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This tutorial explains the concept of buoyant force, a phenomenon in fluid mechanics and is central to the principles of flotation and buoyancy. The buoyant force is the net upward force exerted by a fluid on a submerged or partially submerged object. The magnitude of this force is dependent on the density of the fluid and the volume of the fluid displaced by the object.

kg m^{-3} | |

kg m^{-3} | |

Buoyant Force = Newton |

The principle of buoyancy was first established by the Greek scientist Archimedes, and the associated formula, known as Archimedes' principle, is:

F_{B} = ρ × g × V

Where:

**F**: The buoyant force (in Newtons)._{B}**ρ**: The density of the fluid (in kilograms per cubic meter).**g**: The acceleration due to gravity (9.81 m/s^{2}near the surface of the earth).**V**: The volume of the fluid displaced by the object (in cubic meters).

The principle of buoyancy and the associated formula were first established by Archimedes of Syracuse in the 3rd century BC. It is widely used in physics, specifically in fluid mechanics, as well as in engineering fields, especially those dealing with the design and manufacturing of ships and submarines.

The principle of buoyancy has numerous real-life applications. For example, it is used in the design and operation of ships and submarines. Engineers must carefully calculate the buoyant force to ensure that these vessels stay afloat when filled with cargo or personnel and that they maintain proper balance. In the medical field, Archimedes' principle is used in the method of underwater weighing, used to determine body density and body fat percentage.

Archimedes of Syracuse, a Greek mathematician, physicist, engineer, inventor, and astronomer, is known for formulating the principle of buoyancy. He was born in 287 BC and made significant contributions to the understanding of fundamental principles in physics, mathematics, and engineering.

- The principle of buoyancy is not just applicable to liquids; it also applies to gases. This is the reason why hot air balloons rise - the air inside the balloon is less dense than the surrounding colder air.
- Archimedes reportedly came up with his principle of buoyancy while taking a bath, noticing that water was displaced when he got into the bathtub.
- Buoyancy plays a vital role in the existence of life on Earth, as it influences the global climate system and the marine life ecosystem.

Understanding the concept of buoyant force based on the density of fluid and the volume of the fluid displaced by an object is crucial to many areas of physics and engineering. From the designing of ships to understanding the behavior of gases and liquids under different conditions, the calculations related to buoyant force have a significant impact on our daily lives.

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