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Lecture Outline
Chapter 5
College Physics, 7th Edition
Wilson / Buffa / Lou
© 2010 Pearson Education, Inc.
Chapter 5
Work and Energy
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Units of Chapter 5
Work Done by a Constant Force
Work Done by a Variable Force
The Work–Energy Theorem: Kinetic Energy
Potential Energy
Conservation of Energy
Power
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5.1 Work Done by a Constant Force
Definition of work:
The work done by a constant force acting on an
object is equal to the product of the magnitudes of the
displacement and the component of the force parallel
to that displacement.
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5.1 Work Done by a Constant Force
No Motion = No Work
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5.1 Work Done by a Constant Force
If the force is at an angle to the displacement,
as in (c), a more general form for the work
must be used:
Unit of work: newton • meter (N • m)
1 N • m is called 1 joule.
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5.1 Work Done by a Constant Force
• For example:
– The work done by a force of 25 N on an object
as the object moves parallel displacement of 2.0
m. Calculate work.
5.1 Work Done by a Constant Force
• For example:
– What 50 Joules of work are produced in a 10 m
distance, how much force was applied to the
system?
Question 5.1 To Work or Not to Work
Is it possible to do work on an
a) yes
object that remains at rest?
b) no
5.1 Work Done by a
Constant Force
If the force (or a component) is
in the direction of motion, the
work done is positive.
If the force (or a component) is
opposite to the direction of
motion, the work done is
negative.
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Question 5.2a Friction and Work I
A box is being pulled
across a rough floor at a
constant speed. What
can you say about the
work done by friction?
a) friction does no work at all
b) friction does negative work
c) friction does positive work
5.1 Work Done by a Constant Force
• A student holds her 1.5 kg textbook out a
second story window until her arm is tired;
then she releases it.
– A.) How much work is done on the book by the
student in simply holding it out the window?
– B.) How much work is done by the force of
gravity during the time in which the book falls
3.0 m?
5.1 Work Done by a Constant Force
If there is more than one force acting on an
object, it is useful to define the net work:
The total, or net, work is defined as the work done
by all the forces acting on the object, or the scalar
sum of all those quantities of work.
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5.1 Work Done by a Constant Force
• A worker pulls a 40 kg
crate with a rope. The
coefficient of kinetic
friction between crate
and floor is 0.550. If
he moves the crate
with a constant
velocity for a distance
of 7.00 m, how much
work is done?
5.1 Work Done by a Constant Force
• A passenger at an airport pulls a rolling
suitcase by its handle. If the force used is
10N and the handle makes an angle of 25
degrees to the horizontal, what is the work
done by the pulling force while the
passenger walks 200 m?
Question 5.3 Force and Work
a) one force
A box is being pulled up a rough
b) two forces
incline by a rope connected to a
c) three forces
pulley. How many forces are doing
work on the box?
d) four forces
e) no forces are doing work
5.2 Work Done by a Variable Force
The force exerted by a
spring varies linearly
with the displacement:
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5.2 Work Done by a Variable Force
• An applied force stretches a spring and as the
spring is stretched, the restoring force becomes
greater.
• For most springs, the spring force is directly
proportional to change in length of the spring.
• Force on the spring varies with x (so force is a
function of position).
• Called Hooke’s Law
• W = ½ kx2
Question 5.14 Elastic Potential Energy
How does the work required to
a) same amount of work
stretch a spring 2 cm compare
b) twice the work
with the work required to
c) four times the work
stretch it 1 cm?
d) eight times the work
5.2 Work Done by a Variable Force
• A 0.15 kg mass is attached to
a vertical spring and hangs at
rest at a distance of 4.6 cm
below its original position. An
additional 0.50 kg mass is
then suspended from the first
mass and the system is
allowed to descend to a new
equilibrium. What is the total
extension of the spring?
5.3 The Work–Energy Theorem:
• Work is something done on objects,
whereas energy is something objects
possess.
• When something possesses energy it has the
ability to do _______.
• No _________ = No _________
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5.3 The Work–Energy Theorem
• Consider an object at rest on a frictionless
surface.
• A horizontal force acts on the object and
sets it in motion.
• Work is being done on the object, but where
does that work go?
–
5.3 The Work–Energy Theorem:
Kinetic Energy
Kinetic energy is therefore defined:
The net work on an object changes its
kinetic energy.
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Question 5.5a Kinetic Energy I
By what factor does the
a) no change at all
kinetic energy of a car
b) factor of 3
change when its speed
c) factor of 6
is tripled?
d) factor of 9
e) factor of 12
5.3 The Work–Energy Theorem:
Kinetic Energy
We can use this relation to calculate the
work done:
W = K - K0
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5.3 The Work–Energy Theorem:
Kinetic Energy
This relationship is called the work–energy theorem.
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5.3 The Work–Energy Theorem:
Kinetic Energy
• A shuffleboard player pushes a 0.25 kg
puck that is initially at rest such that a
constant horizontal force of 6.0 N acts on it
through a distance of 0.50m. (Neglect
friction)
– A.) What are the kinetic energy and the speed
of the puck after the force is removed?
– B.) How much work would be required to bring
the puck to rest?
5.3 The Work–Energy Theorem:
Kinetic Energy
• In a football game, a 140 kg guard runs at a
speed of 4 m/s, and a 70 kg free safety
moves at 8 m/s. Which of the following is a
correct statement?
–
–
–
–
A.) Players have the same kinetic energy.
