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Mechanical Advantage Relationships

by Ron Kurtus (22 June 2016)

There are three types of mechanical advantages in machines: force, distance, and speed. For a given machine, there are relationships between these mechanical advantages.

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

Questions you may have include:

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



Mechanical advantages

The mechanical advantage of a machine is defined as its output divided by its input.

Distance mechanical advantage

The distance mechanical advantage is:

MAD = DO/DI

where

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

(See Distance Mechanical Advantage for more information.)

Speed mechanical advantage

The equation for the speed mechanical advantage is:

MAS = SO/SI

where

(See Speed Mechanical Advantage for more information.)

Force mechanical advantage

The force mechanical advantage equation is:

MAF = FO/FI

where

(See Force Mechanical Advantage for more information.)

Distance-speed relationship

Since distance equals speed times time, there is a distinct relationship between distance mechanical advantage and speed mechanical advantage. For a given amount of time, t:

DO = SOt

DI = SIt

Divide output distance by input distance:

DO/DI = SOt/SIt = SO/SI

Thus:

MAD = MAS

Distance MA = Speed MA

Distance-force relationship

According to the Law of Conservation of Energy, the output energy or work equals the input energy or work. Work is defined as a force times the distance moved. Thus:

WO = WI

WO = FODO

WI = FIDI

where

Thus:

FODO = FIDI

Divide to get:

FO/FI = DI/DO

Therefore:

MAF = DI/DO = 1/MAD

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

Example

In jacking up a car, you must move the jack-handle a greater distance than the car is lifted.

Summary

The relationships between the three mechanical advantages is:

Distance MA = Speed MA

and

Force MA = 1/Distance MA = 1/Speed MA


Take advantage of the situation


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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