#### Buoyancy force

Buoyancy force as an important factor of Archimedes' Law

According to Archimedes' law, any body immersed in a liquid or gas is subjected to a certain force. This force is commonly referred to as the buoyancy force. As far as the value of this force is concerned, it turns out that it is exactly equal to the value of the liquid displaced by it. It has been proven that the buoyancy force is always directed upwards, perfectly vertically. The buoyancy force is also a result of the hydrostatic pressure exerted on an immersed solid. The buoyancy force does not depend on the shape of the submerged body and is greater than the volume of the immersed body and the density of the liquid in which it is immersed.
In other words, the buoyancy force occurs when a solid body is immersed in a fluid. The force that arises during immersion and pushes the body upwards is called the buoyancy force.

Where does the buoyancy force come from?

We should ask ourselves a fundamental question: where does this force actually come from? The answer is unambiguous. It arises from the fact that the pressure in a fluid changes with its depth. What exactly does this mean? Namely, the deeper you go, the greater the pressure becomes. Of course, the force acting is different depending on where it acts on a submerged body. It will be different at the bottom of the body and at the top.

How do we know the value of the buoyancy force?
Thanks to Archimedes, today we know that the buoyancy force is equal to the weight of the fluid being displaced (i.e., a body displaces as much liquid as the volume of the part of the body that is immersed in the liquid). Unless the entire body is immersed, then the volume of the entire immersed body is what matters. When we deal with buoyancy, the possibility of bodies swimming immediately comes to mind. With this knowledge, the world has found plenty of applications of this theory. Here are some examples of its application in practice:

- Ships. Their buoyancy force is equal to their gravity force.
- Submarines. Thanks to their manoeuvrability, they can sink or surface as required.
- Ice is lighter than water and, therefore, rises to the surface.

However, not all bodies are sufficiently buoyant. If a body has too much weight, it will not be able to rise above the surface – an example would be stones.
However, most objects that are able to float freely on the surface have a specific gravity close to that of water; hence, the conditions for bodies to float can be derived:
- if the density of the body is greater than the density of the liquid, the body sinks
- if the density of the body is lower than that of the liquid, the body rises to the surface
- if the density of the body is equal to the density of the liquid, the body floats, completely submerged under the surface of the liquid

The formula for buoyancy force:

Fw=pgVot

where Fw = buoyancy force
p = density of the liquid
g = acceleration due to gravity
V = the volume of the submerged part of the body

History of the origin of Archimedes' Law.
According to legend, Hieron II, King of Syracuse, commissioned Archimedes to examine the composition of his crown. He was concerned that it was not made of pure gold. This was to be done without damaging the crown. While taking a bath, Archimedes noticed that the amount of water flowing out of the bathtub was equal to the volume of the body immersed in water. The thought immediately occurred to him to examine the king's crown, so he prepared a lump of silver and a lump of gold. It turned out that when the lump of gold was immersed, less water flowed out – which suggested that the density of gold was greater than that of silver. Then, when he threw the crown into the bathtub, he noticed that more water flowed out than when immersing a lump of the same weight, which proved that there was an admixture of another metal in the composition of the crown.

Archimedes' discovery gave the world new possibilities. Today, his discovery is used in many important sectors of the economy. Above all in maritime transport. This would not have happened had it not been for a somewhat accidental discovery. Thanks to his theory, Archimedes became one of the most famous Greek mathematicians.

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