Mechanical Advantage of a Lever

This post explains what is the Mechanical Advantage of a lever and finds out its formula. This also covers the general description of Lever terminologies.

What is the mechanical advantage of a lever?

Mechanical advantage of a lever is the ratio of the load the lever overcomes and the effort a person or system applies to the lever to overcome some load or resistance. In simple words, it’s the ratio of load and effort. Now if you are hungry enough (you should be) to learn more then please read on.

What is a lever?

A lever is a simple machine that is basically a rigid rod that can rotate on a point (called pivot or fulcrum) on itself.
Example of levers: seesaw, scissors, tweezers, stapler

To understand this a little more we should have at least a basic understanding of the lever structure. So let’s get that in the next paragraph.

How does the lever work?

mechanical advantage of a lever
Lever with Fulcrum, EA and LA

As said, a lever is a rigid rod that can rotate on a point or pivot. This pivot is called Fulcrum (F).
Now how it operates?

1> A force or effort(Fe) is applied at a point of the lever rod depending on the type of the lever. This effort is the input force.

2> The Lever transforms the input force either by amplifying it or by changing its direction and exerts an output force. This output force is called the Resistance force (Fr).
Note that, this output force is actually responsible to lift the Load.
So you can say that magnitude wise the Resistance force is equal to the Load which the lever is capable to overcome for the given Effort.
The load to be lifted is kept at a different point on the same rod or lever.

Here we can say that a lever is used to lift a load by applying a force or effort.

We will use the term LOAD to refer to the resistance force in the next paragraphs.

Refer to the diagram above to get an idea.
Here Fe is the applied force or Effort and Fr is the resistance force. This Fr lifts the Load.

What is the Effort Arm of a lever?

The length between Effort and Fulcrum of a lever is called Effort Arm (EA)

mechanical advantage of a lever
Lever with Fulcrum, EA, and LA

What is the Load Arm of a lever?

The length between Load and Fulcrum of a lever is called Load Arm (LA)

MA formula

How can we derive the Mechanical Advantage formula of a lever?

A lever provides leverage to its users by amplifying the applied force or by providing comfort or convenience to do some specific activities.

Mechanical Advantage of a lever is the amplification factor of a lever. It’s the ratio of Load and Effort. Here for simplicity, we have used the symbols L and E for load and effort respectively.

Mechanical Advantage formula of a lever = Load lifted/Effort applied= L/E ………………(equation 1)

In the diagram below, you can see that the Effort(E) is trying to provide a CW (Clock Wise) rotation to the lever rod. On the contrary, the Load L (the weight to be lifted, say) is trying to give an ACW (Anti Clock Wise) rotation to the rod.

In balanced condition or equilibrium of a lever, the following condition is satisfied:
– If the lever is in rotational equilibrium then the Net torque is zero, which means, clockwise torque on the lever rod = anticlockwise torque on the lever rod.

MA of lever
Net torque is zero, that means, clockwise torque = anticlockwise torque

            We know that torque is the cross product of force and lever arm. Here as per the diagram,
EA * E = LA * L

i.e., Effort Arm * Effort = Load Arm * Load

=> Load / Effort = Effort Arm / Load Arm

As we know, Mechanical Advantage = Load/Effort

that means another expression of MA is obtained here which is the ratio of the effort arm length and the load arm length.

What is the Mechanical Advantage formula for a lever?

We have 2 equations or formulae for MA of a lever.
1> Mechanical Advantage formula – 1
Mechanical Advantage of lever = load / effort
2> Mechanical Advantage formula – 2
Mechanical Advantage of lever = Effort Arm / Load Arm = EA /LA
So either of these 2 equations can help us to get us the value of the Mechanical Advantage of a lever.

 How can you increase the mechanical advantage of a lever?

So it’s clear that to avail of mechanical advantage value more than 1, EA (Effort Arm) has to be more than LA (Load Arm).
This means to get the mechanical advantage of a lever more than 1

the load should be nearer to the fulcrum (to have a smaller Load Arm) and

the Effort should be applied farther from the fulcrum (to make the Effort Arm larger).

**For class I and II, we can get MA more than 1 by following the above-said condition.

How do the first class and the second class levers help in general?

Now remember that, Mech Advantage = Load/effort.
So making Mech Advantage more than 1 means Load lifted is more than the Effort Applied.
That means the input effort is multiplied and a load more than the applied Effort can be lifted by a lever. This is possible by class I and II levers as their effort arm is longer than load arm, making their MA more than one.

How does a class III lever has a Mechanical Advantage less than one?

In class III lever or third class lever, the effort is in between the fulcrum and load.

So the load arm basically takes up the entire length of the lever, starting from the load at one end to the fulcrum at the opposite end.
While effort being in the middle of the fulcrum and load, effort arm is just a part of the entire lever length.
Naturally, the load arm(LA) is always bigger than the effort arm(EA) for class III lever.
As Mech Advantage is the ratio of EA and LA, so for class III (where LA>>EA) Mech advantage is always less than 1.

mechanical advantage of a lever

In Spite of that, we use class III lever in specific conditions where we apply more effort to lift much lighter load but with greater ‘comfort’.

So in this post, we have discussed the mechanical advantage of a lever. Also, we have worked with the derivation of its formulae. Hope you have liked it. So pls share this post among your friends as much as possible.

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