Archimedes’ Principle and Falling Bodies

Abstract

The discussion finally turns to the subject of falling bodies, the second of the two new sciences to which Galileo’s Dialogues are devoted. It is here that we pick up our reading. After challenging Aristotle’s proof that a vacuum cannot exist in nature, Salviati begins to untangle the various factors that might influence the speed of a falling body, factors such as the shape and weight of the falling body and the specific gravity of the medium through which it descends. To this end, Galileo reminds the reader that “the effect of the medium is to diminish the weight of the body by the weight of the medium displaced.”You may recognize this as a statement of Archimedes’ principle, which had been known since ancient times. How does Galileo apply this principle to calculate the amount by which a medium reduces the speed of an object falling through it?

There are bodies which will fall rapidly in air, whereas if placed in water not only will not sink but will remain at rest or will even rise to the top.

—Galileo Galilei