Key words: Machines, mechanical advantage, work, force, distance, speed, moving object, lever, catapult, bicycle, physics, mechanics, Physical Science, Ron Kurtus, School for Champions. Copyright © Restrictions

by Ron Kurtus (revised 5 November 2015)

The purpose of a machine is to create a mechanical advantage that will facilitate your ability to move an object against resistive forces. Mechanical advantage (MA) means that the output of the machine is greater than the input. MA is the output divided by the input. There are three types of mechanical advantage: force, distance and speed.

Note: Most science books only consider force mechanical advantage, but we will discuss all three, since they are equally important.

The Law of Conservation of Energy requires that in gaining a mechanical advantage, it will cost you in another factor. For example, increasing output force may cost you by requiring an increase in distance traveled.

Mechanical advantage is most obvious in simple machines, although it can be measured in highly complex machines and even some tools.

Questions you may have include:

• What is force mechanical advantage?
• What is distance mechanical advantage?
• What is speed mechanical advantage?

This lesson will answer those questions. Useful tool: Units Conversion

If you want to have an output force (FL) that is greater than the input or effort force (FE), you want a machine with a good force mechanical advantage. An example is when you want to lift a weight or load using a lever.

Lever configuration provides force mechanical advantage

The force mechanical advantage equation is:

MAF = FL/FE

where

• MAF is the force mechanical advantage
• FL is the resistance force or load
• FE is the effort force required to move the object

Note: In this notation, MA is NOT M times A. It simply stands for Mechanical Advantage.

### Example of lever

The relationship between forces and lengths of the arms of a lever is:

FL/FE = dE/dL

or

FLdL= FEdE

If you apply a 2 Newton force to a lever in order to lift a 14 N weight, the force mechanical advantage of the lever would be:

MAF = 14 N /2 N

MAF = 7

In other words, you could lift 7 times the force that you pushed on the lever.

A machine has a distance mechanical advantage when the output distance is greater than the applied distance.

There are times when you want to apply a force a short distance to increase the distance an object moves. One good example is when you ride a bicycle. The distance you move the pedals on a bicycle are much less than the distance moved on the circumference of the tires.

The bicycle and other machines may provide a distance mechanical advantage. The equation for this is:

where

• DL is the distance the load moves or the output distance
• DE is the distance the effort moves or the input distance

The distance mechanical advantage is also:

where

• dL is the distance of the load to the fulcrum
• dE is the distance of the effort to the fulcrum

### Example of lever

Suppose you wanted to lift a box weighing 2 pounds up to a 6-foot shelf. You could use a form of a lever

Lever configuration provides distance mechanical advantage

If you want to propel an object at a greater speed than your input motion, you would use a machine with a speed mechanical advantage. Examples are a catapult or a bicycle.

With a catapult, you push on one arm of a level and the end of the other arm moves much faster, throwing the object through the air. With a bicycle, you pedal at a certain speed, but the different sizes between the pedal sprocket and wheels and the gearing results in you going at a faster speed.

The equation for this is:

MAS = SL/SE

where

• MAS is the speed mechanical advantage
• SL is the speed of the load
• SE is the speed of the effort

Since distance equals speed times time, or d = st, there is a distinct relationship between speed mechanical advantage and distance mechanical advantage.

MAD = dL/dE = sLt/sEt = sL/sE = MAS

Thus, Speed MA = Distance MA = 1/Force MA.

### Example for catapult

A catapult moves a large rock a distance of 5 meters in 1 second before releasing it at a speed of 5 m/s. The effort end of the catapult moved at a speed of 1 m/s. Thus the speed mechanical advantage is MAS = 5/1 = 5.

Since in the effort end moved 1 meter for 5 meters of the load end, the distance mechanical advantage is MAD= 5.

Also, since MAD = 1/MAF, the force mechanical advantage is MAF = 1/5. This means that the force required to catapult the rock at 5 m/s was 5 times the weight of the rock. Since the force mechanical advantage was less than 1, it would be more appropriate to call it a mechanical disadvantage.

## Summary

A machine is used to provide you with an advantage in moving an object or doing work. This is called the mechanical advantage of the machine. There are three types of mechanical advantage: force, distance and speed. Most science books only consider force mechanical advantage, but they are equally important.

MAF = FL/FE

MAS = sL/sE

The relationship between the mechanical advantages is

Speed MA = Distance MA = 1/Force MA

## Resources and references

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