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On Floating Bodies (Greek: Περὶ ... Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a centre of ...
For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor. In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero ...
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.
Here, () is the equation air/water interface, is the incremental displacement of the interface, and is the surface tension of water. For a given value of ρ s {\displaystyle \rho _{s}} , stable equilibrium configurations are identified as being those values of h {\displaystyle h} and α {\displaystyle \alpha } that satisfy
Note that the object is floating because the upward force of buoyancy is equal to the downward force of gravity. The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies (Ancient Greek: Περὶ τῶν ὀχουμένων), around 250 BC.
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.
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 ...
Scuba divers work with many buoyancy issues, as divers must know how to float, hover and sink in the water. Scuba divers often wear lead weights to counteract the positive buoyancy of their bodies and gear. Gases are also fluids, and so objects floating in the air may also be trimmed to be neutrally buoyant.