Download 1 Work, Power, and Machines

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CHAPTER 13
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Work and Energy
SECTION
1 Work, Power, and Machines
KEY IDEAS
As you read this section, keep these questions in mind:
• What is work, and how is it measured?
• How are work and power related?
• How do machines make work easier?
What Is Work?
Imagine trying to lift the front end of a car without a
jack. You might exert a lot of force and not move the car
at all. Exerting all that force may seem like hard work,
but in scientific terms, you did no work at all.
In science, there are many different kinds of work.
Here, we will deal only with work against gravity. This
kind of work occurs when a force causes an object to
move away from Earth’s surface. You can use the equation
below to calculate the work done on an object:
work force distance
W Fd
In this equation, distance is the distance the object
moves above Earth’s surface. Work only occurs when the
object is moving. If the object is not moving, no work is
occurring.
READING TOOLBOX
Compare As you read
this section, create a table
comparing work, power,
and mechanical advantage.
Include the equations used
to calculate each, the units
used to measure each, and
the definition of each.
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1. Apply Concepts Is the
weightlifter doing any work
when she holds the barbell
motionless above her head?
Explain your answer.
This weightlifter did work on the
barbell to lift it over her head.
Work is measured in newton-meters (N • m). You can
also use joules (J) to measure work. One newton-meter
equals one joule. Remember that one newton is equal
to one kilogram-meter per second squared (kg • m/s2).
Therefore, one joule is also equal to one kilogram-meter
squared per second squared (kg • m2/s2):
1 N • m 1 J 1 kg • m2/s2
You can use different units for work to make solving
problems easier.
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Work and Energy
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Work, Power, and Machines continued
CALCULATING WORK FROM FORCE AND DISTANCE
Math Skills
2. Calculate A student lifts
an apple to a height of 1 m.
The apple weighs 1 N. How
much work does the student
do on the apple? Show your
work.
To calculate the amount of work done on an object, you
must know the force applied and the distance the object
moved. Let’s look at an example of how to calculate the
work done on an object. A crane uses an average force of
5,200 N to lift a metal beam 25 m into the air. How much
work does the crane do on the beam?
Step 1: List the given and
unknown values.
Given:
force,
F = 5,200 N
distance,
d = 25 m
Unknown:
work, W
Step 2: Write the equation.
W = Fd
Step 3: Insert the known
values and solve for the
unknown value.
W = (5,200 N) × (25 m)
W = 130,000 N • m
W = 130 kJ
So, the crane does about 130 kJ of work on the beam.
CALCULATING WORK FROM MASS AND DISTANCE
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3. Explain If the car were
being moved sideways,
could you determine the
force on the car by using the
weight equation? Explain
your answer.
If you know the mass of an object, you can calculate
how much work it takes to lift the object. For example,
suppose a car has a mass of 1,200 kg. A mechanic uses
an electric lift to raise the car 0.50 m off the ground. How
much work does the lift do on the car?
In order to use the work equation, you must know
the force exerted on the car. Because the car is being
lifted straight up, the force on the car is equal to the car’s
weight. Therefore, you can use the equation for weight,
w mg, to find the force on the car. In this equation, g is
free-fall acceleration (9.8 m/s2). Here’s how to solve this
problem:
Step 1: List the given and
unknown values.
Given:
mass,
m = 1,200 kg
distance,
d = 25 m
Unknown:
force,
F (equal to
weight, w)
work, W
Step 2: Write the equations.
w = mg
W = Fd
Step 3: Insert the known
values and solve for the
unknown values.
w = (1,200 kg) × (9.8 m/s2)
w = 12,000 kg • m/s2 = 12,000 N
W = (12,000 N) × (0.50 m)
W = 6,000 N • m = 6.0 kJ
So, the lift does about 6.0 kJ of work on the car.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Work and Energy
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Work, Power, and Machines continued
How Are Work and Power Related?
Like work, power has a very specific meaning in science. Power is the rate at which work is done or energy
is used. In other words, power is how much work is done
in a given amount of time. The equation for power is:
READING CHECK
4. Define What is power?
work
power _____
time
P _W_
t
The SI unit for power is the watt (W). One watt is the
amount of power needed to do one joule of work in one
second (1 J/s). Be careful not to confuse the symbol for
work, W, which is in italics, with the symbol for watt, W,
which is not in italics.
Power increases when more work is done in a given
amount of time. Power also increases when you do work
in less time. For example, imagine climbing a flight of
stairs slowly. Now, imagine running up the stairs. In both
cases, you do the same amount of work, because you
move your weight through the same distance. However,
it takes less time to climb the stairs running. Therefore,
your power output is higher if you run up the stairs.
Let’s look at an example of how to calculate power.
Lifting an elevator 18 m takes 100 kJ of work. If the
elevator moves 18 m in 20 s, what is the power output of
the elevator?
Step 1: List the given and
unknown values.
Given:
work,
W = 100 kJ
time,
t = 20 s
Step 2: Write the equation.
P = _W_
t
Step 3: Insert the known
values and solve for the
unknown value.
kJ
______
P = 100
20 s
P = 5 kJ/s = 5,000 J/s
READING CHECK
5. Identify Name two things
that can cause power output
to decrease.
