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Mechanical Advantage Formula

With the help of a machine, a small force, or effort, can be applied to move a much greater resistance or load. In doing this. although, the applied force must move through a much greater distance than it would if it could move the load directly. The mechanical advantage i.e. MA of a given machine is the factor by which it multiplies any applied force. In this article, we will discuss this concept and the Mechanical Advantage formula with example. Let us learn the concept!

Mechanical Advantage Formula

What is the mechanical advantage?

Mechanical advantage is a type of measurement which calculates the amplified force gained by the mechanical system. Therefore, it provides the ratio between the force applied to the load and the force required to overcome the given force. As the two quantities are a force means with the same unit, therefore, MA is a unitless parameter.

The MA may be calculated from the ratio of the forces involved there or from the ratio of the distances through which they move. Ideally, the two ratios are equal, and also it is simpler to calculate the ratio of the distance the effort moves to the distance the resistance moves.

In any real machine, some of the efforts is used to overcome friction also. Therefore, the ratio of the resistance force to the effort called the actual mechanical advantage which will be less.

The efficiency of any machine measures the degree to which friction and other factors are reducing the actual work output of the machine from its theoretical maximum value. Obviously, a frictionless machine would have an efficiency of 100 percentages. So, a machine with an efficiency of 20 percentages has an output of only one-fifth of its theoretical output.

Mechanical Advantage Formula

The efficiency of a machine is equal to the ratio of its output to its input. It is also equal to the ratio of the actual and theoretical MAs. But, it does not mean that low-efficiency machines are of limited use. An automobile jack, for example, have to overcome a great deal of friction and therefore it has low efficiency. But still, it is extremely valuable because small effort can be applied to lift a great weight.

Also, in another way the mechanical advantage is the force generated by a machine to the force applied to it which is applied in assessing the performance of the machine.

The mechanical advantage formula is:

MA = \(\frac{F_B}{F_A} \)

Where,

MA mechanical advantage
FB the force of the object
FA the effort to overcome the force

Solved Examples

Q.1: Determine the value of mechanical advantage if 300 Newton force is required to overcome a load of 700 Newton.

Solution:

The given parameters in the problem are,

FA = 300 N

FB = 700 N

Now, Mechanical advantage formula is:

MA = \(\frac{F_B}{F_A} \)

=\(\frac{700 }{ 300} \)

MA = 2.33

Q. 2: Calculate the mechanical advantage value if 500 Newton force is required to overcome a load of 1000 Newton.

Solution:

The given parameters are,

FA = 500 N

FB = 1000N

Thus, using Mechanical advantage formula as,

MA = \(\frac{F_B}{F_A} \)

=\(\frac{1000 }{ 500}\)

MA = 2

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