The brilliant Archimedes grew up in a mathematics family, received an excellent education in Alexandria and lived his whole life in the Sicilian town of Syracuse. He became the founder of theoretical mechanics, successfully worked on the problems of finding the surface area and volume of various figures and bodies. Often recall his famous phrase "Give me a fulcrum, and I will turn the Earth!" and the exclamation of "Eureka!" when he discovered the law, later named after him. But, in addition, he was an outstanding scientist in the field of geometry and mechanics, and his engineering achievements were surprising to contemporaries by the boldness of ideas and the grandeur of the results. He built catapults with high-precision throwing, the system of its block-lever mechanisms made it possible to raise the ship above the water, and the block of sun-reflecting mirrors he invented burned the Roman fleet during the siege of Syracuse.
Among other discoveries that history connects with the name of this ingenious scientist, the power of Archimedes has forever remained in physics. This discovery was connected with practical need: it was necessary to determine the honesty of the jewelers who made the crown for King Hieron II. What is now called specific gravity was already well known in those days, but how to determine the volume of such a complex product was not clear. The legend stubbornly connects the discovery of the law of Archimedes with the adoption of a bath for the scientist. The essence of the discovery lies in the fact that the buoyancy force of Archimedes acts on the body in a liquid, the definition of which is the subject of special attention to designers of swimming equipment, devices operating in liquids, under water, as well as aeronautics objects - balloons, probes, airships, etc. .
The classical formulation of the law says that the strength of Archimedes is equal to the weight of the liquid, which was replaced by the body immersed in it. Under this definition, the formula is written very easily: if we assume that the volume of the body immersed in the liquid is O, and the specific gravity of the liquid is p, then their product will be the sought-after strength of Archimedes. The formula for calculating it is written as follows:
Fa = p * O
Very often there is a temptation to verify the Archimedes law with respect to gases - the densities of liquid and gas differ too much. For skeptics, there is a fairly simple experiment. In a box with the possibility of pumping air, we place on the scales a large ball, for example, a glass one, and balance it with a metal weight.
So, in the air, the weight of the ball is balanced by the weight of the weight, and we can write items are balanced. If we initially assume that the law of Archimedes is valid, then the force of Archimedes Fs and Fg acts on the ball and weight, and then the equilibrium condition can be rewritten differently:
= 1 - and = 1 - , where 1 and 1 the weight of the ball and the weight in the void. Then we proceed as taught at the school: Psh1 - Fsh = Pg1 - Fg, whence Psh1 = Pg1 - Fg + Fsh = Pg1 + (F w - Fg).
The matter remained small - it is necessary to disclose the content of buoyancy forces for the ball and weight: = p * and = p * .
We make substitutions of the buoyancy forces into the expression for Psh1.
Rsh1 = Pr1 - Fg + Fsh = Pr1 + (p * Osh - p * Og) = Pr1 + p * (Osh - Og).
Finally, we obtain an expression for the weight of the ball in the void, which, taking into account the fact that Osh> Og, leaves no doubt: the weight of the ball in the void is greater than the weight of the weight, although they are balanced in air: Psh1 = Pr1 + p * (Osh - Og )
The reason for this conclusion is that the strength of Archimedes depends on the specific gravity of the air and the volume of the ball. In our case, checking this conclusion is very simple - you need to pump air out of the box. If this is done, then one can see firsthand that the law is the law, and it is always and everywhere fulfilled - both in liquid and in gases. Confirmation of this will be a ball that has fallen, previously balanced by a weight.
The device, the very existence of which is a continuous demonstration of the law of Archimedes in all its manifestations, is a submarine. Regulation of the weight of the vessel to implement all the options for moving with the help of ballast tanks is a vivid example of the practical use of a very ancient discovery in modern conditions.