Download Chapter 11

Chapter 11 Lecture
physics
FOR SCIENTISTS AND ENGINEERS
a strategic approach
THIRD EDITION
randall d. knight
© 2013 Pearson Education, Inc.
Chapter 11 Work
Chapter Goal: To develop a more complete understanding
of energy and its conservation.
© 2013 Pearson Education, Inc.
Slide 11-2
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-3
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-3
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-5
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-6
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-7
Chapter 11 Preview
© 2013 Pearson Education, Inc.
Slide 11-8
Chapter 11 Reading Quiz
© 2013 Pearson Education, Inc.
Slide 11-9
Reading Question 11.1
The statement K = W is called the
A. Law of conservation of energy.
B. Work-kinetic energy theorem.
C. Kinetic energy equation.
D. Weight-kinetic energy theorem.
© 2013 Pearson Education, Inc.
Slide 11-10
Reading Question 11.1
The statement K = W is called the
A. Law of conservation of energy.
B. Work-kinetic energy theorem.
C. Kinetic energy equation.
D. Weight-kinetic energy theorem.
© 2013 Pearson Education, Inc.
Slide 11-11
Reading Question 11.2
The transfer of energy to a system by
the application of a force is called
A. Dot product.
B. Power.
C. Work.
D. Watt.
E. Energy transformations.
© 2013 Pearson Education, Inc.
Slide 11-12
Reading Question 11.2
The transfer of energy to a system by
the application of a force is called
A. Dot product.
B. Power.
C. Work.
D. Watt.
E. Energy transformations.
© 2013 Pearson Education, Inc.
Slide 11-13
Reading Question 11.3
A vector has magnitude C. Then the dot
product of the vector with itself,
is
A. 0.
B. C/2.
C. C.
D. 2C.
E. C2.
© 2013 Pearson Education, Inc.
Slide 11-14
Reading Question 11.3
A vector has magnitude C. Then the dot
product of the vector with itself,
is
A. 0.
B. C/2.
C. C.
D. 2C.
E. C2.
© 2013 Pearson Education, Inc.
Slide 11-15
Reading Question 11.4
The work done by a dissipative force
like friction, Wdiss, is
A. Always zero.
B. Always positive.
C. Always negative.
© 2013 Pearson Education, Inc.
Slide 11-16
Reading Question 11.4
The work done by a dissipative force
like friction, Wdiss, is
A. Always zero.
B. Always positive.
C. Always negative.
© 2013 Pearson Education, Inc.
Slide 11-17
Reading Question 11.5
Light bulbs are typically rated in terms of
their watts. The watt W is a measure of
A. The change in the bulb’s potential energy.
B. The energy consumed.
C. The force exerted on the bulb holder.
D. The power dissipated.
© 2013 Pearson Education, Inc.
Slide 11-18
Reading Question 11.5
Light bulbs are typically rated in terms of
their watts. The watt W is a measure of
A. The change in the bulb’s potential energy.
B. The energy consumed.
C. The force exerted on the bulb holder.
D. The power dissipated.
© 2013 Pearson Education, Inc.
Slide 11-19
Chapter 11 Content, Examples, and
QuickCheck Questions
© 2013 Pearson Education, Inc.
Slide 11-20
The Basic Energy Model
W > 0: The environment does work on the system and
the system’s energy increases.
W < 0: The system does work on the environment and
the system’s energy decreases.
© 2013 Pearson Education, Inc.
Slide 11-21
The Basic Energy Model
 The energy of a system is a sum of its kinetic energy
K, its potential energy U, and its thermal energy Eth.
 The change in system energy is:
1. Energy can be transferred to or from a system by
doing work W on the system. This process changes
the energy of the system: Esys = W.
2. Energy can be transformed within the system among
K, U, and Eth. These processes don’t change the
energy of the system: Esys = 0.
© 2013 Pearson Education, Inc.
Slide 11-22
QuickCheck 11.1
A skier is gliding down a slope at a constant speed.
What energy transformation is taking place?
A.
K  Ug
B.
Ug  K
C.
Eth  K
D.
Ug  Eth
E.
K  Eth
© 2013 Pearson Education, Inc.
Slide 11-23
QuickCheck 11.1
A skier is gliding down a slope at a constant speed.
What energy transformation is taking place?
A.
K  Ug
B.
Ug  K
C.
Eth  K
D.
Ug  Eth
E.
K  Eth
© 2013 Pearson Education, Inc.
Slide 11-24
Work and Kinetic Energy
 The word “work” has a
very specific meaning in
physics.
