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The sum force acting on the object, then, is equal to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force). Equilibrium, or neutral buoyancy, is achieved when these two weights (and thus forces) are equal.
By the Pythagorean theorem, the magnitude of the resultant force is [(-10) 2 + (-8) 2] 1/2 ≈ 12.8 N, which is also the magnitude of the equilibrant force. The angle of the equilibrant force can be found by trigonometry to be approximately 51 degrees north of east. Because the angle of the equilibrant force is opposite of the resultant force ...
This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium. The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.
Buoyancy (/ ˈ b ɔɪ ən s i, ˈ b uː j ən s i /), [1] [2] or upthrust is a net upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid.
Heath called it "a veritable tour de force which must be read in full to be appreciated." [ 5 ] The book contains a detailed investigation of the stable equilibrium positions of floating right paraboloids of various shapes and relative densities when floating in a fluid of greater specific gravity, according to geometric and hydrostatic variations.
This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically, = where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of fluid directly above the curved surface. [8]
The increase in weight is equal to the amount of liquid displaced by the object, which is the same as the volume of the suspended object times the density of the liquid. [1] The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. [2]
There is also a tension parallel to the surface at the liquid-air interface which will resist an external force, due to the cohesive nature of water molecules. [2] [3] The forces of attraction acting between molecules of the same type are called cohesive forces, while those acting between molecules of different types are called adhesive forces.