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In On Floating Bodies, Archimedes suggested that (c. 246 BC): Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes' principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated.
The purpose of On Floating Bodies I-II was to determine the positions that various solids will assume when floating in a fluid, according to their form and the variation in their specific gravities. The work is known for containing the first statement of what is now known as Archimedes' principle .
A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up.
Stable floating objects have a natural rolling frequency, just like a weight on a spring, where the frequency is increased as the spring gets stiffer. In a boat, the equivalent of the spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: "G" the centre of gravity of the boat and "M", which ...
Rigid plate submerged below water line. If the plate is flexible, its deformation (dashed) results in the displacement of additional fluid (blue, diagonal). However, doing so results in a simultaneous loss due to the narrowing of the above column (red, vertical).
The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. [12] At 1,469 km Iapetus is neither spherical nor ellipsoid.
Assuming such a state were to exist at some point, any departure of the diver from its current depth, however small, will alter the pressure exerted on the bubble in the diver due to the change in the weight of the water above it in the vessel. It is an unstable equilibrium. If the diver rises, by even the most minuscule amount, the pressure on ...
There are two books of On Floating Bodies. In the first book, Archimedes spells out the law of equilibrium of fluids and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round.