 Work is energy transferred
to or from a body or
system by the application
of force.
 This pitcher is increasing
the ball’s kinetic energy by
doing work on it.
© 2013 Pearson Education, Inc.
Slide 11-25
Work and Kinetic Energy
 Consider a force acting on
a particle which moves
along the s-axis.
 The force component Fs
causes the particle to
speed up or slow down,
transferring energy to or
from the particle.
 The force does work on the particle:
 The units of work are N m, where 1 N m = 1 kg m2/s2 = 1 J.
© 2013 Pearson Education, Inc.
Slide 11-26
The Work-Kinetic Energy Theorem
 The net force is the vector sum of all the forces
acting on a particle
.
 The net work is the sum Wnet = Wi, where Wi is the
work done by each force .
 The net work done on a particle causes the particle’s
kinetic energy to change.
© 2013 Pearson Education, Inc.
Slide 11-27
An Analogy with the Impulse-Momentum Theorem
 The impulse-momentum
theorem is:
 The work-kinetic energy
theorem is:
 Impulse and work are both
the area under a force graph,
but it’s very important to know
what the horizontal axis is!
© 2013 Pearson Education, Inc.
Slide 11-28
QuickCheck 11.2
A tow rope pulls a skier up the slope at constant speed.
What energy transfer (or transfers) is taking place?
A.
W  Ug
B.
WK
C.
W  Eth
D.
Both A and B.
E.
Both A and C.
© 2013 Pearson Education, Inc.
Slide 11-29
QuickCheck 11.2
A tow rope pulls a skier up the slope at constant speed.
What energy transfer (or transfers) is taking place?
A.
W  Ug
B.
WK
C.
W  Eth
D.
Both A and B.
E.
Both A and C.
© 2013 Pearson Education, Inc.
Slide 11-30
Work Done by a Constant Force
 A force acts with a constant
strength and in a constant
direction as a particle moves
along a straight line through a
displacement .
 The work done by this force is:
 Here  is the angle
© 2013 Pearson Education, Inc.
makes relative to
.
Slide 11-31
Example 11.1 Pulling a Suitcase
© 2013 Pearson Education, Inc.
Slide 11-32
Example 11.1 Pulling a Suitcase
© 2013 Pearson Education, Inc.
Slide 11-33
QuickCheck 11.3
A crane lowers a girder into place at constant speed.
Consider the work Wg done by gravity and the work
WT done by the tension in the cable. Which is true?
A.
Wg > 0 and WT > 0
B.
Wg > 0 and WT < 0
C.
Wg < 0 and WT > 0
D.
Wg < 0 and WT < 0
E.
Wg = 0 and WT = 0
© 2013 Pearson Education, Inc.
Slide 11-34
QuickCheck 11.3
A crane lowers a girder into place at constant speed.
Consider the work Wg done by gravity and the work
WT done by the tension in the cable. Which is true?
A.
Wg > 0 and WT > 0
B.
Wg > 0 and WT < 0
C.
Wg < 0 and WT > 0
D.
Wg < 0 and WT < 0
E.
Wg = 0 and WT = 0
© 2013 Pearson Education, Inc.
The downward force of gravity is in the
direction of motion  positive work.
The upward tension is in the direction
opposite the motion  negative work.
Slide 11-35
Tactics: Calculating the Work Done by a
Constant Force
© 2013 Pearson Education, Inc.
Slide 11-36
Tactics: Calculating the Work Done by a
Constant Force
© 2013 Pearson Education, Inc.
Slide 11-37
Tactics: Calculating the Work Done by a
Constant Force
© 2013 Pearson Education, Inc.
Slide 11-38
QuickCheck 11.4
Robert pushes the box to the
left at constant speed. In doing
so, Robert does ______ work
on the box.
A.
positive
B.
negative
C.
zero
© 2013 Pearson Education, Inc.
Slide 11-39
QuickCheck 11.4
Robert pushes the box to the
left at constant speed. In doing
so, Robert does ______ work
on the box.
A.
positive
B.
negative
C.
zero
Force is in the direction of displacement  positive work
© 2013 Pearson Education, Inc.
Slide 11-40
QuickCheck 11.5
A constant force pushes a particle through a
displacement
. In which of these three cases does
the force do negative work?
D.
E.
Both A and B.
Both A and C.
© 2013 Pearson Education, Inc.
Slide 11-41
QuickCheck 11.5
A constant force pushes a particle through a
displacement
. In which of these three cases does
the force do negative work?
D.
E.
Both A and B.
Both A and C.
© 2013 Pearson Education, Inc.
