Chapter 14
Work, Power, and Machines
14.1 Work and Power
What Is Work?
When does a force do
work?
In science, work is the
product of force and
distance.
What Is Work?
For a force to do
work on an object,
the force must cause
the object to move.
•no movement=no
work done.
Any force not acting in the
direction of motion does no
work on an object.
Calculating Work
Work = force x distance
Units of Work
The joule (J) is the SI unit of
work. A joule is equal to 1
newton-meter.
****When using SI units in the work
formula, the force is in newtons, and
distance is in meters.
Calculating Work
Using the Work Formula
A weight lifter raises a 1600newton barbell to a height of
2.0 meters.
Calculating Work
Using the Work Formula
A weight lifter raises a 1600newton barbell to a height of
2.0 meters.
W=fd
W=1600 x 2
W= 3200J
Work Practice
1. A crane uses an average force
of 5200 N to lift a girder 25 m
2. The brakes on a bicycle apply
125 N of frictional force to the
wheels as it travels 14.0 m
Work Practice
1.
A crane uses an average force of 5200 N
to lift a girder 25 m
W=fd
W=5200N x 25m
W = 130,000J
2. The brakes on a bicycle apply 125 N of
frictional force to the wheels as it travels
14.0 m
W=fd
W=125N x 14m
W = 1750J
Work Practice
3. While rowing, John exerts a
force of 165 N per stroke while
pulling the oar 0.8 m. How
much work is done in 30
strokes?
4. A 900-N mountain climber
scales a 100-m cliff
Work Practice
3. While rowing, John exerts a force
of 165 N per stroke while pulling
the oar 0.8 m. How much work is
done in 30 strokes?
W=fd
W=165N x 0.8m
W=132J
4. A 900-N mountain climber scales a
100m cliff
W=fd
W=900N x 100m
W=90,000J
Work Practice
5. A turtle slowly crawls along
carrying a bird feather on its
back. It passes an elephant
standing still with five large
lions on its back. Who is doing
more work, the turtle or the
elephant? Explain.
Work Practice
5.
A turtle slowly crawls along carrying a
bird feather on its back. It passes an
elephant standing still with five large
lions on its back. Who is doing more
work, the turtle or the elephant?
Explain.
W=fd
The turtle, because the elephant
is not moving. W=f x 0, therefore
The elephant’s work is 0
What Is Power?
How are work and power
related?
Power is the rate of doing
work.
To increase power,
• increase the amount of work done in a given time
•you can do a given amount of work in less time.
Calculating Power
Calculating Power
When using SI units in the
power formula, work is
measured in joules (J), and time
is measured in seconds (s).
The SI unit of power is the watt
(W), which is equal to one joule
per second.
Calculating Power
You exert a vertical force of 72
newtons to lift a box to a height of
1.0 meter in a time of 2.0 seconds.
How much power is used to lift the
box?
Calculating Power
You exert a vertical force of 72
newtons to lift a box to a height of
1.0 meter in a time of 2.0 seconds.
How much power is used to lift the
box?
W=fd W=72N x 1m W=72J
P=w/t P = 72J/2s
P = 36Watts
Calculating Power
1. Your family is moving to a
new apartment. While lifting a
box 1.5 m straight up to put it
on a truck, you exert an
upward force of 200 N for 1.0 s.
How much power is required to
do this?
Calculating Power
1. Your family is moving to a new
apartment. While lifting a box 1.5 m
straight up to put it on a truck, you exert
an upward force of 200 N for 1.0 s. How
much power is required to do this?
W=fd
P=W/t
W=200N x 1.5m
P = 300J / 1s
W = 300J
P = 300w
Calculating Power
2. You lift a book from the floor
to a bookshelf 1.0 m above the
ground. How much power is
used if the upward force is 15.0
N and you do the work in 2.0 s?
Calculating Power
2. You lift a book from the floor to a
bookshelf 1.0 m above the ground. How
much power is used if the upward force is
15.0 N and you do the work in 2.0 s?
P = w/t
P = (15N x 1m) / 2s
P = 7.5w
Calculating Power
3. You
apply a horizontal force of 10.0 N
to pull a wheeled suitcase at a
constant speed of 0.5 m/s across flat
ground. How much power is used?
