| Archimedes' Principle (Buoyancy) |
| What Archimedes realized about buoyancy |
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| Archimedes solved many problems for King Heiro of Syracuse. His most famous solution is associated with Heiro's new crown. Heiro had given the goldsmith the exact amount of gold needed for the crown. After it was made, Heiro suspected that it might not have as much gold as it was supposed to. King Heiro summoned Archimedes, and Archimedes was bewildered with the king's problem. But later, when Archimedes got into his full bathtub, it occurred to him that the volume of water that spilled out of the tub was equal to the volume he displaced. Reasoning that a much lower volume of water would be displaced by something denser (like gold) even though of equal weight, he saw the answer to the king's problem. The next day Archimedes told they king of his discovery. Archimedes put the king's new crown in a tub of water and found that the crown indeed displaced more water than the same weight of gold (it occupied more volume because it had been adulterated with lower density silver). The goldsmith was immediately beheaded. |
Modern formulation of Archimedes' Principle on buoyancy
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THE PRINCIPLE: "Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."
Where Fb is the buoyant force, M DISPLACED WATER is the mass of the water that was displaced by the object, V DISPLACED WATER is the volume of the water that was displaced by that same object, D WATER is the density of the water, and g is the acceleration of gravity. The opposing force (green F) is equal to the mass of the object times the acceleration of gravity.
Archimedes' principle works in both gases and liquids (fluids).
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The physical law of buoyancy, discovered by the ancient Greek mathematician and inventor Archimedes, stating that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface for an object partially submerged in a liquid. The weight of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. The buoyant force on a body floating in a liquid or gas is also equivalent in magnitude to the weight of the floating object and is opposite in direction; the object neither rises nor sinks. A ship that is launched sinks into the ocean until the weight of the water it displaces is just equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo.
If the weight of an object is less than that of the displaced fluid, the object rises, as in the case of a block of wood that is released beneath the surface of water or a helium-filled balloon that is let loose in air. An object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced. In fact, in some accurate weighings, a correction must be made in order to compensate for the buoyancy effect of the surrounding air. Buoyancy is caused by the increase in fluid pressure at increasingly greater depths. The pressure on a submerged object, therefore, is greater on the parts more deeply submerged, and the buoyant force is always upward, or opposite to the gravitational force; it is the net effect of all the forces exerted on the object by the fluid pressure. |