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Buoyancy

Buoyancy is the ability to float. In physics, the word buoyancy also refers to the quantity of buoyant force, regardless of whether the object floats or not. If the buoyancy exceeds the weight, then the object floats; if the weight exceeds the buoyancy, it sinks. It was the ancient Greek Archimedes of Syracuse who first discovered the law of buoyancy, sometimes called Archimedes' principle:
The buoyancy is equal to the weight of the displaced fluid.
(Fluid means either a liquid, such as water or oil, or a gas, such as air.) If the weight of an object is less than that of the fluid that the object displaces when it is fully submerged, then it floats at such a level that the weight of the object is equal to the weight of the displaced fluid. If the object's weight exceeds that of the displace fluid, then it sinks.

An object of a material of higher density than the fluid, e.g. a metal object in water, can still float if it has a suitable shape that keeps air below the surface level of the fluid. In that case, for the average density mentioned above, the air is included also, which may reduce this density to less than that of the fluid.

This is the principle of vessels such as boats and ships, discovered by Archimedes.

Although Archimedes' principle gives the force on a buoyant object, it is generally not recognized that this does not determine the related acceleration of the object in the usual way over Newton's first law. This is because not only has the mass of the object to be accelerated but also the mass of the displaced fluid. One can compare the situation to a scale, where the weight on one side is given by the object, and the weight on the other side by the displaced fluid element. Depending on which of the two is heavier, one side of the scale will drop and the other rise, but since both sides are rigidly connected, both masses have to be accelerated together at the same rate (albeit in opposite directions).

It is obvious that without taking the displaced fluid element into account, energy would not be conserved during the buoyant motion of an object as it would gain both potential and kinetic energy when rising in the fluid.