Editing Archimedes' principle (section)

==Formula==
[[Image:Archimedes principle.svg|thumb|A floating object's weight F<sub>p</sub> and its buoyancy F<sub>a</sub> (F<sub>b</sub> in the text of the image)  must be equal in size.]]
Consider a cuboid immersed in a fluid, its top and bottom faces orthogonal to the direction of gravity (assumed constant across the cube's stretch). The fluid will exert a [[normal force]] on each face, but only the normal forces on top and bottom will contribute to buoyancy. The [[pressure]] difference between the bottom and the top face is directly proportional to the height (difference in depth of submersion). Multiplying the pressure difference by the area of a face gives a net force on the cuboid—the buoyancy—equaling in magnitude the weight of the fluid displaced by the cuboid. By summing up sufficiently many arbitrarily small cuboids this reasoning may be extended to irregular shapes, and so, whatever the shape of the submerged body, the buoyant force is equal to the weight of the displaced fluid. 
:<math>\text{ weight of displaced fluid} = \text{weight of object in vacuum} - \text{apparent weight of object in fluid}\,</math>

The [[weight]] of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The [[apparent weight]] of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force (F<sub>b</sub>) on an object is equal to the weight of the fluid displaced by the object, or the [[density]] ([[Rho|ρ]]) of the fluid multiplied by the submerged volume (V) times the [[Gravity of Earth|gravity]] (g)<ref name="khanacademy.org"/><ref>{{cite web|url=http://physics.bu.edu/~duffy/sc527_notes01/buoyant.html|title=The buoyant force|website=bu.edu
|access-date=3 September 2023}}</ref>

We can express this relation in the equation:
:<math> F_{a} = \rho g V</math>
where <math> F_{a} </math> denotes the buoyant force applied onto the submerged object, <math> \rho </math> denotes the [[density]]  of the fluid, <math> V</math> represents the volume of the displaced fluid and <math> g </math> is the acceleration due to [[Gravity of Earth|gravity]].
Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.

Suppose a rock's weight is measured as 10 [[Newton (unit)|newton]]s when suspended by a string in a [[vacuum]] with gravity acting on it. Suppose that, when the rock is lowered into the water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10&nbsp;−&nbsp;3 = 7 newtons. Buoyancy reduces the apparent weight of an object. It is generally easier to lift an object through the water than it is to pull it out of the water.

For a fully submerged object, Archimedes' principle can be reformulated as follows:
:<math>\text{apparent immersed weight} = \text{weight of object} - \text{weight of displaced fluid}\,</math>

then inserted into the quotient of weights, which has been expanded by the mutual volume

:<math> \frac { \text{density of object}} { \text{density of fluid} } = \frac { \text{weight of object}} { \text{weight of displaced fluid} }</math>

yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volume is

:<math> \frac { \text {density of object}} { \text{density of fluid} } = \frac { \text{weight of object}} { \text{weight of object} - \text{apparent immersed weight}}.\,</math>

(This formula is used for example in describing the measuring principle of a [[dasymeter]] and of [[hydrostatic weighing]].)

Example: If you drop wood into water, buoyancy will keep it afloat.

Example: A helium balloon in a moving car. When increasing speed or driving in a curve, the air moves in the opposite direction to the car's acceleration. However, due to buoyancy, the balloon is pushed "out of the way" by the air and will drift in the same direction as the car's acceleration.

When an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force, that is proportional to the weight of the displaced liquid. Consequently, the net force acting on the object is equal to the difference between the weight of the object, or 'down' force, and the weight of the displaced fluid, or 'up' force. Equilibrium, or neutral buoyancy, is achieved when these two weights and thus forces are equal.