Mechanical Advantage : Understand with Example

Mechanical Advantage measures the increase in applied force when force is applied using a mechanical device, tool or mechanism such as lever, gear or pulley system.

For example, As shown in above image, a man is using lever to lift a heavy block. By doing this he has to apply relatively small forces to lift the block.

What is the difference between Mechanical Advantage and Efficiency?

Mechanical Advantage of a machine measures how much force will be required to lift or move an object using a simple machine. It has nothing to do with required energy. It can be the same or higher. Whereas efficiency of a machine is the ratio of output energy and input energy.

For example, with a pulley system ( Mechanical-Advantage = 2) 5kg force will be required to lift a 10kg load. This reduction in required force is achieved at the cost of more displacement. Whereas efficiency remains independent of force applied and depends on loss of energy.

How to Calculate Mechanical Advantage?

Mathematically, Mechanical-Advantage is equal to the ratio of output force to the input force while following the law of conservation of energy with 100% efficiency. But in real life, systems are not perfect. There is always some loss of energy.

Calculation Formula

According to the first law of conservation of energy, the total energy of an isolated system remains constant.

Input Energy to the Lever = Output Energy

Input Force x Input Distance = Output Force x Output Distance

Ideal MA = Output Force / Input Force = Input Distance / Output Distance

In this way we can calculate the ideal mechanical advantage for a mechanism. Simple machines such as lever, pulley and gears are used in various scenarios to achieve higher forces by the application of small force.

Examples of Simple machine with Mechanical Advantage Calculation
MA of a Lever
This image shows lever arrangement to calculate mechanical advantage.

Above image shows a solid bar pivoted at a point to lift the solid block. This arrangement is used to lift solid bodies with relatively smaller forces.

Lever Mechanical Advantage = a / b = Output Force / Input Force

Mechanical Advantage of a Pulley
This image shows mechanical advantage of a pulley system.

As shown in above image, when pulley is fixed, the force required to lift the weight is equal to the weight. In other words MA is equal to one.

Whereas when weight is attached to one moving pulley, MA is equal to two. In other words, 5 kg force will be required to move a 10 kg weight.

MA of a Wheel and Axle
This image shows a representation of wheel and axle.

In a connected axle and wheel, when wheel is rotated force is transferred from wheel to the axle and this can be calculated by calculating mechanical-advantage of the system.

MA of a Wheel and Axle = Diameter of the Wheel / Diameter of the Axle

To sum up, Mechanical advantage of a machine is a unitless quantity and it measures how much less force is required to move or lift a object using a simple machine. We suggest you also read this article on the calculation of gear ratio.

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