Archimedes’ law and its applications
A body immersed in a liquid or gas is acted on by an upward buoyant force. By the law of the ancient Greek scientist Archimedes (287–212 BCE) this force equals the weight of the liquid displaced by the body: F_A = ρ_liquid · g · V_immersed, where V is the volume of the part of the body immersed. A body’s weight in a liquid is less than in air by F_A: P_in liquid = P_in air − F_A. Floating condition: if the density of the body is less than that of the liquid (ρ_body < ρ_liquid) the body floats; if equal it hangs suspended inside the liquid; if greater it sinks. A steel ship does not sink because it is hollow, so its average density is less than that of water. A submarine dives or rises by filling or emptying its tanks with water; balloons and airships rise because they are filled with a gas lighter than air. According to the legend, Archimedes, while checking the composition of a king’s crown, noticed this law in his bath and shouted “Eureka!” (I have found it!).
Experiment: a raw egg sinks in a jar of fresh water; stir in a few spoonfuls of salt and the egg rises and floats. Why? Safety: lower the egg gently, do not eat a broken egg, and wash hands afterwards. Do not spill water on the floor.