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October 19, 2019

Mechanical advantage Formula

In this post we will talk about Mechanical advantage formula for different simple machines.

Just to give you a quick headsup, Mechanical Advantage of a machine is the ratio of output force and the input force. In other words, it is the ratio of Load and Effort.

Now to understand these in details we need to understand the concepts behind. Hope you will be with me to go through this topic and understand the minute details.

Before deriving the mechanical advantage formula, lets see how a machine provides us some kind of advantage and makes our life easier.

Mechanical Advantage formula – machines transforming input force

We use different types of machines in our daily life. They may be:

1>Simple machines – Some machines are simple tools or simple machines like bottle openers, screw drivers and scissors.
2>Complex machines – Some machines are complex like bicycles and automobiles.

We understand that Machines make our lives easier. But how?

The basic mechanism of generating mechanical advantage

1> we apply a force (effort) to the machine; this is the input force.

2> Machine in turns converts that ‘effort force’ by
– either changing its direction or changing its magnitude
– and then exerting another force (‘resistance force‘). This is the output force.
– Now with this resistance force the machine can overcome a resistance or Load.

To sum up, a machine either changes the magnitude or the direction of the input applied force and exerts an output force. This helps the machine or the person to easily overcome the load.

Now we will discuss with an example to understand the concepts of mechanical advantage.

what is mechanical advantage
what is mechanical advantage? it is the ratio of load and effort.

Mechanical Advantage formula – with an example

Consider the bottle opener in Figure 1.

what is mechanical advantage
fig 1: bottle opener
Fe is the input Effort force and
Fr is the output resistance force

When we use the opener the following steps are followed:

Input and Output force , Effort and Resistance force

1) Input force: We lift the handle of the bottle opener. That means we apply an upward input force or Effort force on it.(say Fe as shown in the figure above ) The handle of the bottle opener in our hand experiences an upward displacement. Hence a work is done on the opener.

2) Output force: The opener in turn transfers a force (output force say Fr as shown in the figure above) on the cap and lifts it. Thus the opener does work on the cap. This output force exerted by the bottle opener or any other simple machine is also known as Resistance force, because it overcomes a Load or a Resistance. In this case the Load is the cap of the bottle.

Input and Output Work

3) Input and Output work: Remember, the work that we do is called the input work, Wi. The work that the machine does is called the output work, Wo.
We know that as work is done it causes the transfer of energy by mechanical means.

(a) When we put work into a machine, such as the bottle opener then we transfer energy to the opener.

(b) The opener, in turn, does work on the cap, and transfers energy to the cap.

(c) We must understand that the opener is not a source of energy, and therefore, the opener can’t provide the cap more energy than the amount of energy that we put into the opener.

Thus, the output work can never be greater than the input work.

The machine simply aids in the transfer of energy from us to the bottle cap.

Formula for Mechanical Advantage

4) Now what is the relation between this Resistance force(output force) and the Effort force(input force) of a machine?

Here we get the term we are discussing on in this post. It is Mechanical Advantage.

Here we write,
Mechanical Advantage MA = Fr/Fe = resistance force/effort force.

Machine uses this resistance force to lift or pull a load. So resistance force is equal (magnitude wise) to the load overcome by the machine.

Therefore, we can also write
Mechanical Advantage MA = Load / Effort

Summary – FAQ on Mechanical Advantage Formula

Q) Write different forms of Mechanical Advantage Formula.

The mechanical advantage, MA, of the machine can be formulated as the

1> The ratio of the output force and the input force
2> The ratio of the Resistance Force and the Effort Force
3> The ratio of the Load overcome and the applied Effort Force.


Mechanical Advantage of a lever


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