Eureka!
The experiment illustrates Archimedes' principle. If a silver crown and a silver bar of the same volume are placed on the scales, they will remain balanced when submerged. However, if the crown and bar weigh the same but are made of different materials, the submerged scales will tip.
According to legend, this experiment is linked to a challenge set by the king of Syracuse for the Greek mathematician Archimedes. The ruler wanted to verify if his new crown was made of pure gold. Archimedes found the solution while taking a bath, observing the water displaced when he entered a full tub.
Archimedes' principle is closely related to the legend of King Hiero of Syracuse, who wanted to verify whether his crown was made of pure gold or if a dishonest goldsmith had added another, cheaper metal. He assigned the task to Archimedes – a Greek mathematician, physicist, and inventor. Allegedly, Archimedes discovered the solution while taking a bath. He noticed that as he entered the tub, water spilled out, and his submerged body felt seemingly lighter.
The buoyant force acts on every body submerged in a fluid and is equal to the weight of the displaced fluid. If a 10-liter bag of sand is thrown into the water, upon complete submersion, it will appear "lighter" by 10 kilograms – the weight of 10 liters of water.
The buoyant force can be described by the formula:
Fw = ρgV where: ρ – density of the displaced fluid, g – gravitational acceleration, V – volume of the displaced fluid.
The formula shows that the buoyant force does not depend on the weight of the object but only on its volume.
This explains why even massive and heavy ships can float on water despite being made of steel, which does not naturally float. Ships have a large volume, and despite their steel structure, most of their volume is filled with air. As a result, the "density" of the entire ship is low enough for the buoyant force to keep it afloat.
The buoyant force acts not only in liquids but also in gases. Thanks to it, balloons filled with gases lighter than air, such as helium, hydrogen, or hot air, rise into the air. However, the density of air is too low for us to directly perceive this force.