B.) Safety has 2x as much kinetic energy.
C.) Guard has 2x as much kinetic energy.
D.) Safety has 4x as much kinetic energy.
5.4 Potential Energy
Potential energy may be thought of as stored
work, such as in a compressed spring or an
object at some height above the ground.
Work done also changes the potential energy
(U) of an object.
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5.4 Potential Energy
We can, therefore, define the potential
energy of a spring; note that, as the
displacement is squared, this expression is
applicable for both compressed and
stretched springs.
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5.4 Potential Energy
Gravitational
potential energy:
Most well
known type
Formula?
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Question 5.16 Down the Hill
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the greater
speed at the bottom of its ramp?
d) same speed
for all balls
a
b
c
5.4 Potential Energy
• To walk 1000m on level
ground, a 60 kg person
requires an expenditure of
about 100,000 J of energy.
What is the total amount
of energy required if the
walk is extended another
1000m along a 5 degree
incline. (Neglect friction)
5.4 Potential Energy
• A 0.50 kg ball is
thrown vertically
upward with an initial
velocity of 10 m/s.
– A.) What is the change
in the ball’s kinetic
energy between the
starting point and the
ball’s maximum
height?
– B.) What is the change
in the ball’s potential
energy?
5.4 Potential Energy
Only changes in potential energy are
physically significant; therefore, the point
where U = 0 may be chosen for convenience.
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5.5 Conservation of Energy
Some physical quantities are conserved,
meaning constant.
We observe that, once all forms of energy are
accounted for, the total energy of an isolated
system does not change. This is the law of
conservation of energy:
The total energy of an isolated system is always
conserved.
[Energy can never be created nor destroyed…only
converted to different forms]
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5.5 Conservation of Energy
• We define a conservative force:
• A force is said to be conservative if the work
done by it in moving an object is
independent of the object’s path.
• Force depends only on the initial and final
positions of an object.
• What does it mean to be independent of
path?
5.5 Conservation of Energy
So, what types of forces are conservative?
Gravity is one; the work done by gravity
depends only on the difference between the
initial and final height, and not on the path
between them.
Similarly, a nonconservative force:
A force is said to be nonconservative if the work
done by it in moving an object does depend on the
object’s path.
The quintessential nonconservative force is
friction.
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5.5 Conservation of Energy
We define the total mechanical energy:
Sum of kinetic and potential energies
The sum of these are _________
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5.5 Conservation of Energy
For a conservative force:
Total Mechanical Energy is constant
E = E0
For nonconservative forces, mechanical
energy is usually lost.
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5.5 Conservation of Energy
• A painter on a scaffold drops a 1.5 kg can of
paint from a height of 6.00m.
– A.) What is the kinetic energy of the can when
the can is at a height of 4.00m?
– B.) With what speed will the can hit the
ground? (Neglect air resistance)
5.5 Conservation of Energy
Three balls of equal mass are projected with
the same speed in different locations.
If air resistance is
neglected, which ball
would you expect to
strike the ground with
the greatest speed:
a.) ball 1
b.) ball 2
c.) ball 3
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d.) all balls same
5.5 Conservation of Energy
If a nonconservative force or forces are
present, the work done by the net
nonconservative force is equal to the change
in the total mechanical energy.
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5.5 Conservation of Energy
• A skier with a mass of
80 kg starts from rest
at the top of a slope
and skis down from an
elevation of 110 m.
The speed of the skier
at the bottom of the
slope is 20 m/s.
– A.) Show that the
system is
nonconservative.
– B.) How much work is
done?
5.6 Power
The average power is the total amount of
work done divided by the time taken to do the
work.
S.I. Unit: J/s = Watt (W)
1 horsepower (hp) = 746 Watts
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Question 5.21a Time for Work I
Mike applied 10 N of force over 3 m in
a) Mike
10 seconds. Joe applied the same force
b) Joe
over the same distance in 1 minute.
Who did more work?
c) both did the same work
Question 5.21b Time for Work II
Mike performed 5 J of work in
a) Mike produced more power
10 secs. Joe did 3 J of work
b) Joe produced more power
in 5 secs. Who produced the
c) both produced the same
greater power?
amount of power
5.6 Power
• A crane hoist lifts a load of 1.0 metric ton a
vertical distance of 25 m in 9.0 s at a
constant velocity. How much useful work is
done by the hoist each second?
5.6 Power
• The motors of two vacuum cleaners have
net power outputs of 1.00 hp and 0.500 hp,
respectively.
– A.) How much work in Joules can each motor
do in 3.00 min?
– B.) How long does each motor take to do 97.0
kJ of work?
5.6 Power
Mechanical efficiency:
The measure of what you get out for what
you put in.
The efficiency of any real system is always
less than 100%.
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5.6 Power
• The motor of an electric drill with an
efficiency of 80% has a power input of 600
Watts. How much useful work is done by
the drill in 30 seconds?
5.6 Power
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Review of Chapter 5
Work done by a constant force is the
displacement times the component of force in
the direction of the displacement.
Kinetic energy is the energy of motion.
Work–energy theorem: the net work done on
an object is equal to the change in its kinetic
energy.
Potential energy is the energy of position or
configuration.
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Review of Chapter 5
The total energy of the universe, or of an
isolated system, is conserved.
Total mechanical energy is the sum of kinetic
and potential energy. It is conserved in a
conservative system.
The net work done by nonconservative forces
is equal to the change in the total mechanical
energy.
Power is the rate at which work is done.
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