Imagine the following situation: you need to lift a bag full of groceries.

The total mass of the bag is 120 kg. Few people succeed, and usually only those who prepare for it. However, throughout history, people have often had to lift stones or objects, and have no machines to assist them.

For over 22 centuries, a man named Archimedes (287 - 212 BC) found an extremely simple method to solve this problem: he discovered the levers.

A lever is nothing more than a rigid bar that can pivot around a fulcrum.

In the middle of the 3rd century BC Archimedes stated:Give me a lever that will move the world

How could you, with the help of a lever, lift a 120kg sack with the same force as you would lift a 20kg sack of rice? In other words, how do you lift one mass six times the weight, doing the same strength you would lift it?

Simple! It is only the distance between the point of the rigid bar at which you apply the force and the fulcrum (from P to A) to be six times greater than the distance from the mass to the fulcrum (from A to R).

Let's name it:

  • Tough strength - is the force we want to balance. In the example above, it is the weight of the grocery bag.
  • Potent force - is the force that will sustain the resistance. In the example, it is the strength we make.

Levers Types


This is when the fulcrum (A) is between applying the force (P) and applying the force (R).


This is when the application of the powerful force (P) is between the application of the resistant force (R) and the fulcrum (A).


This is when the application of the resisting force (R) is between the application of the powerful force (P) and the fulcrum (A).

Levers equation

We'll ask math help to find an expression for the following situation.

Balance a very large mass by making a force much smaller than the weight of that mass we want to sustain.

Let's name it:

R: tough strength value - the strength we want to balance.

P: value of potent force - is the force that will sustain the resistance.

BR: resistance arm - is the distance from the body's center of gravity to the fulcrum.

BP: power arm - is the distance from the point of force application to the fulcrum.

O: Support point

We find that equilibrium will be achieved when:

Application Example

Let's calculate the strength that a bricklayer has to do to carry 80 kg of earth with the help of a wheelbarrow that is 1.80 meters long. Knowing that the distance between the center of gravity of the ground volume to the center of the cart wheel is 90 cm.

First let's look at what kind of lever we have.

Since what is in the middle of the cart is the ground, ie the resistance, the lever is inter-resistant.

We have:

resistance arm = 90 cm = 0.9 m

power arm = 1.80 m

resistance = 80 kgf.


The physical interpretation of this calculation is as follows: the bricklayer needs to force half the weight of the earth to lift the trolley and carry the load.

VDid you realize the great utility of such a simple machine?