# 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:

• What is force mechanical advantage equation?
• How is force mechanical advantage used with levers?
• What about friction?

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

• MAF is the force mechanical advantage
• FO is the output force or load
• FI is the input force or effort required to move the object

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

• DI is the distance the effort moves or the input distance
• DO is the distance the load moves or the output distance

(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

In a lever,

MAF = FO/FI

FO/FI = DI/DO = dI/dO

where

• dI is the length of the effort or input arm
• dO is the length of the load or output arm

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

• MA'F is the force mechanical advantage with friction
• FO is the output force or load
• FI is the ideal input force or effort required to move the object

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.

## 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

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