Mechanical Advantage Formula

Mechanical Advantage Formula in Detail

The term mechanical advantage is used when we study the mechanism of the lever. Mechanical advantage is a term frequently referred to in the context of physical, simple machines. In many situations in order to perform work, an external force will be acted through a distance by a user. We know that the work done is the product of force and the distance or the displacement measured along the direction of the force. 


A considerably small or extremely light force applied through a long distance can perform the same work as a large force acted through a small distance on the output end of the considered machine. This ratio of the force generated at the output to the force acted at the input is known as the mechanical advantage. In this article, we will learn the mechanical advantage formula, what is mechanical advantage, define mechanical advantage and a few solved examples to understand the mechanical advantage formula.


Mechanical Advantage:

The mechanical advantage is nothing but a kind of estimation used to calculate the increased force or force gained by the mechanical system. Hence, the mechanical advantage provides the ratio of the externally applied force to the load and the force needed to subdue or overcome the applied force. 


What is the Unit of Mechanical Advantage?

Since the two factors in the mechanical advantage formula are of the same units (as both are the forces) implies that the mechanical advantage is a dimensionless parameter.


The efficiency of any machine estimates the extent to which friction and other factors are decreasing the actual work output of the machine from its theoretical maximum value. Certainly, a frictionless machine would have an efficiency of 100%. So, a machine with an efficiency of 20% will have an output of only \[\frac{1}{5}\]th of its theoretical output.


What is Mechanical Advantage?

Now, what is the mechanical advantage and what is the formula for mechanical advantage?

The mechanical advantage of any machine is basically the ratio of the input force to the output force. The mechanical advantage of any machine can be calculated by the ratio of the forces included to do the work or from the ratio of the displacements as a result of the applied external forces. For an ideal case, the two ratios are assumed to be equal, and also it will make the calculations.


In any practical machine, some of the applications are utilised to overcome friction also. Consequently, the ratio of the resistance force to the effort is known as the actual mechanical advantage which will be comparatively less.


The efficiency of a machine is always calculated by equating the ratio of its output to its input. The efficiency of the machine is also equal to the ratio of the actual mechanical advantage and theoretical mechanical advantage. But, it does not imply that low-efficiency machines are of restricted use. For example, an automobile jack has to overcome vast friction and therefore it will have low efficiency. But still, it is remarkably worthy because a small effort can be implemented to lift a great weight.


Also, in a different approach, the mechanical advantage is the force produced by a machine to the force applied to it which is applied in evaluating the performance of the machine.


Now, the mechanical advantage formula is given by:

⇒ MA = \[\frac{F_{B}}{F_{A}}\]

Where,

MA - The mechanical advantage

F\[_{B}\] - The force of the object

F\[_{A}\] - The effort to overcome the applied force

The above expression is known as the mechanical advantage formula and it explains what is mechanical advantage.


Examples:

1) Calculate the Value of Mechanical Advantage if 400 Newton Force is Needed to Overcome a Load of 800 Newton.

Sol:

Given,

Force required to overcome the load = F\[_{A}\] = 400 Newton

Value of applied load = F\[_{B}\] = 800 Newton

We are asked to determine the mechanical advantage when a400 Newtonforce is required to overcome a load of 800 Newton.

We know that the mechanical advantage formula is given by:

⇒ MA = \[\frac{F_{B}}{F_{A}}\] ……..(1)

Where,

MA - The mechanical advantage

F\[_{B}\] - The force of the object

F\[_{A}\] - The effort to overcome the applied force

Substituting the values of the force of the object and the effort to overcome the applied force in the equation (1) and simplify. We get:

⇒ MA = \[\frac{F_{B}}{F_{A}}\] 

⇒ MA = \[\frac{800}{400}\] = 2 

Therefore, the mechanical advantage when a 400 Newton force is required to overcome a load of 800 Newton is 2.


2) If the Mechanical Advantage of the Machine is 5, Then Calculate the Force Required to Overcome a Load of 900 Newton.

Sol:

Given,

The mechanical advantage of the machine = MA = 5

Value of applied load = F\[_{B}\] = 900 Newton

We are asked to determine the force is required to overcome a load of 900 Newton if the mechanical advantage of the machine is 5.

We know that the mechanical advantage formula is given by:

⇒ MA = \[\frac{F_{B}}{F_{A}}\]  ……..(1)

Where,

MA - The mechanical advantage

F\[_{B}\] - The force of the object

F\[_{A}\] - The effort to overcome the applied force

Rearranging the equation (1) for the effort to overcome the applied force and substituting the values of the force of the object and the mechanical advantage in the equation (1) and simplifying. We get:

⇒ MA = \[\frac{F_{B}}{F_{A}}\] 

⇒ F\[_{A}\] = \[\frac{F_{B}}{MA}\] = \[\frac{900}{5}\] = 180 Newtons 

Therefore, 180 Newtons of force is required to overcome a load of 900 Newtons.


3) Calculate the Value of Mechanical Advantage if 300 Newton Force is Needed to Overcome a Load of 900 Newton.

Sol:

Given,

Force required to overcome the load = F\[_{A}\] = 300 Newton

Value of applied load = F\[_{B}\] = 900 Newton

We are asked to determine the mechanical advantage when a 300 Newton force is required to overcome a load of 900 Newton.

We know that the mechanical advantage formula is given by:

⇒ MA = \[\frac{F_{B}}{F_{A}}\] ……..(1)

Where,

MA - The mechanical advantage

F\[_{B}\] - The force of the object

F\[_{A}\] - The effort to overcome the applied force

Substituting the values of the force of the object and the effort to overcome the applied force in the equation (1) and simplify. We get:

⇒ MA = \[\frac{F_{B}}{F_{A}}\] 

⇒ MA = \[\frac{900}{300}\] = 3 

Therefore, the mechanical advantage when a 300 Newton force is required to overcome a load of 900 Newton is 3.

FAQs (Frequently Asked Questions)

1) What are the Two Formulas Used to Estimate the Mechanical Advantage of Any Machine?

Ans: We know that according to the definition of mechanical advantage it is the ratio of input force to the force required to overcome the applied force. Mathematically we write:

⇒ MA = FB/FA ……..(1)

Where,

MA - The mechanical advantage

FB - The force of the object

FA - The effort to overcome the applied force

Similarly, the mechanical advantage of a machine can also be calculated by considering the ratio of the resistance force to the effort force. Mathematically we write:

⇒ MA = Fr/F

2) What is the Formula for Maximum Mechanical Advantage?

Ans: The maximum mechanical advantage can be evaluated when the applied force is equal to the resistance force. I.e., if the input force to the force is equal to the required force to overcome the applied force then we get the maximum mechanical advantage.

I.e.,

⇒ MA = FB/FA

⇒ MA = FA/FA x 100 = 100%