# Features of the technology of melting bodies and their practical application

Why don’t iron ships sink? Archimedes’ law answers these questions. The discovery made by the ancient Greek physicist predetermines the conditions for floating bodies in a liquid, explains the possibility of flying balloons and airships. The mathematical formula, derived by the great Greek after experiments and experiments, is used in the projects of shipbuilders and aircraft designers.

## The condition for bodies to float in a liquid

The location of an object in space is explained by the forces acting on it. Violation of the balance of the applied efforts brings the object out of equilibrium and gives a start to movement. In a gaseous medium and liquid, the vertical course of a body depends on a pair of forces – buoyancy and gravity. The law describing the interaction of two main components was discovered by Archimedes three centuries before the birth of Christ.

Archimedes was born in 287 BC. e. in Sicily in the Greek colony of Syracuse. In childhood, his father, the astronomer and mathematician Phidias, took up the upbringing of the boy. The young man received a comprehensive education in Alexandria, where he studied the works of Democritus and Eudoxus, communicated with Eratosthenes and Conon. Life in the scientific capital of the ancient world formed Archimedes as a talented researcher and experimenter.

Scientists who influenced the formation of Archimedes:

- Greek philologist and geographer Eratosthenes – calculated the size of the Earth;
- mathematician and astronomer Konon, who made weather forecasts and calendars showing the times of sunrise and sunset;
- in the works of the thinker Democritus, the theory of an indivisible particle – the atom – was developed, which formed the basis of materialistic philosophy;
- Asia Minor philosopher Eudoxus, who is considered the ancestor of integral computing and theoretical astronomy.

After studying in Egypt, Archimedes returned to Syracuse, where he lived until his tragic death in 212 BC. e. Three years earlier, the Romans began a siege of the Sicilian city, which was helping the Carthaginian state. The engineering talent of the Greek mathematician helped the townspeople hold back the attacking legions. The besieged Greeks used catapults of various calibers and cranes, which turned enemy galleys with hooks. Curved mirrors, focusing beams in one point, burned the enemy fleet.

There are several versions of the legend about the death of Archimedes. But the descriptions coincide in one thing – the thinker, busy at that moment in scientific research, was killed by a Roman soldier, after Syracuse surrendered to the mercy of the victor.

Archimedes wrote thirteen treatises. In the books of the scientist, the main provisions of hydrostatics and theoretical mechanics are determined. Calculating the surface areas of figures and the volumes of bodies, the mathematician laid the foundations for the integral and differential calculation of quantities. Engineering developments of the great inventor find application in modern designs.

## Body immersed in liquid

There are examples in the history of science when the practical demands of society lead to scientific discoveries. In a similar way, the basic law of statics was discovered. Calculating the volume of the royal crown, Archimedes immersed the symbol of state power in a vessel with water. At the same time, the scientist drew attention to the fact that an object dipped into a liquid becomes lighter. Subsequent reflections lead the great Greek to the discovery of the hydrostatic law, named after him.

Archimedes’ law states that a body immersed in a gaseous medium or liquid is acted upon by a force equal to the weight of the volume of gas or liquid that has been displaced by this body. In the language of mathematics, the postulate is expressed by the equation:

F = gρV.

Semantic definition of mathematical symbols used in the formula:

F – buoyancy or Archimedean force;

g – coefficient of acceleration of gravity, equal to 9.8 m / s²;

ρ is the density of the medium in which the body is placed;

V is the volume of the displaced liquid or gas.

Archimedean force is opposite to the force of gravity and is always directed from the center of the Earth strictly vertically upwards. In zero gravity, where g = 0, Archimedes’ law does not work. The interaction of two forces – gravity Ft and buoyancy Fa – determines the behavior of an object in space. A vivid example of the manifestation of the Archimedes force is the rise of an air bubble to the surface of the water.

A body floating on the boundary of media with different densities is acted upon by a total force:

Fa = (ρ₁V₁ + ρ₂V₂ + ρ₃V₃ + …),

where ρ₁, ρ₂, ρ₃ are the densities of various media, and V₁, V₂, V₃ are the volumes of parts of the object.

There are three options for the development of events:

If Ft ˂ Fa, then the body begins to float.

Provided Ft = Fa, the object is at rest.

If Ft ˃ Fa, then the object is immersed.

The situation develops in a similar way if the values of the forces are replaced by the values of the densities of the body and liquid or gas. That is, instead of the gravity force Ft, use the density of the object, and instead of the buoyant force Fa, consider the density of the medium in which the object is placed.

## Ships don’t sink, airships fly

The buoyancy of a ship is the ability of a ship to remain in equilibrium without floating or sinking to depth. According to Archimedes’ law, the conditions for floating bodies arise when the force of gravity is equal to the buoyant force. The buoyancy margin is defined as the percentage of the volume of the watertight cavity above the waterline to the volume of the entire ship. Surface ships are calculated with a buoyancy reserve of at least 50%.

The formula for calculating the buoyancy margin:

W = v / V * 100%,

where W is the buoyancy reserve, v is the volume of the compartments above the waterline, V is the volume of the entire ship.

Displacement is the main characteristic of water transport and is equal to the amount of water displaced by the underwater part of the watercraft. The waterline, being a horizontal section, is indicated on the hull and visually shows the level of normal displacement. Subtracting the weight of the vessel from the displacement will represent the carrying capacity of the vehicle.

In the physical sense, the buoyancy reserve means the ability to be on the surface of the reservoir. Distinguish between neutral and negative buoyancy. In the first case, W = 0% and the ship is submerged in water to the level of the deck. The slightest external impact leads to flooding. In the second case, the ship is not able to stay afloat.

An object in the air is also affected by Archimedean force. If the lifting force exceeds the force of gravity, then the body begins to move away from the earth’s surface. The principle of aeronautics is based on this postulate. The formula for Archimedes’ law uses air density.

In order for the aircraft to rise, the envelope of the balloon or airship is filled with a gas lighter than air. For this, hydrogen and helium are suitable, whose densities are less than a mixture of atmospheric gases. Due to the explosive nature of hydrogen, helium is more commonly used.

The ideal option is to use heated air in the balloon envelope. The burner is installed under the hole in the bottom of the sphere. Periodically turning on the heating element changes the temperature and density of the air inside the ball, which allows you to adjust the rate of ascent or descent.