Download Ch_11

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
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
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
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
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
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
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