(Hint: The suitcase moves 0.5 m/s.
Consider how much work the force
does each second and how work is
related to power.)
Calculating Power
3. You apply a horizontal force of 10.0 N to pull a
wheeled suitcase at a constant speed of 0.5 m/s
across flat ground. How much power is used?
(Hint: The suitcase moves 0.5 m/s. Consider how
much work the force does each second and how
work is related to power.)
P=w/t
P = 10N x 0.5m / 1s
P = 5w
Power Practice
1. John does 3960 J of work on the
oars in 60 s
2. A mechanic does 5350 J of work
to lift a car 0.5 m in 50 s
3. Anna weighs 565 N and goes up
3.25 m vertically by stairs. What
is power if her time is 12.6 s?
Power Practice
1.
John does 3960 J of work on the oars in
60 s
P = 3960J / 60s = 66w
2.
A mechanic does 5350 J of work to lift a
car 0.5 m in 50 s
P = 5350J /50s = 107w
3.
Anna weighs 565 N and goes up 3.25 m
vertically by stairs. What is power if her
time is 12.6 s?
P = 565N x 3.25 / 12.6s = 145.73w
James Watt and Horsepower
Another common unit of power is the
horsepower. One horsepower (hp) is
equal to about 746 watts.
Power Practice
Suppose you ride in a sleigh being
pulled by horses at 16 km/h.
Another sleigh being pulled at 10
km/h travels the same distance you
do. Which horses are more
powerful? How is speed related to
power?
Power Practice
Suppose you ride in a sleigh being pulled
by horses at 16 km/h. Another sleigh
being pulled at 10 km/h travels the
same distance you do. Which horses
are more powerful? How is speed
related to power? 16km/h because they
are capable of doing more work
(traveling farther in less time)
Assessment Questions
1. In which of the following cases is
work being done on an object?
a. pushing against a locked door
b. suspending a heavy weight with a
strong chain
c. pulling a trailer up a hill
d. carrying a box down a corridor
Assessment Questions
1. In which of the following cases is
work being done on an object?
a. pushing against a locked door
b. suspending a heavy weight with a
strong chain
c. pulling a trailer up a hill
d. carrying a box down a corridor
Assessment Questions
2. A tractor exerts a force of 20,000
newtons to move a trailer 8 meters.
How much work was done on the
trailer?
a. 2,500 J
b. 4,000 J
c. 20,000 J
d. 160,000 J
Assessment Questions
2. A tractor exerts a force of 20,000
newtons to move a trailer 8 meters.
How much work was done on the
trailer?
a. 2,500 J
b. 4,000 J
c. 20,000 J
d. 160,000 J
Assessment Questions
3. A car exerts a force of 500 newtons
to pull a boat 100 meters in
10 seconds. How much power does
the car use?
a. 5000 W
b. 6000 W
c. 50 W
d. 1000 W
Assessment Questions
3. A car exerts a force of 500 newtons
to pull a boat 100 meters in
10 seconds. How much power does
the car use?
a. 5000 W
b. 6000 W
c. 50 W
d. 1000 W
Assessment Questions
4. One horsepower is a unit of
power equal to
a.0.746 W.
b.1.0 W.
c.746 W.
d.2,000 W.
Assessment Questions
4. One horsepower is a unit of
power equal to
a.0.746 W.
b.1.0 W.
c.746 W.
d.2,000 W.
Chapter 14
Work, Power, and Machines
14.2 Work and Machines
Machines Do Work
A machine is a device that
changes a force.
Machines make work easier to
do by
–changing the size, direction,
or distance over which a
force acts.
Work Input and Work Output
How are work input and
work output related for a
machine?
Because of friction, the work
done by a machine is always
less than the work done on the
machine.
Work Input and Work Output
Work Input to a Machine
• The force exerted on a machine
is the input force.
• The distance the input force
acts through is the input
distance.
work input = input force X input distance
Work Input and Work Output
Work Output of a Machine
• force exerted by a machine =
output force
• The distance the output force is
exerted through = output distance.
work output of a machine = output
force X output distance.
