The Power of Archimedes

The genial Archimedes grew up in a mathematician's family, received an excellent education in Alexandria and spent his entire 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 the volume of various figures and bodies. Often recall his famous phrase "Give me a point of support, and I will turn the Earth!" And the exclamation of "Eureka!" When he discovered the law, later named after him. But, besides, he was an outstanding scientist in the field of geometry and mechanics, and his engineering achievements aroused surprise among his contemporaries with the courage of his designs and the grandeur of the results. He built catapults with high-throwing, the system of its block-leverage mechanisms allowed to lift the ship over the water, and the block of sun reflecting mirrors invented by him burned the Roman fleet at the siege of Syracuse.

Among the other discoveries that history associates with the name of this brilliant scientist, in physics Archimedes' force remained forever. This discovery was associated with a practical need: it was required to determine the honesty of the jewelers who produced the crown for King Hiero II. What is now called the specific gravity was well known already in those times, but how to determine the volume of such a complex product was incomprehensible. The legend persistently links the discovery of Archimedes' law to the acceptance of a bath by a scientist. The essence of the discovery is that Archimedes' buoyancy force acts on the body in the liquid, the definition of which is the subject of special attention of designers of swimming equipment, devices operating in liquids, under water, as well as objects of ballooning - balloons, probes, airships, etc. .

The classical formulation of the law says that the Archimedes' force is equal to the weight of the liquid that the body immersed in it has displaced. Under this definition, the formula is described very easily: if we assume that the volume of the body immersed in the liquid is 0, and the specific gravity of the liquid is p, then their product is the desired Archimedes force. The formula for its calculation is written as follows:

Φα = ρ * 0

Very often there is a temptation to check Archimedes' law with respect to gases - the density of the liquid and gas is much too different. For skeptics, there is a fairly simple experiment. In the box with the possibility of pumping air, we place on the scales a large ball, for example, glass, and balance its metal weight.

So, in the air, the weight of the ball is balanced by the weight of the weight and we can write the equality Pm = Pr, which is satisfied, since Objects are balanced. If we initially assume that Archimedes' law is valid, then the force of Archimedes Φι and Φ2 acts on the ball and the weight, and then the equilibrium condition can be rewritten in another way:

Pm = Pi, - Pi and Pi = Pi, - Pi, where Pi, and Pi, are the weight of the ball and the weight in the void. Then we act as we were taught at school: Pm1 = Pm = Pi1 - P2, whence Pm1 = Pi1 - P2 + Pm = Pi + ($ m - F2).

The matter remains for small - it is necessary to disclose the content of the pushing forces for the sphere and the dumbbell: $ m = p * Ow and $ i = p * Oz.

We make substitutions of the values of the pushing forces in the expression for Pm.

Pm1 = Pr1 - Φι + Φω = Pr1 + (p * Ow - p * Og) = Pr1 + p * (Oy - O2).

Finally, for the weight of the ball in the void, we obtain an expression which, given that Gm> Gg, leaves no doubt: the weight of the ball in the void is greater than the weight of the dumbbell, although in the air they are balanced: Pm = Pr2 + p * ).

The reason for this conclusion is that the strength of Archimedes depends on the specific weight of the air and the volume of the sphere. In our case, it is very easy to check this conclusion - you need to evacuate the air from the box. If this is done, then one can make sure that the law is a law, and it is always and everywhere fulfilled, both in liquid and in gases. Confirmation of this will be a lowered, previously balanced weight, a ball.

The device, the very existence of which is a continuous demonstration of Archimedes' law in all its manifestations, is a submarine. The regulation of the weight of a vessel for the realization of all variants of movement with the help of ballast tanks is a vivid example of the practical use of a very ancient discovery in modern conditions.