Archimedes' Principle in High School: the hydrostatic balance and Galileo's paradox
Archimedes Principle; hydrostatic balance; buoyancy; Hydrostatic Paradox.
This work aims to contribute to the approach of Archimedes' Principle, considering the nuances of its historical development. It takes as a starting point the historical episode involving Archimedes and the mission assigned to him to determine whether the crown of King Hieron of Syracuse had been forged. There is a widespread version of this event, according to which Archimedes solved the problem by discovering buoyancy when bathing. This version was narrated by the Roman architect Marcos Vitruvius, who lived about two centuries after Archimedes, in the 1st century BC. Despite having a series of physical and historical conceptual inconsistencies, the narrative continues to be propagated in textbooks, including in some collections approved in the PNLD 2021. On the other hand, Galileo Galilei, a great admirer of Archimedes' work, suggested, in 1586, in his work called "The small balance", that Archimedes would have used a hydrostatic balance to solve the crown problem. Galileo's version of the episode is physically consistent and supported by historical evidence discovered by historians in recent centuries. This version, however, is practically absent from the school context. Equally absent is the existence of a validity limit for Archimedes' Principle, the so-called Galileo's Hydrostatic Paradox. In order to overcome these gaps and distortions, the present work proposes an educational product that problematizes the popular version of the crown episode. It is a didactic sequence that introduces original excerpts from the works of Vitruvius and Galileo into High School classrooms, in an investigative manner, as well as contemplating demonstrative experimental activities, explored according to a dialogical and investigative bias, which include the hydrostatic balance.