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Force Mechanical Advantage

by Ron Kurtus (28 June 2016)

A machine's force mechanical advantage shows the effectiveness of the machine in providing an output force greater than the input force. The equation for the force mechanical advantage is the output force divided by the input force.

In the ideal case, there is no friction. However, the resistance from the force of friction can change the mechanical advantage.

Examples where force mechanical advantage is employed include the lever, bicycle, and cranes.

Questions you may have include:

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



Force mechanical advantage equation

If you want to have an output force that is greater than the input or effort force, you want a machine with a good force mechanical advantage.

The force mechanical advantage equation is:

MAF = FO/FI

where

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

Related to distance moved

The force mechanical advantage can also be a function of the distance moved.

MAF = DI/DO

where

(See Mechanical Advantage Relationships)

Application in lever

An application of force mechanical advantage equation is when you want to lift a weight or load using a lever.

Lever configuration provides force mechanical advantage

Lever configuration provides force mechanical advantage

In a lever,

MAF = FO/FI

FO/FI = DI/DO = dI/dO

where

Also:

FOdO = FIdI

Example

How much input force would be needed to move a 20 pound weight when the input arm of the lever was 4 feet and the output arm was 2 feet? What is the mechanical advantage?

Solution

Since FI = FOdO/dI then:

FI = 20*2/4 =10 pounds

MAF = FO/FI = 20/10 = 2

Affected by friction

Although resistance due to the force of friction is negliable in most levers, it can be a factor in other machines and affect the force mechanical advantage by adding to the required input force.

MA'F = FO/(FI + fr)

where

 

Thus, if the input force required to move an object without friction was 10 pounds, and the added friction was 2 pounds, then the new input would be have to be 10 + 2 = 12, thus reducing the mechanical advantage.

MA = (Fo - fr)/Fi

Summary

A machine's force mechanical advantage (MAF) shows the effectiveness of the machine in providing an output force greater than the input force. The equation for the force mechanical advantage is the output force divided by the input force.

In the ideal case, there is no friction. However, the resistance from the force of friction can change the mechanical advantage. Examples where force mechanical advantage is employed include the lever, bicycle, and cranes.


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Resources and references

Ron Kurtus' Credentials

Websites

The Mechanical Advantage of Machines - Carolina Curriculum (PDF)

Introduction to mechanical advantage - Khan Academy (video)

Mechanical advantage - Wikipedia

Machines Resources

Books

Top-rated books on Machines


Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.


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