# Simple Machines and How They Work

Simple machines are tools with few or no moving parts that change the magnitude or direction of a force. Basically, they multiply force and make work easier. Here is a look at the types of simple machines, how they work, and their uses.

### What Is a Simple Machine?

A machine is a device that performs work by applying a force over a distance. Simple machines do work against a single load force in a way that increases the output force by decreasing the distance the load moves. The ratio of the output force to the applied force is called the mechanical advantage of the machine.

### How Simple Machines Work

Basically, a simple machine relies on one or more of the following strategies:

• It changes the direction of a force.
• It increases the magnitude of a force.
• The machine transfers a force from one location to another.
• It increases the speed or distance of a force.

### 6 Simple Machines

There are six simple machines: the wheel and axle, lever, inclined plane, pulley, screw, and wedge.

#### Wheel and Axle

The wheel and axle makes transporting heavy goods easier and helps people travel distances. A wheel has a small footprint, so it reduces friction when you move an object over a surface. For example, there is a lot more friction in sliding a refrigerator across the floor than in wheeling it in a cart. A wheel and axle is also a force multiplier. The input force turns the wheel, generating a rotational force or torque, but the torque is much greater on the axle than on the rim of the wheel. A long handle attached to an axle achieves a comparable effect.

#### Lever

A lever makes a trade-off between force and distance. A see-saw is a familiar example of this type of simple machine. A lever has a long beam and a pivot or fulcrum. Depending on the placement of the fulcrum, you either use a lever for lifting a heavy load over a smaller distance than the input force or a lighter load over a larger distance than the input force.

#### Inclined Plane

An inclined plane is a ramp or angled flat surface. It increases the distance of a force. An inclined plane helps with lifting loads that are too heavy to lift straight up. But, the steeper the ramp, the more effort you need. For example, climbing a ramp is much easier than jumping a great height. Climbing a steep ramp takes a lot more effort than walking up a gentle slope.

#### Pulley

A pulley either changes the direction of a force or else trades increased force for decreased distance. For example, it takes a lot of force to pull a bucket of water straight up from a well. Attaching a pulley lets your pull down on the rope instead of up, but it takes the same force. However, if you use two pulleys, with one attached to the bucket and the other attached to an overhead beam, you only apply half the force to pull up the bucket. The trade-off is that you double the distance of rope you pull. A block and tackle is a combination of pulleys that reduces the necessary force even more.

#### Screw

A screw is essentially an inclined plane, except it is wrapped around a shaft. The incline makes it easier to exert a greater force for turning the screw. Using a long handle, such as a screwdriver, increases the mechanical advantage. Screws find use in daily life as lug nuts on car wheels and for holding parts together in machines and furniture.

#### Wedge

A wedge is a moving inclined plane that works by changing the direction of the input force. Common uses of wedges are for splitting pieces and lifting loads. For example, an axe is a wedge. So is a doorstop. The axe directs the force of a blow outward, splitting a log into pieces. A doorstop transfers the force of a moving door downward, producing friction that keeps it from sliding over the floor.

### Ideal Simple Machines

An ideal simple machine is one that does not lose energy through friction, deformation, or wear. In such a situation, the power you put into the machine equals its power output.

Pout = Pin

In an ideal simple machine, the mechanical advantage is the ratio of force out to force in:

MA = Fout / Fin

Power equals the velocity multiplied by force:

Foutνout = Finνin

It follows that the mechanical advantage of an ideal machine is its velocity ratio:

MAideal = Fout / Fin = νin / νout

The velocity ration also equals the ratio of distance covered over time:

MAideal = din /dout

Note that ideal simple machines obey the law of conservation of energy. In other words, they cannot do more work than they get from the input force.

• If MA > 1 then the output force is greater than the input force, but the load moves a smaller distance than the distance moved by the input force.
• If MA < 1 then the output force is less than the input force and the load moves a greater distance than the distance moved by the input force.

### Friction and Efficiency

In real life, machines have friction. Some of the input power gets lost as heat. Energy is conserved, so input power equals the sum of output power and friction:

Pin = Pout + Pfriction

Mechanical efficiency η is the ratio of power out to power in. It is a measure of friction energy loss and ranges from 0 (all power lost to friction) to 1 (an ideal simple machine):

η = Pout / Pin

Since power equals the product of force and velocity, the mechanical advantage of a real simple machine is:

MA = Fout / Fin = η (νin / νout)

In a non-ideal machine, mechanical advantage is always less than the velocity ratio. What this means it that a machine with friction never moves as large a load as its corresponding ideal machine.

### History

People used simple machines since ancient time, without understanding how they work. The Mesopotamians likely invented the wheel between 4200 to 4000 BC. Historians credit the Greek philosopher Archimedes with the description of simple machines. In the 3rd century BC, Archimedes described the concept of mechanical advantage in the lever. He studied the screw and pulley, as well. Greek philosophers calculated the mechanical advantage of five of the six simple machines (not the inclined plane). In the 16th century, Leonardo da Vinci described the rules of sliding friction, although he did not publish this work. Guillaume Amontons rediscovered the rules of friction in 1699.

### References

• Asimov, Isaac (1988). Understanding Physics. New York: Barnes & Noble. ISBN 978-0-88029-251-1.
• Morris, Christopher G. (1992). Academic Press Dictionary of Science and Technology. Gulf Professional Publishing. ISBN 9780122004001.
• Ostdiek, Vern; Bord, Donald (2005). Inquiry Into Physics. Thompson Brooks/Cole. ISBN 978-0-534-49168-0.
• Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005). Mechanical Sciences: Engineering Mechanics and Strength of Materials. Prentice Hall of India. ISBN 978-81-203-2611-8.
• Usher, Abbott Payson (1988). A History of Mechanical Inventions. US: Courier Dover Publications. ISBN 978-0-486-25593-4.