Mechanical Advantage Formula

Overview of Mechanical Advantage Formula

Mechanical Advantage actually uses the amplification in the force that we achieve by using a device or a complete mechanical system. Therefore is input force I this device that gives out to you a certain output desirable force that is amplified. The law that these machines use is the law of the lever.


The machines give specially designed structures and they are designed in a particular way in order to get the maximum output, this is designed to manage the forces. An ideal machine is one that transmits the power without adding or subtracting from it.


If we talk about mechanical advantage in terms of mathematics then it is the ratio of output force to the input force. This mechanical advantage is used to analyze the forces in machines; they can be simple machines such as levers or complex ones. The conservation of energy is true in these machines. The output force in some cases can be the same as that of the input force resulting in the value of mechanical advantage to be 1. The value of mechanical advantage can be less than 1 if the input force is more than the output force and the value of mechanical advantage can be greater than 1 If the input force is less than the output force. In all these cases of machines and levers, the conservation of energy is true.


The concept of mechanical advantage can be applied to many physical situations with rigid bodies and it can be used to calculate the force advantage that is gained in various tools. Simple machines such as levers use the mechanical advantage as the key property of their functioning. They are used to help humans in performing various tasks without actually using much force. 


Here, in this article provided to you, Vedantu will help you to get a brief view of the mechanical advantage topic. In the end, you are being provided with a number of frequently asked questions that serve the main purpose of clearing your queries regarding this topic of mechanical advantage.


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 1/15th 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 utilized 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:


\[ \Rightarrow M_{A} = \frac{F_{B}}{F_{A}} \]


Where,


MA - The mechanical advantage


FB - The force of the object


FA - The effort to overcome the applied force


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


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 Newton force is required to overcome a load of 800 Newton.

We know that the mechanical advantage formula is given by:

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

Where,

MA - The mechanical advantage

FB- The force of the object

FA - 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 = \[ \frac{F_{A}}{F_{B}}\]

⇒ 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 = FB = 900 Newton

We are asked to determine the force 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:

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

MA - The mechanical advantage

FB - The force of the object

FA - 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: 

⇒ \[M_{A} = \frac{F_{B}} {F_{A}}\] 

\[ F_{A}= \frac{F_{B}}{M_{A}} =\frac{900}{5} \] = 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 = FA = 300 Newton

Value of applied load = FB = 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

FB - The force of the object

FA - 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:

\[\Rightarrow = \frac{F_{B}} {F_{A}} \]

\[\Rightarrow M_{A} = \frac{900}{300} = 3 \]

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

FAQs on Mechanical Advantage Formula

1. What are the two formulas used to estimate the mechanical advantage of any machine?

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?

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%. 


Maximum Mechanical Advantage enables that there is no wastage of energy in the process if work is done. If any machine has a mechanical advantage equal to 1 then it is an ideal machine and suitable for helping humans in their work.

3. What does it mean by having a good mechanical advantage?

The ideal mechanical advantage refers to the change in input force that would be achieved only when there is no friction to overcome present in the machines. The ideal mechanical advantage is always greater than the actual mechanical advantage. Because there 9s a fact that all the machines need to overcome friction in the machines. There are hardly any machines that are having no friction and when the force is applied to a machine a part of the energy is wasted in overcoming this friction. This is the reason that in real life this is not possible to achieve the mechanical advantage as ideal.

4. What do you mean by higher mechanical advantage?

Mechanical advantage is actually the ratio of input force to output force. For performing any particular work we make use of the machines. If the mechanical advantage comes to be less than 1 then the machine is not regarded as ideal because the input force is higher than the output force. If we talk about higher mechanical advantages such as that in the screw. It will be the condition in which the amount of input force we are adding to do work in the machine is lesser than the output force that we get. This means for an ideal machine or higher mechanical advantage, the output force should be either equal to the input force or greater than the input force.

5. How can you calculate the mechanical advantage of a pulley?

A pulley is the machine air system that is used to help humans in order to do their work efficiently and in a much easier way. Firstly since the mechanical advantage is a ratio quantity it does not have any units. Then to calculate the mechanical advantage of the belt-driven pulley wheel,  you have to divide the inside diameter of the driven pulley by the inside diameter of the drive pulley wheel. The other way by which you can calculate the mechanical advantage of the pulley is to compare the number of rotations of the driven pulley wheel to one rotation of the drive pulley wheel.

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