An object immersed in a fluid, whether a liquid or a gas, receives an upward push called Archimedes’ thrust, equal to the weight of the fluid the body displaces by taking its place. This thrust explains an apparently paradoxical fact: a steel ship floats, while a coin made of the same metal sinks. What matters is not the material itself, but how much fluid the body manages to displace relative to its own weight.
The origin of the thrust is the same hydrostatic pressure that grows with depth. The lower walls of an immersed body lie deeper than the upper ones and therefore experience greater pressure: the resultant of all these forces pressing on the body’s surface is directed upward, and the calculation shows that its magnitude exactly matches the weight of the displaced fluid.
Law — Archimedes' principle
A body immersed in a fluid receives an upward thrust, opposite to its weight, of magnitude where is the fluid density, the volume of fluid displaced and its mass.
The comparison between the thrust and the weight of the body decides its fate. If the body is denser than the fluid, its weight wins and it sinks; if it is less dense, the thrust prevails and the body rises until it floats, submerging only for the fraction of its volume needed to displace a weight of fluid equal to its own. Since air is also a fluid, Archimedes’ thrust acts on all of us as we walk through the atmosphere: it is, however, very small, because the density of air is about a thousand times lower than that of water, and for this reason we usually neglect it.
Historical context — Archimedes and "Eureka!"
According to legend, Archimedes (287–212 BC) discovered his principle while taking a bath: as he lowered himself into the tub, he noticed the water level rising. He leapt up and ran naked through the streets of Syracuse shouting Eureka! (“I have found it!”). The tyrant of Syracuse had asked him to determine whether a crown was pure gold or a gold-silver alloy, and Archimedes had worked out how: by comparing the volume of fluid displaced by the crown with that displaced by an equal weight of pure gold, he could expose any fraud.
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Topics: Fluidostatica e fluidodinamica Concepts: Principio di Archimede · Pressione
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