Work Input and Work Output
All machines use some amount
of input work to overcome
friction.
Assessment Questions
1. What is the output distance of a machine
that requires 2 newtons of force exerted
over 6 meters and whose output force is
4 newtons?
a. 2 meters
b. 3 meters
c. 6 meters
d. 12 meters
Assessment Questions
1. What is the output distance of a machine
that requires 2 newtons of force exerted
over 6 meters and whose output force is
4 newtons?
a. 2 meters
b. 3 meters
c. 6 meters
d. 12 meters
Assessment Questions
2. The work output of a machine is
always greater than the work input
to the machine.
True
False
Assessment Questions
2. The work output of a machine is
always greater than the work input
to the machine.
True
False
Chapter 14
Work, Power, and Machines
14.3 Mechanical
Advantage and Efficiency
Mechanical Advantage
The mechanical advantage of a
machine is the number of
times that the machine
increases an input force.
•MA greater than one multiplies the
input force
•MA less than one increases the
distance and speed
Mechanical Advantage
Mechanical Advantage
Ideal Mechanical Advantage
The ideal mechanical advantage (IMA)
of a machine is the mechanical
advantage in the absence of friction.
Because friction reduces mechanical
advantage, engineers often design
machines that use low-friction
materials and lubricants.
Mechanical Advantage
Because friction is always present,
the actual mechanical advantage is
always less than the ideal
mechanical advantage
Calculating Mechanical Advantage
Calculating Mechanical Advantage
Calculating IMA
A woman drives her car up onto
wheel ramps to perform some
repairs. If she drives a distance of
1.8 meters along the ramp to raise
the car 0.3 meter, what is the ideal
mechanical advantage (IMA) of the
wheel ramps?
Calculating Mechanical Advantage
Calculating IMA
A woman drives her car up onto wheel ramps
to perform some repairs. If she drives a
distance of 1.8 meters along the ramp to raise
the car 0.3 meter, what is the ideal mechanical
advantage (IMA) of the wheel ramps?
Input distance = 1.8m
Output distance = 0.3m
IMA = input distance = 1.8m = 6
pit[it distance
0.3m
MA Example
• Calculate the mechanical
advantage of a ramp that is 5.0 m
long and 1.5 m high
MA Example
• Calculate the mechanical
advantage of a ramp that is 5.0 m
long and 1.5 m high
IMA = input/output
IMA = 5m / 1.5m
IMA =
Calculating Mechanical Advantage
1. A student working in a grocery store
after school pushes several grocery
carts together along a ramp. The ramp
is 3 meters long and rises 0.5 meter.
What is the ideal mechanical
advantage of the ramp?
Calculating Mechanical Advantage
1. A student working in a grocery store
after school pushes several grocery carts
together along a ramp. The ramp is 3
meters long and rises 0.5 meter. What is the
ideal mechanical advantage of the ramp?
IMA = input distance / output distance
IMA = 3m / .5m
IMA = 6
Calculating Mechanical Advantage
2. A
construction worker
moves a crowbar through a
distance of 0.50 m to lift a
load 0.05 m off of the
ground. What is the IMA of
the crowbar?
Calculating Mechanical Advantage
2. A
construction worker moves a
crowbar through a distance of 0.50 m
to lift a load 0.05 m off of the ground.
What is the IMA of the crowbar?
IMA = input distance / output distance
IMA = .5m / .05m
IMA = 10
Calculating Mechanical Advantage
3. The
IMA of a simple
machine is 2.5. If the output
distance of the machine is
1.0 m, what is the input
distance?
Calculating Mechanical Advantage
3. The
IMA of a simple machine is 2.5. If
the output distance of the machine is
1.0 m, what is the input distance?
IMA = input distance / output distance
2.5 = input / 1m
2.5m = input distance
MA Practice
1. A ramp is 6.0 m long and 1.5 m
high
2. An automobile jack lifts a 9900 N
car with an input force of 150 N
3. A sailor pulls down on a sail
weighing 140 N with a force of
140 N
MA Practice
1.
A ramp is 6.0 m long and 1.5 m high
IMA = in distance / out distance
IMA = 6m / 1.5m
IMA = 4m
2.