Slide 11-42
Example 11.2 Work During a Rocket Launch
© 2013 Pearson Education, Inc.
Slide 11-43
Example 11.2 Work During a Rocket Launch
© 2013 Pearson Education, Inc.
Slide 11-44
Example 11.2 Work During a Rocket Launch
© 2013 Pearson Education, Inc.
Slide 11-45
Example 11.2 Work During a Rocket Launch
© 2013 Pearson Education, Inc.
Slide 11-46
QuickCheck 11.6
Which force below does the most work? All three
displacements are the same.
A.
B.
C.
D.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
© 2013 Pearson Education, Inc.
sin60 = 0.87
cos60 = 0.50
Slide 11-47
QuickCheck 11.6
Which force below does the most work? All three
displacements are the same.
A.
B.
C.
D.
The 10 N force.
The 8 N force
The 6 N force.
They all do the same work.
© 2013 Pearson Education, Inc.
sin60 = 0.87
cos60 = 0.50
Slide 11-48
QuickCheck 11.7
A light plastic cart and a heavy
steel cart are both pushed with
the same force for a distance
of 1.0 m, starting from rest.
After the force is removed, the
kinetic energy of the light
plastic cart is ________ that of
the heavy steel cart.
A.
B.
C.
D.
greater than
equal to
less than
Can’t say. It depends on how big the force is.
© 2013 Pearson Education, Inc.
Slide 11-49
QuickCheck 11.7
A light plastic cart and a heavy
steel cart are both pushed with
the same force for a distance
of 1.0 m, starting from rest.
After the force is removed, the
kinetic energy of the light
plastic cart is ________ that of
the heavy steel cart.
A.
B.
C.
D.
greater than
Same force, same distance  same work done
equal to
Same work  change of kinetic energy
less than
Can’t say. It depends on how big the force is.
© 2013 Pearson Education, Inc.
Slide 11-50
Force Perpendicular to the Direction of Motion
 The figure shows a particle
moving in uniform circular
motion.
 At every point in the motion,
Fs, the component of the
force parallel to the
instantaneous displacement,
is zero.
 The particle’s speed, and hence its kinetic energy,
doesn’t change, so W = K = 0.
 A force everywhere perpendicular to the motion
does no work.
© 2013 Pearson Education, Inc.
Slide 11-51
QuickCheck 11.8
A car on a level road turns a
quarter circle ccw. You learned
in Chapter 8 that static friction
causes the centripetal
acceleration. The work done
by static friction is _____.
A.
positive
B.
negative
C.
zero
© 2013 Pearson Education, Inc.
Slide 11-52
QuickCheck 11.8
A car on a level road turns a
quarter circle ccw. You learned
in Chapter 8 that static friction
causes the centripetal
acceleration. The work done
by static friction is _____.
A.
positive
B.
negative
C.
zero
© 2013 Pearson Education, Inc.
Slide 11-53
The Dot Product of Two Vectors
 The figure shows two
vectors, and , with angle
 between them.
 The dot product of
is defined as:
and
 The dot product is also called the scalar product,
because the value is a scalar.
© 2013 Pearson Education, Inc.
Slide 11-54
The Dot Product of Two Vectors
 The dot product
© 2013 Pearson Education, Inc.
as  ranges from 0 to 180.
Slide 11-55
Example 11.3 Calculating a Dot Product
© 2013 Pearson Education, Inc.
Slide 11-56
The Dot Product Using Components
If
and
,
the dot product is the sum of the products
of the components:
© 2013 Pearson Education, Inc.
Slide 11-57
Example 11.4 Calculating a Dot Product
Using Components
© 2013 Pearson Education, Inc.
Slide 11-58
Work Done by a Constant Force
 A force acts with a
constant strength and
in a constant direction
as a particle moves along
a straight line through a
displacement
.
 The work done by this
force is:
© 2013 Pearson Education, Inc.
Slide 11-59
Example 11.5 Calculating Work Using the
Dot Product
© 2013 Pearson Education, Inc.
Slide 11-60
Example 11.5 Calculating Work Using the
Dot Product
© 2013 Pearson Education, Inc.
Slide 11-61
The Work Done by a Variable Force
To calculate the work done on an object by a force
that either changes in magnitude or direction as the
object moves, we use the following:
We must evaluate the integral either geometrically,
by finding the area under the curve, or by actually
doing the integration.
© 2013 Pearson Education, Inc.
Slide 11-62
Example 11.6 Using Work to Find the Speed
of a Car
© 2013 Pearson Education, Inc.
