Archimedes discovered the law of buoyancy when taking a bath, that is, an object immersed in a fluid is subjected to upward buoyancy, which is equal to the weight of the fluid displaced by the object. Legend has it that the monarch of a city-state ordered craftsmen to build a golden crown. When the craftsman presented the finished crown, it seemed that something was wrong with the monarch holding the crown. He suspects that artisans may be involved and get extra gold from this misconduct. So he ordered Archimedes, a famous scientist in this city-state, to solve this mystery. After receiving the order, Archimedes thought of various ways to solve the problem. At that time, people already knew that if the density of the same substance was different, if the volume of the crown could be known, the density of the crown could be obtained from the ratio of its weight to its volume. If the density of the crown is less than gold, it can be proved that there are impurities in the crown. However, due to the irregular shape of the crown, it is impossible to measure the volume of the crown and know its density. Archimedes returned to the laboratory, filled a crock with water, put it in a big basin, and then put the golden crown in the crock, and the water overflowed from the crock. The volume of this overflowing water is the volume of the golden crown. If the crown is pure gold, then the volume and weight of the water it displaces should be equal to the pure gold nugget. So, he measured the pure gold nugget with the same weight in the same way and found that the volume of the gold crown was larger than that of the pure gold nugget, indicating that the gold crown was adulterated. However, the volume of the crown is larger than pure gold, indicating that the crown is mixed with impurities with lower density than gold, so Archimedes discovered the law of buoyancy and enriched the mechanical system at that time.