An automobile jack lifts a 9900 N car with an
input force of 150 N
MA = out force / in force
MA = 9900N / 150N
MA = 66
3.
A sailor pulls down on a sail weighing 140 N with
a force of 140 N
MA = out force / in force
MA = 140N / 140N
MA = 1
Efficiency
Why is the efficiency of a machine
always less than 100 percent?
The percentage of the work input
that becomes work output is the
efficiency of a machine.
Because there is always some friction, the
efficiency of any machine is always less
than 100 percent.
Efficiency
Efficiency is usually expressed as a
percentage.
Efficiency
If a machine requires 10.0 J of work
input to operate, then the work output
is 75% of 10.0 J.
Efficiency Example
• Alice and Jim calculate that
they must do 1800 J of work
to push a piano up a ramp.
Because of friction, they
actually must do 2400 J of
work. What is the efficiency?
Efficiency Example
• Alice and Jim calculate that they must do
1800 J of work to push a piano up a
ramp. Because of friction, they actually
must do 2400 J of work. What is the
efficiency?
Efficiency = work out / work in x 100%
Eff = 1800J / 2400J x 100%
Eff = 75%
How can efficiency be maximized?
Reducing friction increases the
efficiency of a machine.
–Roller bearings reduce the friction
of the rotating wheels because
rolling friction is less than sliding
friction.
–To further reduce the rolling
friction, the roller bearings are also
lubricated with grease.
Assessment Questions
1. Which statement about the actual mechanical
advantage of a machine is true?
a. The actual mechanical advantage is greater than
one if the input force is greater than the output
force.
b. The actual mechanical advantage of a machine is
greater than its ideal mechanical advantage when
the output force is greater than the input force.
c. The actual mechanical advantage of a machine is
always less than its ideal mechanical advantage.
d. The actual mechanical advantage of a machine is
never affected by friction.
Assessment Questions
1. Which statement about the actual mechanical
advantage of a machine is true?
a. The actual mechanical advantage is greater than
one if the input force is greater than the output
force.
b. The actual mechanical advantage of a machine is
greater than its ideal mechanical advantage when
the output force is greater than the input force.
c. The actual mechanical advantage of a machine is
always less than its ideal mechanical advantage.
d. The actual mechanical advantage of a machine is
never affected by friction.
Assessment Questions
2. If a lever raises a large rock 0.1
meters when the other end of the
lever moves downward 2 meters,
what is the ideal mechanical
advantage of the lever?
a. 0.05
b. 0.5
c. 2
d. 20
Assessment Questions
2. If a lever raises a large rock 0.1
meters when the other end of the
lever moves downward 2 meters,
what is the ideal mechanical
advantage of the lever?
a. 0.05
IMA = in dist / out dist
b. 0.5
IMA = 2m / .1m
c. 2
d. 20
Assessment Questions
3. A machine is used to accomplish 300 J
of work. If the efficiency of the machine
is 60 percent, what is the necessary work
input?
a. 180 J
b. 360 J
c. 500 J
d. 750 J
Assessment Questions
3. A machine is used to accomplish 300 J
of work. If the efficiency of the machine
is 60 percent, what is the necessary work
input?
a. 180 J Eff = work out / work in x 100%
b. 360 J 60% = 300J / work in x 100%
c. 500 J .60 = 300J / work in
d. 750 J
Assessment Questions
4. The efficiency of any machine is
less than 100% because of losses
due to friction.
True
False
Assessment Questions
4. The efficiency of any machine is
less than 100% because of losses
due to friction.
True
False
Chapter 14
Work, Power, and Machines
14.4 Simple Machines
What are the six types of
simple machines?
The six types of simple machines are
•the lever
•the wheel and axle
•the inclined plane
•the wedge
•the screw
•the pulley.
Levers
What determines the mechanical
advantage of the six types of
simple machines?
To calculate the ideal mechanical
advantage of any lever, divide the
input arm by the output arm.
Levers
A lever is a rigid bar that is
free to move around a fixed
point.
The fixed point the bar rotates
around is the fulcrum.
