# 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.