at constant velocity.
Units of Power Joules/s or Watts W. 1 W is
the power necessary to do 1 J of Work in 1 second.
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Four toy cars accelerate from rest to their top
speed in a certain amount of time. The masses of
the cars, the final speeds, and the time to reach
this speed are noted in the table. Which car has
the greatest power?
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Answer
Four toy cars accelerate from rest to their top
speed in a certain amount of time. The masses of
the cars, the final speeds, and the time to reach
this speed are noted in the table. Which car has
the greatest power?
Slide 10-27
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Four toy cars accelerate from rest to their top
speed in a certain amount of time. The masses of
the cars, the final speeds, and the time to reach
this speed are noted in the table. Which car has
the smallest power?
Slide 10-28
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Answer
Four toy cars accelerate from rest to their top
speed in a certain amount of time. The masses of
the cars, the final speeds, and the time to reach
this speed are noted in the table. Which car has
the smallest power?
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• Data for one stage of the 2004 Tour de France
  show that Lance Armstrongs average speed was 15
  m/s, and that keeping Lance and his bike moving
  at this quick pace required a power of 450 W.
• What was the average forward force keeping Lance
  and his bike moving forward?
• To put this in perspective, compute what mass
  would have this weight.

Slide 10-32
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• Data for one stage of the 2004 Tour de France
  show that Lance Armstrongs average speed was 15
  m/s, and that keeping Lance and his bike moving
  at this quick pace required a power of 450 W.
• What was the average forward force keeping Lance
  and his bike moving forward? Fv P so F (450
  W/15 m/s) 30 N.
• To put this in perspective, compute what mass
  would have this weight.

Slide 10-32
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• Data for one stage of the 2004 Tour de France
  show that Lance Armstrongs average speed was 15
  m/s, and that keeping Lance and his bike moving
  at this quick pace required a power of 450 W.
• What was the average forward force keeping Lance
  and his bike moving forward? Fv P so F (450
  W/15 m/s) 30 N.
• To put this in perspective, compute what mass
  would have this weight. A little more than 3 kg.

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Additional Conceptual Question
Each of the 1.0 kg boxes starts at rest and is
then pushed for 2.0 m across a level,
frictionless floor by a rope with the noted
force. Which box has the highest final speed?
Slide 10-33
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Answer
Each of the 1.0 kg boxes starts at rest and is
then pushed for 2.0 m across a level,
frictionless floor by a rope with the noted
force. Which box has the highest final speed?
Slide 10-34
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Additional Conceptual Question
Each of the 1.0 kg boxes starts at rest and is
then pushed for 2.0 m across a level,
frictionless floor by a rope with the noted
force. Which box has the lowest final speed?
Slide 10-35
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Answer
Each of the 1.0 kg boxes starts at rest and is
then pushed for 2.0 m across a level,
frictionless floor by a rope with the noted
force. Which box has the lowest final speed?
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Additional Conceptual Question
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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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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Additional Conceptual Question
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 smallest distance?
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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 smallest distance?
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Additional Conceptual Question

• Three balls are thrown off a cliff with the same
  speed, but in different directions. Which ball
  has the greatest speed just before it hits the
  ground?
• Ball A
• Ball B
• Ball C
• All balls have the same speed

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Answer

• Three balls are thrown off a cliff with the same
  speed, but in different directions. Which ball
  has the greatest speed just before it hits the
  ground?
• All balls have the same speed

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Additional Conceptual Question

• I swing a ball around my head at constant speed
  in a circle with circumference 3 m. What is the
  work done on the ball by the 10 N tension force
  in the string during one revolution of the ball?
• 30 J
• 20 J
• 10 J
• 0 J

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Answer

• I swing a ball around my head at constant speed
  in a circle with circumference 3 m. What is the
  work done on the ball by the 10 N tension force
  in the string during one revolution of the ball?
• 0 J

Slide 10-46