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How do you calculate mechanical advantage?

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Quick Answer

Mechanical advantage is calculated differently depending on the type of simple machine being used. In general, mechanical advantage is a ratio of the force exerted by the machine to the force applied to the machine.

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How do you calculate mechanical advantage?
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Full Answer

In the case of a lever, the ideal mechanical advantage, or IMA, is the ratio of the length of the effort arm to the length of the load arm, or IMA = Le / Lr. The effort arm measures the distance from the force applied to the fulcrum, and the load arm measures the distance from the weight, or output force, to the fulcrum.

In the case of a wheel and axle, ideal mechanical advantage is the ratio of the radius of the wheel, R, to the radius of the axle, r. In short, IMA = R/r.

In the case of a pulley system, the ideal mechanical advantage is equal to the number of support strings, N. IMA = N. Alternatively, ideal mechanical advantage is equal to two times the number of movable pulleys.

In the case of an inclined plane, the ideal mechanical advantage is the ratio of the length traveled up the inclined plane, L, to the height difference, h. IMA = L/h.

In the case of a wedge, the ideal mechanical advantage is the ratio of the depth of penetration, L, to the length of the separation of wedged surfaces, t. IMA = L/t.

In the case of a screw, the mechanical advantage is the ratio of the circumference of the screw to the distance traveled after each revolution. In other words, IMA = 2*pi*L / P, where L is the radius of the screw and P is the distance traveled after each revolution.

The actual benefits of a simple machine when compared to its ideal mechanical advantage are reduced due to energy loss caused by friction. The efficiency measures how close a simple machine is to its ideal mechanical advantage. Efficiency is the ratio of the work supplied to the work put into the machine.

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