Adriana González Lebrón: Why do we weight less underwater?

Physics surrounds us every instant of every day of our lives, even though we do not notice it. A common event that almost every child gets to experience is the fact that even though you are a heavy person (in weight), when you are in a pool anyone can grab you in his or her arms.

How does physics relate with this? The answer is that physics is the reason why anyone can grab you underwater. The person who discovers why a person weights less underwater was a Greek physicist, mathematician, engineer, inventor and astronomer called Archimedes of Syracuse. Archimedes invented a method to determine the volume of an object with irregular shape. There is a legend that says that he invented the method when he was asked if there was some silver in the gold crown made for King Hiero II. Because he cannot damage the crown he then noticed that when an object is submerged into water its level rose and that effect could be used to determine the volume of the crown. Since water is incompressible, the submerged crown would displace an amount of water equal to its own volume. Therefore, dividing the mass by that volume will give the density of the crown. If the density were less than that of gold, the silver would have been used.

A more concrete definition for Archimedes’ principle states that a body immersed in fluid experiences a buoyant force equal to the weight of the fluid it displaces but opposite in direction. Since the legend of the crown does not appear on Archimedes’ works, Galileo considered that the method that will soon be explained was more accurate since it was based in demonstrations made by Archimedes. The method was to compare the density of the golden crown with the density of solid gold by balancing the crown on a scale with a piece of solid gold as reference and then immersing them in water. The difference in density will tell whether the crown was pure gold or not.

It is important to recall that Archimedes’ principle does not only explain the buoyancy of an object in water but also the apparent loss of weight of objects underwater. When determining whether an object will float in a fluid, its weight and volume must be considered. This is likely known as the relative density or the weight per unit volume of the object, which compared to the fluid, determines the buoyant force exerted. When the object is less dense than the fluid, it will float. If the object is denser than the fluid, it will sink. The relative density also helps determining the proportion of a floating object that will be submerged in the fluid. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid. That is why we weight less underwater. It is not because we have loss weight, but because the buoyant force exerted on us is equal to the weight of the displaced fluid and makes our body weight less.