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Mechanical Advantage and Efficiency of Machines

By means of a machine, a small force, or effort, can be applied to move a much greater resistance, or load. In doing so, however, the applied force must move through a much greater distance than it would if it could move the load directly. The mechanical advantage (MA) of a machine is the factor by which it multiplies any applied force. The MA may be calculated from the ratio of the forces involved or from the ratio of the distances through which they move. Ideally, the two ratios are equal, and it is simpler to calculate the ratio of the distance the effort moves to the distance the resistance moves; this is called the ideal mechanical advantage (IMA). In any real machine some of the effort is used to overcome friction. Thus, the ratio of the resistance force to the effort, called the actual mechanical advantage (AMA), is less than the IMA.

The efficiency of any machine measures the degree to which friction and other factors reduce the actual work output of the machine from its theoretical maximum. A frictionless machine would have an efficiency of 100%. A machine with an efficiency of 20% has an output only one fifth of its theoretical output. The efficiency of a machine is equal to the ratio of its output (resistance multiplied by the distance it is moved) to its input (effort multiplied by the distance through which it is exerted); it is also equal to the ratio of the AMA to the IMA. This does not mean that low-efficiency machines are of limited use. An automobile jack, for example, must overcome a great deal of friction and therefore has low efficiency, but it is extremely valuable because small effort can be applied to lift a great weight.

Although most machines are used to multiply an effort so that it may move a greater resistance, they may have other purposes. For example, a single, fixed pulley merely changes the direction of the applied force; the pulley may make it easier to lift the load, since a person can pull down on a rope, thus adding his or her own weight to the effort, rather than simply lifting the load. In a catapult an effort greater than the load moves through a short distance, causing the load to be moved through a large distance before being released. As the load is being moved, it picks up speed so that it is traveling at a considerable velocity when it leaves the catapult.

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The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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