Slide 11-63
Example 11.6 Using Work to Find the Speed
of a Car
© 2013 Pearson Education, Inc.
Slide 11-64
Example 11.6 Using Work to Find the Speed
of a Car
© 2013 Pearson Education, Inc.
Slide 11-65
Example 11.6 Using Work to Find the Speed
of a Car
© 2013 Pearson Education, Inc.
Slide 11-66
Conservative Forces
 The figure shows a particle
that can move from A to B
along either path 1 or path
2 while a force is exerted
on it.
 If there is a potential energy
associated with the force,
this is a conservative force.
 The work done by as the
particle moves from A to B
is independent of the path
followed.
© 2013 Pearson Education, Inc.
Slide 11-67
Nonconservative Forces
 The figure is a bird’s-eye view
of two particles sliding across
a surface.
 The friction does negative
work: Wfric = kmgs.
 The work done by friction
depends on s, the distance
traveled.
 This is not independent of
the path followed.
 A force for which the work is not independent of the
path is called a nonconservative force.
© 2013 Pearson Education, Inc.
Slide 11-68
Mechanical Energy
 Consider a system of objects interacting via both
conservative forces and nonconservative forces.
 The change in mechanical energy of the system is
equal to the work done by the nonconservative forces:
 Mechanical energy isn’t
always conserved.
 As the space shuttle lands,
mechanical energy is being
transformed into thermal
energy.
© 2013 Pearson Education, Inc.
Slide 11-69
Example 11.8 Using Work and Potential Energy
© 2013 Pearson Education, Inc.
Slide 11-70
Example 11.8 Using Work and Potential Energy
© 2013 Pearson Education, Inc.
Slide 11-71
Example 11.8 Using Work and Potential Energy
© 2013 Pearson Education, Inc.
Slide 11-72
Finding Force from Potential Energy
 The figure shows an object moving
through a small displacement
s while being acted on by a
conservative force .
 The work done over this
displacement is:
 Because is a conservative force, the object’s potential
energy changes by U = −W = −FsΔs over this
displacement, so that:
© 2013 Pearson Education, Inc.
Slide 11-73
Finding Force from Potential Energy
 In the limit s  0, we
find that the force at
position s is:
 The force on the object is the negative of the
derivative of the potential energy with respect to
position.
© 2013 Pearson Education, Inc.
Slide 11-74
Finding Force from Potential Energy
 Figure (a) shows the
potential-energy diagram
for an object at height y.
 The force on the object
is (FG)y = mg.
 Figure (b) shows the
corresponding F-versus-y
graph.
 At each point, the value
of F is equal to the
negative of the slope
of the U-versus-y graph.
© 2013 Pearson Education, Inc.
Slide 11-75
Finding Force from Potential Energy
 Figure (a) is a more general
potential energy diagram.
 Figure (b) is the
corresponding F-versus-x
graph.
 Where the slope of U
is negative, the force is
positive.
 Where the slope of U is
positive, the force is negative.
 At the equilibrium points,
the force is zero.
© 2013 Pearson Education, Inc.
Slide 11-76
QuickCheck 11.9
A particle moves along the
x-axis with the potential
energy shown. At x = 4 m,
the x-component of the
force on the particle is
A.
–4 N.
B.
–2 N.
C.
0 N.
D.
2 N.
E.
4N
© 2013 Pearson Education, Inc.
Slide 11-77
QuickCheck 11.9
A particle moves along the
x-axis with the potential
energy shown. At x = 4 m,
the x-component of the
force on the particle is
A.
–4 N.
B.
–2 N.
C.
0 N.
D.
2 N.
E.
4 N.
© 2013 Pearson Education, Inc.
Slide 11-78
Thermal Energy
 Figure (a) shows a mass
M moving with velocity vobj
with macroscopic kinetic
energy Kmacro = ½ Mvobj2.
 Figure (b) is a microphysics
view of the same object.
 The total kinetic energy of
all the atoms is Kmicro.
 The total potential energy
of all the atoms is Umicro.
 The thermal energy of the
system is:
© 2013 Pearson Education, Inc.
Slide 11-79
Dissipative Forces
As two objects slide against
each other, atomic interactions
at the boundary transform the
kinetic energy Kmacro into thermal
energy in both objects.
K  Eth
Kinetic friction is a
dissipative force.
© 2013 Pearson Education, Inc.
Slide 11-80
Dissipative Forces
 The figure shows a box
being pulled at a constant
speed across a horizontal
surface with friction.
 Both the surface and the
box are getting warmer
as it slides.
 Dissipative forces always increase the thermal energy;
they never decrease it.
