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- transferring a force from one place to another,
- changing the direction of a force,
- increasing the magnitude of a force, or
- increasing the distance or speed of a force.

When a machine takes a small input force and increases the magnitude of the output force, a
__mechanical advantage__ has been produced. If a machine increases an input force of 10 pounds to
an output force of 100 pounds, the machine has a mechanical advantage (MA) of 10. This is
shown below:

MA = __Output Force__ = __100 lbs.__ = __10__

Input Force 10 lbs.

The automobile jack is a common device used to produce a mechanical advantage. The jack multiples the amount of force applied to the jack handle so that a small force (exerted by the operator) can be used to produce the larger force necessary to lift the automobile.

No machine can increase *both* the magnitude and the distance of a force at the same time. When
a machine produces an increase in force, there is always a proportional decrease in the distance
moved. Conversely, when a machine produces an increase in distance, there will be a
proportional decrease in force.

Another way to state this concept is that no machine can produce more work than the amount of
work that is put into the machine. In fact, if you ignore the work lost due to friction and its
inefficiencies, the amount of work produced by a machine is always exactly the same as the
amount of work put into the machine. This is known as the __Law of Conservation of Energy__.

This concept can also be put into the form of an equation. (Remember that work is equal to force times distance.)

F1 X D1 = F2 X D2

where, F1 = Input Force F2 = Output Force

D1 = Input Distance D2 = Output Distance

As an example, assume that it requires 50 pounds of input force in the handle of an automobile jack in order to raise a 500 pound weight a distance of one foot. What distance must the jack handle be moved in order to accomplish this task? The answer can be calculated as follows: F1 X D1 = F2 X D2

50 lbs. X D1 = 500 lbs. X 1 ft.

50 lbs. X D1 = 500 ft.-lbs.

50 lbs. X D1 = 500 ft.-lbs.

__ 50 lbs. X D1 __ = __500 ft.-lbs.__

50 lbs. 50 lbs. D1 = __10 ft.__

The calculations show that with an input force of 50 pounds the jack handle must move 10 feet in order to raise the 500 pound weight a distance of one foot. Therefore, the amount of input work and output work are equal (F1 X D1 = F2 X D2).

You are probably familiar with many different machines. Some of these machines appear highly complex. However, all machines, no matter how complex, are made up of one or more of the six simple machines. The six simple machines are:

- Lever
- Wheel and Axle
- Pulley
- Inclined Plane
- Wedge
- Screw

Individually, each of these machines is a simple machine. When two or more simple machines
are combined in such a way that they work as a single mechanism, the device is classified as a
__complex__ machine.

__LEVER__

A lever is a rigid bar that rotates around a fixed point called the fulcrum. The bar may be either straight or curved. In use, a lever has both an applied force and a resistance force.

The mechanical advantage of a lever is the ratio of the length of the lever on the applied force side of the fulcrum to the length of the lever on the resistance force side of the fulcrum. The mechanical advantage of the lever below is 10:1. Therefore, an applied force of 10 pounds will balance a resistance force of 100 pounds. However, the applied force end of the lever must move 10 feet for every one foot the resistance force s raised.

There are three different classes of levers. The class of a lever is determined by the location of the applied and resistance forces relative to the fulcrum. Each of the three classes of levers will be discussed next.

A first-class lever always changes the direction of force (I.e. a downward effort force on the lever results in an upward movement of the resistance force). A first-class lever is illustrated below:

With a first-class lever, when the fulcrum is closer to the resistance, the output force is increased. However, there is a corresponding decrease in both output speed and distance. Conversely, when the fulcrum is closer tot he effort, the output force is decreased and there is a corresponding increase in both output speed and distance.

A second-class lever does not change the direction of force. When the fulcrum is located closer to the resistance than to the force, an increase in force (mechanical advantage) results. A second-class lever is illustrated below:

The wheel and axle is a simple machine consisting of a large wheel rigidly secured to a smaller wheel or shaft, called an axle. When either the wheel or axle turns, the other part also turns. One full revolution of either part causes one full revolution of the other part. If the wheel turns and the axle remains stationary, it is not a wheel and axle machine.

When the force is applied to the wheel in order to turn the axle, force is increased and distance and speed are decreased. When the force is applied to the axle in order to turn the wheel, force is decreased and distance and speed are increased.

The mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle. In the wheel and axle illustrated below, the radius of the wheel is five times larger than the radius of the axle. Therefore, the mechanical advantage is 5:1 or 5.

*Note: The radius is equal to 1/2 the diameter
of a circle.*

As previously indicated, the wheel and axle can also be used to increase speed. This is done by applying the input force tot he axle rather than a wheel.

The increase in the output speed will be directly proportional to the ratio of the diameter of the wheel and axle. For example, if the diameter of the wheel is 10 inches and the diameter of the axle is 2 inches, the output speed will be increased 5 times (10:2 or 5:1).

