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Work and Simple Machines
Work is a force acting over a distance.
Work
Work can be defined by the following equation:
Work = Force × Distance
When Teddy the Bear pulls a wagon a distance of 5 meters then he is doing work.
Using a spring scale, Teddy measured that he is used 10 Newtons of force pull the wagon. Based
on the measurements of force and distance, Teddy calculated the amount of work he performed.
Work = Force × Distance
Work = 10 Newtons × 5 meters
Work = 50 Newton⋅meters (N⋅m)
Notice that the unit for work is a Newton⋅meter or N⋅m. Since Newtons and meters measure
different properties, the units cannot be cancelled out.
Though it may be heavy, work is not being done on the chest because the man is not moving the
chest; he is standing still.
Work is not done in this image either. Even though the man is pushing with all his might, the
chair is not moving. Work requires an applied force and movement.
Simple Machines
Simple machines are tools that can make a task easier to perform. There are two ways in which
simple machines can help:


by reducing the input force needed to perform the task or
by changing the direction of the input force needed to perform the task.
There are six basic types of simple machines. Different machines help in different ways.
However, no machine is capable of reducing the amount of work needed to perform a task.
Inclined Plane
An inclined plane is a flat surface that is slanted. The moving van ramp shown below is an
example of an inclined plane.
Inclined planes reduce the size of the input force needed for a task by increasing the distance
through which the force is applied.
Two of the six simple machines are actually special kinds of inclined planes. A wedge is a
triangle-shaped tool made of two inclined planes. And a screw is an inclined plane that is
wrapped around a shaft.
Wedge
A wedge is a double-sided inclined plane. An axe blade, like the ones shown in the picture, is a
good example of a wedge.
An axe blade works by pushing two parts of a log apart as the blade enters the wood. A wedge
makes it easier to push objects apart by changing the direction of the input force. As a person
puts downward pressure on the axe blade, the blade pushes outward on the two parts of the
wood.
Screw
A screw is another simple machine that is a kind of inclined plane.
The very tip of a screw is usually shaped like a triangle, which makes it a tiny wedge. Higher up
on the screw are the threads. The threads of a screw are actually one long spiral, reaching from
the bottom of the screw to the top. If this spiral was unwound, it would simply be an inclined
plane.
This structure gives screws two interesting properties. First, just like an inclined plane, screws
reduce the amount of force needed by increasing the distance over which that force is applied.
This means that it requires less force to twist a screw in than it would to push it in directly.
Second, screws also change the direction of the applied force. A twisting, or rotational force is
applied to a screw, but the screw transforms this into a straight-line force.
Pulley
A pulley is a rope threaded through a wheel or disk. It is used to lift objects. In the picture shown
below, a pulley is being used to lift a bucket of water up out of a well.
A pulley changes the direction of the input force. A pulley system, which consists of multiple
wheels, can also reduce the size of the input force. A flag is raised on a flagpole using a pulley.
Lever
A lever is a rigid object that pivots around a point. The pivot point is called the fulcrum. In the
picture below, the pole is the lever and the rock is the fulcrum.
A lever can reduce the amount of input force needed for a task by increasing the distance through
which the force is applied. A seesaw, crowbar, wheelbarrow, and the human arm are all
examples of levers.
Wheel and Axle
A wheel and axle consists of an axle attached to the center of a wheel. The wheels on the wagon
shown in the picture below are examples of wheels and axles.
The wheel and axle reduces the size of the input force needed for a task by increasing the
distance through which the force is applied. When the wheel is turned, the axle is turned in the
same direction. Because the wheel has a larger radius than the axle, the wheel moves a greater
distance than the axle. As a result, the input force needed to turn the axle is reduced.
Conservation of Energy
It is important to note that while simple machines can reduce the amount of force needed to
perform a task, they do not reduce the amount of energy or work needed to perform a task. For
example, a ramp (inclined plane) reduces the amount of force needed to lift an object, but it
increases the distance through which the force is applied. So, simple machines do not reduce
work; they make work easier.
Compound Machines
A compound machine is a system made from two or more simple machines.
Compound machines consist of two or more simple machines working together. There are six
simple machines that can be used to make compound machines:
1.
2.
3.
4.
5.
6.
inclined plane
wedge
wheel and axle
pulley
screw
lever
Systems made up of simple machines can do things that the simple machines cannot do by
themselves. Some examples of compound machines and the simple machines they contain are
shown below.
Corkscrew
Corkscrews are compound machines that contain levers and screws. The screw plunges into the
cork in the neck of a bottle, and then the levers are used to pry the cork out.
Scissors
A pair of scissors is a compound machine because it is made up of a lever and wedges. The
handles of the scissors are levers that pivot around a common fulcrum, and the blades are
wedges.
Bicycle
Bicycles contain levers, wheels and axles, and screws. A wheel and axle is a wheel that is
connected to a shaft through its center. When the shaft moves, its wheel moves, and vice versa.
On a bicycle, the chain turns a shaft through the center of the rear wheel. The shaft turns the
wheel itself. The hand brakes use a lever to move the brakes onto the wheel.
Mechanical Advantage & Efficiency
Simple machines decrease the amount of force needed to do something by increasing the
distance over which the force is applied. Thus, although simple machines don't decrease the total
amount of work needed, they do make the work seem easier.
Work & Mechanical Advantage
The amount of work required to do any particular task depends on both the force used and the
distance over which it is used.
Work = Force × Distance
Therefore, it is possible to do the same amount of work using less force, but there is a trade off.
Imagine you needed to lift a statue of an elephant to the top of a platform. (Figure 1.) The force
required to lift this statue is far too great for any human alone. However, as long as the distance
over which the work is done is increased, it is possible to do the same amount of work using less
force. Simple machines are devices that do just this; they reduce the amount of force required to
do work by increasing the distance over which the force is applied.
The ratio between the amount of force needed without a simple machine to the amount of force
needed with a simple machine is the mechanical advantage. The force needed without a simple
machine can be called the resistive force (Fr). The force actually used with a simple machine can
be called the equilibrium force (Fe) or the effort force.

