Nueva visita a la torre de Pisa

Abstract

Different web pages and other publications erroneously present Galileo's experience in the Leaning Tower of Pisa, which produces misunderstandings and often reinforce errors in the interpretation of classroom demonstrations. In order to detect the difference in falling speed of similar objects, but of different mass, we made demonstrations in the classroom with two new tennis balls, one filled with water. The difference in arrival time on the floor does not allow, in some cases to discern, with the bare ear, if two or only one sound is produced. Unlike what happened in Galileo’s time, nowadays filming with the cell phone allows to appreciate the difference. Using elementary concepts of fluid mechanics, we discuss the fall of bodies in air, and find that air flow around the body is turbulent. The speed limit reached is proportional to the square root of the mass and thus a heavy object falls faster than a light one. The calculation method is also applied to a lead and to a wooden ball of equal dimensions, supposedly similar to those used by Galileo in Pisa. We find that, in such case, the asynchrony exceeds the persistence limit of the human ear, so that Galileo, with his educated ear, could have detected the lack of simultaneity.