The relationship between the input speed and axle diameter and the output speed and wheel
diameter is expressed by the following equation.

S1 X D1 = S2 X D2

where,

S1 = Input Speed S2 = Output Speed

D1 = Axle Diameter D2 = Wheel Diameter

A pulley consists of a grooved wheel that turns freely in a frame called a block. A pulley can be used to simply change the direction of a force or to gain a mechanical advantage, depending on how the pulley is arranged.

A pulley is said to be a __fixed pulley__ if it does
not rise or fall with the load being moved. A
fixed pulley changes the direction of a force;
however, it does not create a mechanical
advantage. A fixed pulley is illustrated
below.

A __moveable pulley__ rises and falls with the load that is being moved. A single moveable pulley
creates a mechanical advantage; however, it does not change the direction of a force.

The mechanical advantage of a moveable pulley is equal to the number of ropes that support the
moveable pulley. (When calculating the mechanical advantage of a moveable pulley, count each
end of the rope as a __separate rope__). As shown in the following illustration, two rope ends
support the moveable pulley. Therefore, an effort force of 50 pounds will lift a resistance force
of 100 pounds. The mechanical advantage is 2.

In many applications, both fixed and moveable pulleys are used in combination to form a device
known as a __block and tackle__. A block and tackle is capable of both changing the direction of a
force and creating a mechanical advantage.

An inclined plane is an even sloping surface. The inclined plane may slope at any angle between the horizontal ( ---------- ) and the vertical ( | ). The inclined plane makes it easier to move a weight from a lower to higher elevation. An inclined plane is illustrated below:

The mechanical advantage of an inclined plane is equal to the length of the slope divided by the
height of the inclined plane. (This assumes that the effort force is applied parallel to the slope.)
As an example, for the inclined plane previously illustrated, assume that the length of the slope
(S) is 15 feet and the height (H) is 3 feet. The mechanical advantage would be 5. These
calculations are shown below:

Mechanical Advantage = S/H = 15/3 = 5

While the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move. In the previous example, the object moved 15 feet along the slope in order to increase the vertical distance by 3 feet.

The wedge is a modification of the inclined plane. Wedges are used as either separating or holding devices.

There are two major differences between inclined planes and wedges. First, in use, an inclined plane remains stationary while the wedge moves. Second, the effort force is applied parallel to the slope of an inclined plane, while the effort force is applied to the vertical edge (height) of the wedge. See the illustration below:

A wedge can either be composed of one or
two inclined planes. A double wedge can be
thought of as two inclined planes joined
together with their sloping surfaces outward.
Single and double wedges are illustrated
below:

The mechanical advantage of a wedge can be found by dividing the length of either slope (S) by
the thickness (T) of the big end. As an example, assume that the length of the slope is 10 inches
and the thickness is 4 inches. The mechanical advantage is equal to 10/4 or 2 1/2. As with the
inclined plane, the mechanical advantage gained by using a wedge requires a corresponding
increase in distance.

The screw is also a modified version of the inclined plane. While this may be somewhat difficult to visualize, it may help to think of the threads of the screw as a type of circular ramp (or inclined plane).

The vertical distance between two adjacent screw threads is called the __pitch__ of a screw. One
complete revolution of the screw will move it into an object a distance to the pitch of the screw.
The pitch of any screw can be calculated as follows:

Pitch = __ 1 __

Number of threads/inch of screw

As an example, assume that you place a ruler parallel to a screw and count 10 threads in a distance of one inch. The pitch of the screw would be 1/10.

Since there are 10 threads per inch of screw, the distance between two adjacent screw threads is 1/10 of an inch. Also, remember that one complete revolution of a screw will move the screw into an object a distance equal to the pitch of the screw. Therefore, one complete revolution will move a screw with 1/10 pitch a distance of 1/10 of an inch into an object.

The mechanical advantage of a screw can be found by dividing the circumference of the screw by the pitch of the screw. This formula is shown below:

Mechanical Advantage = | Circumference
Pitch |

In actual applications, the screw is often turned by another simple machine such as a lever or a wheel and axle. In this case, the total mechanical advantage is equal to the circumference of the simple machine to which the effort force is applied divided by the pitch of the screw.

For example, suppose a screw with 12 threads per inch is turned by a screwdriver having a handle with a diameter of 1 inch. The mechanical advantage would be calculated as follows:

First, determine the pitch of the screw...

Pitch = __ 1 __ = __ 1 __ = .083

12 threads/inch of screw 12

Second, determine the circumference of the handle of the screwdriver...

Circumference = 3.14 x diameter = 3.14 x 1 = 3.14 inches

Finally, insert the values obtained into the formula and solve the equation...

Mechanical Advantage = __Circumference__ = __3.14 inches__ = 37.83

Pitch .083

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