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A Closer Look

Simple Machines
imple machines are tools that people use
Sto help them do work. Recall that work
is a force times a distance, and you can see
that the simple machine helps you do work
by changing a force or a distance that some-
thing is moved. The force or distance advan-
60 N
tage you gain by using the machine is called
Effort 1 m
the mechanical advantage. The larger the me- force 300 N Resistance force
Effort distance
chanical advantage, the greater the effort that
0.2 m
you would save by using the machine.
Fulcrum Resistance distance
A lever is a simple machine, and Box Fig-
ure 3.1 shows what is involved when a lever BOX FIGURE 3.1 The lever is one of six simple
reduces a force needed to do work. First, note machines.
there are two forces involved. The force that
you provide by using the machine is called the
effort force. You and the machine are working
against the second force, called the resistance Ignoring friction, the work you get out For the example lever, we find
force. In the illustration, a 60 N effort force is of any simple machine is the same as the d
E _

used to move a resistance force of 300 N. work you put into it. The lever enabled you MA =
d
There are also two distances involved to trade force for distance, and the mechan- R
1 m

in using the lever. The distance over which ical advantage (MA) can be found from a = _
0.2 m
your effort force acts is called the effort dis- ratio of the resistance force (F R ) divided by
tance, and the distance the resistance moves the effort force (F E ): = 5
is called the resistance distance. You pushed F So, we can use either the forces or the
R _

down with an effort force of 60 N through MA = distances involved in simple machines to
F
E
an effort distance of 1 m. The 300 N rock, calculate the mechanical advantage. In
Therefore, the example lever in Box Figure 3.1
on the other hand, was raised a resistance summary, a simple machine works for you
had a mechanical advantage of
distance of 0.2 m. by making it possible to apply a small force
You did 60 N × 1 m, or 60 J, of work on F over a large distance to get a large force
R _
MA =

the lever. The work done on the rock by the F working over a small distance.
E
lever was 300 N × 0.2 m, or 60 J, of work. The 300 N There are six kinds of simple machines:
_
work done by you on the lever is the same as = 60 N inclined plane, wedge, screw, lever, wheel
the work done by the lever on the rock, so and axle, and pulley. As you will see, the
= 5
work input = work output screw and wedge can be considered types of
You can also find the mechanical advantage inclined planes; the wheel and axle and the
Since work is force times distance, we can by dividing the effort distance (d E ) by the pulley can be considered types of levers.
write this concept as resistance distance (d R ):
1. The inclined plane is a stationary ramp
effort force × effort distance = d
E _
MA = that is used to trade distance for force.

resistance force × resistance distance d You are using an inclined plane when
R
CONCEPTS Applied
POWER
You are doing work when you walk up a stairway, since you Book Work
are lifting yourself through a distance. You are lifting your
Place a tied loop of string between the center pages of a
weight (force exerted) the vertical height of the stairs (distance small book. Pick up the loop so the string lifts the book,
through which the force is exerted). Consider a person who supporting it with open pages down. Use a spring scale
weighs 120 lb and climbs a stairway with a vertical distance of to find the weight of the book in newtons. Measure the
10 ft. This person will do (120 lb)(10 ft) or 1,200 ft·lb of work. done work in lifting the book 1 m. Use the spring scale
Will the amount of work change if the person runs up the stairs? to measure the work done in pulling the book along a
The answer is no; the same amount of work is accomplished. tabletop for 1 m. Is the amount of work done lifting the
Running up the stairs, however, is more tiring than walking up book the same as the amount of work done pulling the
the stairs. You use the same amount of energy but at a greater book along the tabletop? Why or why not?
rate when running. The rate at which energy is transformed
64 CHAPTER 3 Energy 3-4