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http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/dens.html
Archimedes' principle states that the buoyant force experienced by a submerged object is equal to the weight of the liquid displaced by the object. Experimentally this appears in the fact that the submerged object apparently weighs less by an amount equal to the weight of the liquid displaced. The buoyant force can be expressed as http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html#arch3 Buoyancy
Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object. Since the "water ball" at left is exactly supported by the difference in pressure and the solid object at right experiences exactly the same pressure environment, it follows that the buoyant force on the solid object is equal to the weight of the water displaced (Archimedes' principle).

Archimedes' Principle
The buoyant force on a submerged object is equal to the weight of the fluid displaced. This principle is useful for determining the volume and therefore the density of an irregularly shaped object by measuring its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter). This effective mass under water will be its actual mass minus the mass of the fluid displaced. The difference between the real and effective mass therefore gives the mass of water displaced and allows the calculation of the volume of the irregularly shaped object (like the king's crown in the Archimedes story). The mass divided by the volume thus determined gives a measure of the average density of the object. Archimedes found that the density of the king's supposedly gold crown was actually much less than the density of gold -- implying that it was either hollow or filled with a less dense substance. Examination of the nature

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