The resistive force (Fr) is the force needed without a simple machine.

The effort force (Fe) is the force needed with a simple machine.
As the mechanical advantage increases, the amount of force required to do the same amount of
work decreases.
The mechanical advantage equation shown above is for the actual mechanical advantage (AMA)
of a machine. A machine's ideal mechanical advantage (IMA) is what is desired of the machine.
In other words, it is the amount by which a machine would multiply the force applied to it if no
energy were lost due to friction. This number is imaginary, however. In the real world, no
machine is frictionless, so people who design machines attempt to build them so they perform as
closely to their ideal mechanical advantage as possible.
Inclined Planes
When moving an object upward against gravity, the resistive force—the force that must be
overcome to do work—is the weight of the object. Lifting an object a certain height (h) requires
the same amount of work no matter what path is taken. So, the force required can be reduced as
long as the distance over which the force is exerted increases.
An inclined plane is a simple machine that makes it possible to reduce the force required to do
work by increasing the distance over which work is done. The mechanical advantage for an
inclined plane can be calculated by:
Figure 1.The force required to lift the elephant is equal to the weight of the elephant.
Figure 2.The force required to lift the elephant with this inclined plane is reduced by half.
The effort force needed to move an object up an inclined plane can be calculated using the
formula:
or more specifically,
To illustrate the effect of doubling the length of the distance on the force, refer to the example in
Figure 2.
By doubling the distance, the force required to lift the elephant is cut in half.
Simple Machines Related to the Inclined Plane
A wedge is formed by placing two inclined planes back to back. The mechanical
advantage of a wedge is also L/h, where L is the length of the sides and h is the width of the wide
end.
A screw is another form of an inclined plane. The mechanical advantage of a screw is the total
length of the thread—the inclined plane that is wrapped around its core—divided by the length
of the screw. Remember, the greater the mechanical advantage, the smaller the force required.
Pulleys
A single pulley that is fixed in place has a mechanical advantage of one.
The same amount of force is required to lift the object with one fixed pulley as with none,
although the direction of the force may be different. Pulling one end of the rope a distance h
moves the load—an elephant in this case—up the same distance h.
A single pulley that is not fixed in place, but instead
connects two sections of the same rope, each of which supports half of the weight of the load,
has a mechanical advantage of two. Lifting the load—the elephant—a distance h requires that
each section of rope get shorter by the same distance h. The end of the rope must be pulled a
distance of 2h to do that.
Similarly, two pulleys that are not fixed in place can give a mechanical
advantage of four. Adding any fixed pulleys to the top of the rope will not change the
mechanical advantage.
From these examples, we see that the mechanical advantage of a system of pulleys is equal to
the number of sections of rope that are supporting the weight of the load. For example, look at
the diagram below. If the top pulley is fixed in place, what is the mechanical advantage of the
pulley system shown?
Four sections of the rope would need to become shorter by a distance h in order to lift the
elephant a height h so the mechanical advantage of the system is 4. That means that the pulley
system will multiply the effort force applied by a factor of 4.
Wheel and Axle
The mechanical advantage of a wheel and axle is found by dividing the radius of the wheel (R)
by the radius of the axle (r). For example, if the radius of the wheel below (R) is 20 cm and the
radius of its axle (r) is 4 cm, the mechanical advantage of the wheel and axle is 20 ÷ 4 = 5.
Efficiency
The efficiency of a machine is the ratio of its work output to the work input. In other words, it is
determined by dividing the work output of the system by the work put into the system. An ideal
machine has an efficiency of 1, or 100%. Because of the energy lost to friction, an ideal machine
cannot exist.