Unknown:
power, P
P = 5,000 W = 5 kW
So, it takes about 5 kW of power to lift the elevator.
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Work and Energy
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Work, Power, and Machines continued
How Do Machines Make Work Easier?
READING CHECK
6. Describe How do
machines make work easier?
Many people think that machines reduce the amount
of work we have to do to move an object. However,
machines do not change the amount of work done on
an object. Instead, they make work easier by changing
the way the force is applied. For example, in the picture
below, the ramp increases the distance over which the
force is applied.
F = 225 N
W=F×d
W = 225 N × 1.00 m
W = 225 N · m = 225 J
d = 1.00 m
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7. Compare How does the
amount of work done in the
top picture compare with
the work done in the bottom
picture?
W=F×d
W = 75.0 N × 3.00 m
W = 225 N · m = 225 J
F = 75.0 N
d = 3.00 m
READING CHECK
8. Explain Why doesn’t a
machine that increases force
break the law of conservation
of energy?
To lift a box straight up, the
mover applies a large force over
a small distance.
To move the box up the ramp,
the mover applies a smaller
force over a longer distance.
Many machines make work easier by changing the
size or direction of the force we apply. The force we
apply is called the input force. For example, people use
jacks to lift cars off the ground. A person applies a light,
downward input force to the handle of the jack. The jack
changes the input force into a stronger, upward force, the
output force. The output force lifts the car. In this way, a
person can lift a very heavy car.
It may seem that changing a small force into a large
force breaks the law of conservation of energy. However,
the jack doesn’t only increase the force applied. It also
decreases the distance over which the force is applied.
Therefore, the total amount of work stays the same.
Many machines increase force by decreasing the
distance over which the force is applied. This process is
called multiplying the force. The car jack is an example
of a machine that multiplies force. Other machines, such
as ramps, multiply distance. They make work easier by
allowing you to exert a smaller force over a longer distance.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Interactive Reader
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Work and Energy
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Work, Power, and Machines continued
What Is Mechanical Advantage?
Scientists and engineers use a quantity called mechanical
advantage to describe how much a machine multiplies force
or distance. Mechanical advantage is the ratio between output
force and input force. It is also the ratio between input distance
and output distance. The mechanical advantage equation is:
output force
input distance
mechanical advantage ___________ _______________
input force
output distance
A machine with a mechanical advantage greater than
one multiplies force. Such machines can help you move
or lift large objects, such as cars and heavy boxes, more
easily. Jacks and many pulleys multiply force.
A machine with a mechanical advantage of one does
not multiply force. Such machines only change the
direction of the force. Some pulleys work this way.
A machine with a mechanical advantage less than one
multiplies distance. It also produces an output force that
is smaller than the input force. Ramps work this way.
Some of the joints in your body, such as your elbow, also
work this way.
CALCULATING MECHANICAL ADVANTAGE
You can calculate mechanical advantage if you know
input and output forces or distances. For example, imagine
a jack that lifts a 9,900 N car with an input force of 150 N.
What is the mechanical advantage of the jack? Follow these
steps to solve this problem:
Step 1: List the given
and unknown values.
Step 2: Write the
equation.
Given:
input force = 150 N
output force = 9,900 N
Unknown:
mechanical
advantage
output force
input force
mechanical advantage = ___________
READING CHECK
9. Identify What does
mechanical advantage
measure?
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Apply Concepts How
can you tell without doing
any calculations whether a
machine has a mechanical
advantage greater or less
than one? In a small group,
brainstorm some ideas about
how you could figure this
out.
Math Skills
10. Calculate A ramp is
5.0 m long and 1.5 m high.
What is the mechanical
advantage of the ramp?
Show your work.
(Hint: The height of the ramp
is the output distance.)
Step 3: Insert the
9,900 N
mechanical advantage = ________
150 N
known values and solve
for the unknown value. mechanical advantage = 66
The jack has a mechanical advantage of 66. Therefore,
the output force from the jack is 66 times greater than
the input force.
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Section 1 Review
SECTION VOCABULARY
mechanical advantage a number that tells how
many times a machine multiplies force; it can
be calculated by dividing the output force by
the input force
power a quantity that measures the rate at
which work is done or energy is transformed
work the transfer of energy to a body by the
application of a force that causes the body to
move in the direction of the force; it is equal to
the product of the magnitude of the component
of a force along the direction of displacement
and the magnitude of the displacement
1. Apply Concepts A short ramp and a long ramp each reach a height of 1 m. Which
ramp has a greater mechanical advantage? Explain your answer.
2. Calculate A student weighs 565 N. She climbs 3.25 m vertically up a flight of
stairs. It takes her 12.6 s. What is her power output? Show your work.
3. Describe The student from the question above carries a stack of books up the
same flight of stairs. If she still takes 12.6 s, how will her power output change?
Explain your answer.
4. Compare What is the difference between work and power?
5. Apply Concepts A certain machine changes a large input force into a smaller
output force. How does the machine affect the distance over which the force is
applied? Explain your answer.
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Work and Energy