Archimedes's Principle
Archimedes's principle states that an object immersed in a liquid will be supported by a pressure equal to the weight of the liquid displaced by the object. This is caused by an equilibrium of forces. The two forces seeking equilibrium are gravity and pressure from the surrounding liquid. Gravity pulls the object down through the liquid. The pressure of the surrounding liquid is resisting the free fall of the immersed object. The degree to which the weight of the object corresponds to the weight of the displaced liquid determines whether the object sinks quickly or slowly or floats. The intensity of the pressure is in direct relationship to the depth.
A cubic foot of water weighs 62.4 lb (28.3 kg). Therefore, if an object placed in water has a volume of a cubic foot and weighs more than 62.4 lb, it will sink. Rocks sink because most rocks have a greater mass than water (except pumice). A block of wood will likely float in water because most wood has a mass less than 62.4 lb per cubic foot. If an object has a mass exactly 62.4 lb per cubic foot, weighing exactly the same as the water it displaces, it will neither sink nor float but remain suspended where it is placed.
The story of the discovery of the principle is apocryphal; however it is a good example of an application of the principle. Archimedes lived in the Greek city-state of Syracuse on the island of Sicily about 200 B.C. and was friends with the king, Heron. As the story goes, Heron suspected that his crown was not pure gold but gilded silver. He asked Archimedes to determine if the crown was truly gold or mostly silver. Archimedes thought of the problem while he stepped into a full bath. As the water ran over the sides of the tub, he realized the solution. He immediately ran to Heron's house, through the streets of Syracuse, naked, yelling "Eureka", which means "I found it".
Archimedes realized that he could determine the volume of the crown by placing it in water and measuring the amount of displaced water. Since the mass of gold and the mass of silver were already known, he would need only to multiply the calculated volume of the crown by its weight. The result was then compared to the known mass of gold and silver. Another way the principle could be used to determine the substance of an object is to weigh the object before placing it in water and again while it is in the container of water. Determine the difference in the weight of the object outside of water and the weight of the object when submerged. The ratio of that difference to the weight outside the water should equal the ratio of the mass of water to the mass of the substance. Using the crown as an example again, the ratio of the mass of gold to the mass of water is 1/18. The submerged crown would be expected to weigh 17/18 as much as the crown outside of water, if it was indeed gold.
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