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# What is Archimedes’ principle?

## Archimedes’ principle

The principle of Archimedes is also known as the physical law of buoyancy , was discovered by the ancient Greek mathematician and inventor Archimedes , who said that any body wholly or partially submerged in a fluid whether it was gas or liquid but were at rest is actuated by an upward or floating force of the magnitude of which is equal to the weight of the fluid displaced by the body. In this way, the volume of fluid displaced is equivalent to the volume of an object immersed in a fluid.

## What is Archimedes’ principle?

Archimedes’ principle is the principle which states that every body is immersed in a fluid experiences a push so vertically and upwards equal to the weight of fluid that has been evicted.

• What is Archimedes’ principle?
• History
• Statement of Archimedes’ principle
• Formula
• Floatation
• Applications of Archimedes’ principle
• Demonstration
• Examples
• Conclusions

## What is Archimedes’ principle?

Archimedes’ principle is a physical principle that consists in affirming that a body that is totally or partially submerged in a fluid at rest receives a push from the bottom up equal to the weight of the volume of the fluid it displaces. This force is known as the hydrostatic or Archimedean thrust , and it is measured in newtons . The principle states that every body immersed in a fluid experiences a vertical and upward thrust equal to the weight of fluid dislodged.

## History

Archimedes grew up in an environment where science was familiar, traveled through the Iberian Peninsula and studied in Alexandria where, together with Eratosthenes of Cyrene , he made the measurement of the earth’s circumference. When he returned to Syracuse , he devoted himself to studying mathematics, physics , geometry, mechanics, optics, and astronomy .

The anecdote from the beginning story tells how Archimedes created a method to determine the volume of an object with an irregular shape. According to Vitruvius , a new crown with had been made for Hiero II, who asked Archimedes to determine whether the crown was made of solid gold or silver . Archimedes had to solve the problem without damaging the crown, so he could not melt it to calculate its density.

When taking a bath , he noticed the water level rise in the tub as he entered, and he knew this could be used to determine the volume of the crown. Since the compression of the water would be negligible, the corona, when submerged, would displace a quantity of water equal to its own volume . When he divided the mass of the corona by the volume of displaced water, he obtained the density of the corona which would be lower if other cheaper and less dense metals had been added.

## Statement of Archimedes’ principle

The statement of Archimedes’ principle tells us that “every body totally or partially submerged in a fluid (liquid or gas) experiences a vertical and upward force (thrust) equal to the weight of the dislodged fluid .”

## Formula

Mathematically, the thrust force or Archimedes’ principle can be represented by the following formula:

Pfluid = E = m ⋅g = d ⋅V ⋅g

Where:

• Pfluid is the weight of the fluid that moves when submerging a body in it.
• E is the thrust force of the submerged body.
• m is the mass of the displaced fluid.
• d is the density of the fluid.
• V is the volume of the fluid dislodged.
• g is gravity .

## Floatation

The principle of flotation consists of the apparent loss of weight suffered by objects when they are submerged in a liquid. This happens because when an object is submerged in a liquid, the same liquid is responsible for exerting pressure on all the walls of the container that contains them, and on the bodies that are submerged within that liquid.

Due to the presence of hydrostatic pressure , the forces located laterally and acting on the body manage to find an equilibrium and then have the same value at the same depth . The opposite case occurs in the forces that are exerting pressure on the bodies both in the lower and upper parts since these forces are opposite , because one pushes downwards and the other pushes upwards.

With depth, the pressure also undergoes an increase and the forces that are exerted in the internal part of the object become greater than those that are located in the upper part, so the force is directed upwards and as a result we obtain that the objects can float, preventing them from sinking into liquids.

## Applications of Archimedes’ principle

Some applications of Archimedes’ principle are:

• In the submarine that does not change in volume but does change in weight, it gains water to submerge and expels it with air to reduce its weight and go up.
• Construction of life-saving floats , taking advantage of the low density of the float material.
• This principle applies to balloons that are filled with a gas less heavy than air, such as hot air balloons , montgolfiers , aero airships and others.
• When we immerse ourselves in a pool or in the sea it seems that we weigh less.
• Balloons sold for children can be lifted into the air when released.
• In general, a piece of iron does not float in water, but if we give it the proper shape , such as a ship, we see that it floats.

## Demonstration

To demonstrate Archimedes’ principle we must first consider the forces on a portion of fluid in equilibrium with the rest of the fluid. The force exerted by the fluid pressure on the parting surface is equal to p · dS , where p only depends on depth and dS is a surface element .

Because the fluid portion is in equilibrium, the resultant of the forces must cancel out with the weight of the fluid portion. We call this resultant thrust and its point of application is the center of mass of the fluid portion, called the center of thrust .

Thrust = weight = rfgV

Then the weight of the fluid portion will be the same as the product of the fluid density rf times the acceleration of gravity g and the volume of said portion V.

## Examples

Some examples of Archimedes’ principle applied to daily life are the following:

• The floats we use in pools and seas.
• The submarines .
• The balloons hot air.
• The buoyancy of boats, ships or any means of water transport.
• The artifacts used to measure the density of liquids.

## Conclusions

The conclusions obtained after studying Archimedes’ principle are the following:

• The density does not depend on the shape of the object.
• An object weighs less when it is in water.
• If the density of the body is greater than that of the fluid, the body will descend with an accelerated movement.
• If the density of the body is less than that of the fluid, the body will be able to ascend rapidly .
• If the density of the body is equal to that of the fluid, the body will be in equilibrium in the middle of the fluid column.