© 2013 Pearson Education, Inc.
Slide 11-81
Example 11.9 Calculating the Increase in
Thermal Energy
© 2013 Pearson Education, Inc.
Slide 11-82
Conservation of Energy
For a system with both internal interaction forces and
external forces, the energy equation is:
© 2013 Pearson Education, Inc.
Slide 11-83
Conservation of Energy
© 2013 Pearson Education, Inc.
Slide 11-84
The Basic Energy Model
For a system with both internal interaction forces and
external forces, Esys, the total energy of the system,
changes only if external forces transfer energy in or
out of the system.
© 2013 Pearson Education, Inc.
Slide 11-85
The Basic Energy Model
When a system is isolated, Esys, the total energy of the
system, is constant.
© 2013 Pearson Education, Inc.
Slide 11-86
Energy Bar Charts
We may express the conservation of energy concept
as an energy equation.
We may also represent this equation graphically with
an energy bar chart.
© 2013 Pearson Education, Inc.
Slide 11-87
QuickCheck 11.10
How much work is done
by the environment in the
process represented by
the energy bar chart?
A.
–2 J
B.
–1 J
C.
0J
D.
1J
E.
2J
© 2013 Pearson Education, Inc.
Slide 11-88
QuickCheck 11.10
How much work is done
by the environment in the
process represented by
the energy bar chart?
A.
–2 J
B.
–1 J
C.
0J
D.
1J
E.
2J
© 2013 Pearson Education, Inc.
The system started with 5 J but ends with 4 J.
1 J must have been transferred from the system
to the environment as work.
Slide 11-89
Problem-Solving Strategy: Solving Energy
Problems
© 2013 Pearson Education, Inc.
Slide 11-90
Problem-Solving Strategy: Solving Energy
Problems
© 2013 Pearson Education, Inc.
Slide 11-91
Example 11.10 Energy Bar Chart I
© 2013 Pearson Education, Inc.
Slide 11-92
Example 11.10 Energy Bar Chart I
© 2013 Pearson Education, Inc.
Slide 11-93
Example 11.11 Energy Bar Chart Il
© 2013 Pearson Education, Inc.
Slide 11-94
Example 11.11 Energy Bar Chart Il
© 2013 Pearson Education, Inc.
Slide 11-95
Example 11.12 Energy Bar Chart Ill
© 2013 Pearson Education, Inc.
Slide 11-96
Example 11.12 Energy Bar Chart Ill
© 2013 Pearson Education, Inc.
Slide 11-97
Power
 The rate at which energy is transferred or transformed
is called the power P.
 The SI unit of power is the
watt, which is defined as:
Highly trained athletes have a tremendous
power output.
1 watt = 1 W = 1 J/s
 The English unit of power
is the horsepower, hp.
1 hp = 746 W
© 2013 Pearson Education, Inc.
Slide 11-98
Example 11.13 Choosing a Motor
© 2013 Pearson Education, Inc.
Slide 11-99
Example 11.13 Choosing a Motor
© 2013 Pearson Education, Inc.
Slide 11-100
Examples of Power
© 2013 Pearson Education, Inc.
Slide 11-101
Power
 When energy is transferred by a force doing work,
power is the rate of doing work: P = dW/dt.
 If the particle moves at velocity while acted on by
force , the power delivered to the particle is:
© 2013 Pearson Education, Inc.
Slide 11-102
QuickCheck 11.11
Four students run up the stairs in the time shown.
Which student has the largest power output?
© 2013 Pearson Education, Inc.
Slide 11-103
QuickCheck 11.11
Four students run up the stairs in the time shown.
Which student has the largest power output?
© 2013 Pearson Education, Inc.
Slide 11-104
Example 11.14 Power Output of a Motor
© 2013 Pearson Education, Inc.
Slide 11-105
Example 11.14 Power Output of a Motor
© 2013 Pearson Education, Inc.
Slide 11-106
Chapter 11 Summary Slides
© 2013 Pearson Education, Inc.
Slide 11-107
General Principles
© 2013 Pearson Education, Inc.
Slide 11-108
General Principles
© 2013 Pearson Education, Inc.
Slide 11-109
General Principles
© 2013 Pearson Education, Inc.
Slide 11-110
Important Concepts
© 2013 Pearson Education, Inc.
Slide 11-111
Important Concepts
© 2013 Pearson Education, Inc.
Slide 11-112
Important Concepts
© 2013 Pearson Education, Inc.
Slide 11-113
Important Concepts
© 2013 Pearson Education, Inc.
Slide 11-114