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 its the ratio of load and effort. Now if you are hungry enough (you should be) to learn more then please read on.
A lever is a simple machine which is basically a rigid rod which can rotate on a point on itself.
To understand this a little more we should have at least the basic understanding of the lever structure. So let’s get that in the next paragraph.
Lever – Fulcrum, Load and Effort
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 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.
We will use the term LOAD to refer to the resistance force in the next paragraphs.
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.
Refer to the diagram below to get an idea.
Here Fe is the applied force or Effort and Fr is the resistance force. This Fr lifts the Load.
Effort Arm definition
The length between Effort and Fulcrum of a lever is called Effort Arm (EA)
Load Arm definition
The length between Load and Fulcrum of a lever is called Load Arm (LA)
Mechanical Advantage of a lever -formula derivation
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:
– In rotational equilibrium Net torque is zero, that means, clockwise torque = anticlockwise torque.
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.
Mechanical Advantage formula – for lever
We have 2 equations or formulae for MA
Mechanical Advantage formula – 1
Mechanical Advantage of lever = load / effort
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.
MA Values and Implications
So its clear that to avail mechanucal advantage value more than 1, EA (Effort Arm) has to be more than LA (Load Arm).
This means to get MA 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.
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. (possible in class I and II)
In class III lever – Mechanical Advantage
In class III , effort is in between the fulcrum and load.
So load arm basically takes up the entire length of the lever, starting from 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, 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.
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 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.
LEVER – More information
Types of levers
The lever is divided into 3 types on the basis of the location of fulcrum, load and effort.
Class I lever – (Fulcrum is in the middle)
Here the pivot or fulcrum is in the middle of load and effort.
Class II lever – (Load is in the middle)
Here the nut (load here) is in the middle of effort and fulcrum.
Class III lever – (Effort in the middle)
Here effort is applied in the middle of fulcrum and load.