Levers
The input arm = the distance between
the input force and the fulcrum.
The output arm = the distance between
the output force and the fulcrum.
Levers are classified into three
categories based on the locations of
the input force, the output force, and
the fulcrum.
Le
IMA 
Lr
Levers
First-Class Levers
The fulcrum of a first-class lever is
always located between the input
force and the output force.
Depending on the fulcrum position,
the mechanical advantage can be
greater than 1, equal to 1, or less
than 1.
Levers
Second-Class Levers
• In a second-class lever, the output
force is located between the input
force and the fulcrum.
• The input distance is larger than the
output distance.
• The mechanical advantage of a
second-class lever is always greater
than 1.
Levers
Third-Class Levers
• The input force of a third-class lever
is located between the fulcrum and
the output force.
• The output distance over which the
third-class lever exerts its force is
larger than the input distance.
• The mechanical advantage of a thirdclass lever is always less than 1.
Wheel and Axle
To calculate the ideal mechanical
advantage of the wheel and axle,
divide the radius (or diameter)
where the input force is exerted by
the radius (or diameter) where the
output force is exerted.
Wheel and Axle
A wheel and axle is a simple machine
that consists of two disks or cylinders,
each one with a different radius.
The outer disk is the wheel and the
inner cylinder is the axle. The wheel
and the axle rotate together as a unit.
Wheel and Axle
The input force can be exerted on the wheel
or the axle.
• If the force is applied to the wheel, the
input distance is larger than the output
distance. The mechanical advantage is
greater than 1.
• If the force is applied to the axle, the
output distance is larger than the input
distance. The mechanical advantage is
less than 1.
Inclined Planes
The ideal mechanical advantage of
an inclined plane is the distance
along the inclined plane divided by
its change in height.
Inclined Planes
An inclined plane is a slanted surface
along which a force moves an object
to a different elevation.
• The distance traveled is the input
distance.
• The change in height of the ramp is
its output distance.
• The mechanical advantage of an
inclined plane is greater than 1.
Wedges and Screws
Wedges
A wedge is a V-shaped object
whose sides are two inclined
planes sloped toward each
other.
A wedge has a mechanical
advantage greater than 1.
Wedges and Screws
Screws
A screw is an inclined plane wrapped
around a cylinder.
For two screws of the same length, the
one whose threads are closer together
moves forward less for each turn of
the screw.
A screw has a mechanical advantage
greater than 1.
Pulleys
The ideal mechanical
advantage of a pulley or
pulley system is equal to the
number of rope sections
supporting the load being
lifted.
Pulleys
A pulley is a simple machine that
consists of a rope that fits into a
groove in a wheel.
• Pulleys produce an output force
that is different in size, direction, or
both, from that of the input force.
• The mechanical advantage of a
pulley can be equal to or greater
than 1.
Pulleys
Fixed Pulleys
A fixed pulley is a wheel attached in a
fixed location. The direction of the
exerted force is changed by a fixed
pulley, but the size of the force is not.
The ideal mechanical advantage of a
fixed pulley is always 1.
Pulleys
Movable Pulley
A movable pulley is attached to the
object being moved rather than to
a fixed location.
• Both sections of the rope pull
up with the same force.
• The movable pulley has a
mechanical advantage of 2.
Pulleys
Pulley System
A large mechanical advantage can be
achieved by combining fixed and movable
pulleys into a pulley system.
• The mechanical advantage depends on
how the pulleys are arranged.
• The ideal mechanical advantage of a
pulley system is equal to the number of
rope sections supporting the load being
lifted.
Compound Machines
• A compound machine is a combination of two
or more simple machines that operate together.
Most of the machines you use are compound
machines.
Assessment Questions
1. A bar that is rotating about a fixed
point is called a
a.fulcrum.
b.lever.
c. wedge.
d.compound machine.
Assessment Questions
2. A 3-meter-long ramp is used to lift a
piano to a moving truck, which is
1 meter off the ground. What is the
ideal mechanical advantage of the
ramp?
a. 1
b. 2
c. 3
d. 33
Assessment Questions
3. A machine, such as a bicycle, that
combines many simple machines
is known as a complex machine.
True
False