Archimedes Principle

More than half of the world is water, and businesses to date have largely depended upon these waterways. Furthermore, the waterways or the sea route use ships to ferry commodities from one part of the world to another, and ships are huge vessels that float on these sea routes and provide an excellent medium for the transportation of commodities and people. Since these units are very important and have been important for a long time, the technology and principles related to the field have held high importance since ancient times. Thus, the Archimedes principle holds immense value.

Statement of Archimedes Principle

The Archimedes principle states that the upward or the buoyant force exerted on a body (floating or fully submerged in a fluid) is equal to the weight of the displaced fluid. This is because the force acts in an upward direction, and the point of action is the centre of mass of the fluid displaced.

The Story of Archimedes and Eureka

The theorising of the Archimedes principle is a very funny tale in the history of physics. The king of Syracuse in Greece wanted to dedicate a pure gold crown to god, and thus he called for the best sculptor to work out the best possible design.
Once the crown was ready, the king suspected that the gold worker (sculptor) had cheated him. He felt that the metal used in making the crown was not pure gold. Unfortunately, technology was not present at that time, and the only way to check for purity was to melt the crown. So, on one hand, the king didn't want to melt the crown, and on the other, he wanted to check the purity of gold used.
The king called for Archimedes to solve the problem, and Archimedes came up with the idea a few days later while taking a bath. It is said that he was so excited with his discovery that Archimedes ran naked shouting Eureka! Eureka through the streets of Syracuse till he reached the palace. Eureka means I have found it.

Weight Loss in Archimedes Principle

There is a weight loss experienced when a body is submerged in a fluid, which is due to the buoyant force. The apparent weight is the difference between weight and buoyancy force.

Derivation of expression

The mass of the fluid displaced = Volume of fluid displaced x Density of fluid displaced
= ⍴ x V
Weight of fluid displaced = mass of the fluid displaced x acceleration due to gravity
= ⍴ x V x g

According to the Archimedes Principle

Apparent weight = Weight of the body- Buoyant force
= mg - (⍴ x V x g)
=g (m- ⍴V)
Where
⍴ is the density of the fluid
V is the volume of fluid displaced by the body or the volume of the body submerged
m is the mass of the body
g is the acceleration due to gravity

Applications of the Archimedes Principle

The application of the Archimedes Principle include the following:

Hot air balloon is the oldest mode of air travel, and it works on Archimedes principle. The hot air is lighter, and by heating the air trapped in the balloon, we make it displace the cold air, which exerts a buoyant force on the balloon, raising the balloon.
The Archimedes principle is vital in shipbuilding. Builders make changes in the load-bearing capacity of the ship, keeping in mind the buoyant forces.
Archimedes' principle is vital in the working of a submarine which increases its weight by taking in water in the ballast tanks and dives below the water surface. The pumping of compressed air in the ballast tanks reduces weight and helps the submarine to surface.
We use a hydrometer to measure the relative density of various liquids, and it works on the Archimedes Principle. It determines the density by sinking in the liquid. If the density is high, the liquid will prevent the sinking of the hydrometer, but if the density is low, the hydrometer will sink more.
Archimedes' principle also finds its use in Geology. For example, the principle helps measure the average density of the rocks.

Frequently Asked Questions about Archimedes Principle

Ques: Why does the weight of the submerged body appear to be lower than the unsubmerged body?
When a body is submerged in a fluid, the fluid applies an upward force on the body, which reduces the body's weight. Thus, a submerged body appears to have a reduced weight compared to the unsubmerged one.

Ques: How is Archimedes Principle vital to ships?
The density of iron, steel or aluminium is very high compared to water, and anything having a very high density compared to water is supposed to sink in the water. Thus, it begs the question of how ships float? The volume of the ships is increased to displace a large amount of water which can support the weight of the entire ship and its cargo. Thus, the average density of the ship is reduced by combining it with vacant spaces (cabins) filled with air. It no longer remains a block of solid metal, and thus it displaces enough water to float.