Often, scientific discoveries are the result of mere chance. But only people with a trained mind can appreciate the importance of simple 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 water.

In Syracuse about Archimedes legends were made. Once the ruler of this glorious city questioned the honesty of his jeweler. The crown made for the ruler was supposed to contain a certain amount of gold. Check this fact commissioned Archimedes.

Archimedes found that in the air and in the water the bodies have different weights, with the difference being directly proportional to the density of the body being measured. By measuring the weight of the crown in the air and in the 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 made crown.According to legend, Archimedes made this discovery in the bath, watching the splashed water. What happened next with a dishonest jeweler, history is silent, but the conclusion of a Syracuse scientist formed the basis of one of the most important laws of physics, which we know as the Archimedes law.

## Wording

The results of his experiments Archimedes stated in the work "On floating bodies", which, unfortunately, reached our days only in the form of passages. Modern physics describes the law of Archimedes as the total force acting on a body immersed in a liquid. The buoyant force of the body in the liquid is directed upwards; its absolute value is equal to the weight of the displaced fluid.

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

Any object immersed in a liquid experiences pressure forces. At each point on the surface of the body, these forces are perpendicular to the surface of the body. If these were the same, the body would only be squeezed. But the pressure forces increase in proportion to the depth, therefore 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 the various consequences of it. Archimedean forces operate in the gases. It is thanks to these pushing forces that airships and balloons fly in the sky: due to air displacement, they become lighter than air.

## Physical formula

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

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

here Pabout   - weight in vacuum;

Fbut   - the power of Archimedes.

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

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

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

Analyzing the simplest experiments with body weight in various environments, it can be concluded that body weight in various environments depends on the mass of the object and the density of the immersion medium. And the denser the environment, the greater the power of Archimedes. Archimedes' law linked this dependence and the density of a liquid or gas is reflected in its final formula. What else affects this power? In other words, on what characteristics does Archimedes' law depend?

Archimedean power and the forces that influence it can be determined with the help of simple logical conclusions. Suppose that a body of a certain volume, immersed in a liquid, consists of the same liquid in which it is immersed. This assumption does not contradict any other prerequisites. After all, the forces acting on the body are in no way dependent on the density of this body. In this case, the body is likely to be in balance, and the force of ejection will be compensated by gravity.

Thus, the balance of the body in water will be described as follows.

But the force of gravity, from the condition, is equal to the weight of the fluid that it displaces: the mass of the fluid is equal to the product of density and volume. Substituting known values, you can find out the weight of the body in the liquid. This parameter is described as 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 study. But in the initial conditions it was stated that the density of the body is identical to the density of the surrounding liquid. Thus, in this formula, you can safely substitute the value of the density of the liquid. Visual observation, according to which the force of pushing out is greater in a denser medium, received a theoretical substantiation.

## Application of Archimedes Law

The first experiments, demonstrating the law of Archimedes, are known from school. The metal plate is sinking 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 the Archimedes rule, it determines the possibility of constructing river and sea vessels taking into account their maximum capacity (displacement). After all, the density of sea and fresh water is different and ships, and submarines must take into account the differences of this parameter when entering the mouths of rivers. The wrong calculation can lead to a catastrophe - the ship will run aground, and its lifting will require considerable effort.

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