How to Calculate AMA & IMA of Simple Machines

By Kevin Lee
Pulleys are simple machines that help you life large weights.

Most of the mechanical devices that people use today consist of simple machines or combinations of them. Simple machines have mechanical advantages, but they do not reduce the amount of work you perform. Instead, they help you do the same amount of work with less effort. You can calculate two types of mechanical advantage. Ideal mechanical advantage, or IMA, is the mechanical advantage of an ideal machine. Actual mechanical advantage, or AMA, represents the mechanical advantage of a real-world machine where energy losses occur due to friction.

Important Work Definitions

Work occurs when you apply a force over a distance, as expressed in the following formula:

W = F x D

The work you put into a machine -- the input force -- is the force you apply times the distance you apply it. The work done by the machine equals the resisting weight times the distance it moves when you perform the work.

Ideal Mechanical Advantage: Perfection

In real life, factors such as friction prevent machines from performing perfectly -- they lose efficiency because of energy loss. IMA represents an ideal machine's mechanical advantage. Calculate IMA by dividing the distance over which you apply effort by the distance moved. For instance, if you push or pull a weight a distance of 4 feet up an incline whose upper end sits 2 feet above the surface, mechanical advantage equals 4/2 or 2. In this example, 4 is the distance you pushed and 2 is the distance your load moved in relation to the surface.

Actual Mechanical Advantage: Reality

Actual mechanical advantage varies according to the amount of energy loss that occurs during work. If you push or pull a load up a rough surface, you encounter more resistance from friction -- you exert more effort. If the incline is smooth, you exert less effort because there's less friction. In other words, AMA is the resistance force divided by the effort force. In the incline example, the effort force is the load's weight in newtons. Sometimes someone gives you the effort force -- perhaps in a physics problem. You could also determine the effort force on an incline by attaching a spring scale to the load and measuring the force as you pull the load up the incline. If the resistance force is 40 newtons and the effort force equals 20 newtons, the AMA is 40/20, or 2, in this example.

Work and Other Simple Machines

You'll encounter five other simple machines in life: screws, wheels and axels, levers, pulleys and wedges. The specific equations you use to compute IMA and AMA may differ because the machines do not work the same. For instance, a screw is not an incline -- you don't move a weight up a screw. However, the basic principles behind IMA and AMA computations are the same for all machines -- IMA is always the distance over which you apply effort divided by the distance moved. AMA always equals the resistance force divided by effort force.

About the Author

After majoring in physics, Kevin Lee began writing professionally in 1989 when, as a software developer, he also created technical articles for the Johnson Space Center. Today this urban Texas cowboy continues to crank out high-quality software as well as non-technical articles covering a multitude of diverse topics ranging from gaming to current affairs.