Often, scientific discoveries are the result of a simple accident. But only people with a prepared mind can appreciate the importance of mere coincidence and draw far-reaching conclusions from it. It was thanks to a chain of random events in physics that Archimedes' law appeared explaining the behavior of bodies in the water.

In Siracusa, Archimedes made legends. Once the ruler of this glorious city doubted the honesty of his jeweler. In the crown made for the ruler, there should have been a certain amount of gold. Check this fact instructed Archimedes.

Archimedes established that in the air and in water the bodies have different weights, and the difference is directly proportional to the density of the measured body. Measuring the weight of the corona in air and water, and having conducted a similar experiment with a whole piece of gold, Archimedes proved that there was an admixture of lighter metal in the manufactured crown.According to legend, Archimedes made this discovery in the bath, watching the splashed water. What happened next to the dishonest jeweler, history is silent, but the inference of the Syracusan scientist formed the basis of one of the most important laws of physics, which is known to us as the law of Archimedes.

## The wording

The results of his experiments Archimedes outlined in the work "On floating bodies", which, unfortunately, came to our days only in the form of excerpts. Modern physics is described by Archimedes as an aggregate force acting on a body immersed in a liquid. The buoyancy force of the body in the liquid is directed upwards; its absolute value is equal to the weight of the displaced liquid.

## The action of liquids and gases on the submerged body

Any object immersed in a liquid experiences pressure forces. At each point of the surface of the body, these forces are directed perpendicular to the surface of the body. If they were the same, the body would experience only contraction. But the pressure forces increase in proportion to the depth, so the lower surface of the body experiences more compression than the upper one. You can consider and add up all the forces acting on the body in the water. The final vector of their direction will be directed upwards, the body is ejected from the liquid. The magnitude of these forces determines the law of Archimedes. The swimming of bodies is entirely based on this law and on various consequences from it. Archimedes forces act in gases. It is thanks to these expulsion forces that airships and air balloons fly in the sky: thanks to the air displacement they become lighter than air.

## The physical formula

Visually, the strength of Archimedes can be demonstrated by simple weighing. Weighing the training weight in vacuum, in air and in water, you can see that its weight varies significantly. In vacuum, the weight of the weight is one, in the air - a little lower, and in the water - even lower.

If we take the body weight in vacuum for Pabout. then its weight in the air can be described by the following formula: Pat  = Pabout  - Fa;

here Pabout  - weight in vacuum;

Fa  - the strength of Archimedes.

As can be seen from the figure, any actions with weighing in water greatly facilitate the body, so in such cases the Archimedes' force must be taken into account.

For air, this difference is negligible, so usually the weight of the body immersed in the air medium is described by the standard formula.

## The density of the medium and the strength of Archimedes

Analyzing the simplest experiments with body weight in various media, one can come to the conclusion that the weight of a body in different media depends on the mass of the object and the density of the immersion medium. And the denser the environment, the greater the strength of Archimedes. Archimedes' law linked this dependence and the density of a liquid or gas is reflected in its final formula. What else influences this force? In other words, on which characteristics does Archimedes' law depend?

The Archimedes force and the forces that influence it can be determined with the help of simple logical deductions. Suppose that a body of a certain volume, immersed in a liquid, consists of the same fluid in which it is immersed. This assumption does not contradict any other premises. After all, the forces acting on the body, in no way depend on the density of this body. In this case, the body will most likely be in equilibrium, and the force of ejection will be compensated by gravity.

Thus, the body's equilibrium in water will be described as follows.

But the force of gravity, from the condition, is equal to the weight of the liquid that it displaces: the mass of the liquid is equal to the product of density per volume. Substituting known quantities, one can know the weight of a body in a liquid. This parameter is described in the form ρV * g.

Substituting the known values, we get:

This is the law of Archimedes.

The formula deduced by us describes the density as the density of the body under investigation. But in the initial conditions it was stated that the density of the body is identical to the density of its surrounding liquid. Thus, the value of the density of a liquid can be easily substituted into this formula. Visual observation, according to which in a more dense medium, the ejection force is larger, has received theoretical justification.

## Application of the Archimedes Law

The first experiments demonstrating the law of Archimedes are known from the school's bench. The metal plate is drowning in water, but, folded in the form of a box, can not only be kept afloat, but also carry a certain weight. This rule is the most important conclusion from Archimedes' rule, it determines the possibility of constructing river and sea vessels, taking into account their maximum tonnage (displacement). After all, the density of sea and fresh water is different and ships, and submarines should take into account the differences in this parameter when entering the mouth of rivers. Incorrect calculation can lead to a catastrophe - the ship will run aground, and it will take considerable effort to raise it.

Archimedes' law is also necessary for submariners. The fact is that the density of sea water changes its value depending on the depth of immersion. Correct calculation of the density will allow the submariners to correctly calculate the air pressure inside the suit, which will affect the maneuverability of the diver and ensure his safe diving and ascent. Archimedes' law should also be taken into account in deep-sea drilling, huge drilling rigs lose up to 50% of their weight, which makes their transportation and operation less costly.