Archimedes' Law


August 13, 2022

Archimedes' law is a classical law of physics that reads: The buoyant force experienced by a body in a liquid or gas is equal to the weight of the displaced liquid or gas. This buoyant force is referred to as the Archimedes force and is named after the Greek mathematician Archimedes. The buoyant force is caused by the hydrostatic pressure increasing with depth. In the simple case of a submerged cube with horizontal top and bottom face, the pressure on the bottom face is greater than on the top face. The difference causes the buoyant force. By dividing an arbitrary body into horizontal slices, an analogous explanation can be given for each of the slices. The sum of the buoyant forces is an approximation for the Archimedes force on the body and the sum of the volumes approximates the volume of the body. These approximations become more accurate for thinning slices.

Accurate wording

When a body is submerged in a liquid or gas, the displaced amount of the medium is equal to the volume of the body. A floating object is the part of the volume that is below the surface. The "amount displaced" is the volume of the medium that could be there if the body were not there. The Archimedes force is equal to the weight of the displaced liquid or gas. If the liquid or gas is homogeneous, the weight is f a {\displaystyle F_{a}} equal to: f a g V {\displaystyle F_{a}\rho \cdot g\cdot V} In it is: {\displaystyle \rho } (Greek letter 'rho') the mass density of the liquid or gas in which the object is contained; g {\displaystyle g} the acceleration of gravity; V {\displaystyle V} the volume of the amount of liquid or gas displaced. In some cases the density of the liquid or gas is only horizontally homogeneous and depends vertically on the position, as with layers of different liquids. The Archimedes force can then be determined by assuming that the layers continue in the repressed space. The Archimedes force, like all forces in the SI system, is expressed in newtons (N). Whether a body floats or a balloon rises or falls or balances does not depend on the magnitude of the acceleration of gravity g {\displaystyle g} (provided it is not zero).


Archimedes' law is connected with the following story: King Hiero of Syracuse wanted to offer the gods a golden crown and commissioned an artist to make one. After receiving the completed crown, the king doubted whether the crown was made of pure gold. It may have been made of a mixture of silver and gold, a trick counterfeiters used at the time to counterfeit coins. The king asked Archimedes if he could determine whether the crown was made of pure gold. However, the crown was not to be damaged. Lost in thought, Archimedes walked home and decided to take a bath to relax. As Archimedes lowered himself into the bath filled to the brim, he realized that the amount of water overflowing was equal to the volume of his body. He compared the crown to a bar of pure gold of the same weight as the crown by holding both on a balance under water. If the crown were also made of pure gold, the balance would remain in equilibrium, but if there were silver in the crown, the volume would be greater and the