Abstract
In the present work, the theoretical solution of a problem extracted from a historical context is addressed, in which Galileo supposedly conducted an experiment to measure the percussion force of a water jet. The experimental apparatus consists of a balance, in which a counterweight hangs on to one of its extremities, and two buckets hang on to the other extremity. The water jet from the bottom of the upper bucket strikes the lower bucket. The objective is to find the jet percussion force on the lower bucket. The result of the analysis revealed that the method proposed by Galileo for the calculation of the jet percussion force is incorrect. The analysis also revealed that the resultant force during the process is practically null, which would make Galileo’s account of the major movements of the balance credible, despite his having not identified all the forces acting on the system.
Highlights
Galileo’s Discourses is originally divided into four days—as published in the Leiden edition of 1638, to which were posthumously added another two days, all written in dialogic form in Two New Sciences
The result of the analysis revealed that the method proposed by Galileo for the calculation of the jet percussion force is incorrect
The analysis revealed that the resultant force during the process is practically null, which would make Galileo’s account of the major movements of the balance credible, despite his having not identified all the forces acting on the system
Summary
Galileo’s Discourses is originally divided into four days—as published in the Leiden edition of 1638—, to which were posthumously added another two days, all written in dialogic form in Two New Sciences. The first experiment about this force discussed by the trio begins when Aproíno narrates to Sagredo an experiment with two buckets conducted by the Academic (Galileo) to investigate the effect of the percussion force. The present study has the objective of finding the forces acting on the balance in unsteady state, since the opening of the orifice in the bottom of the upper bucket until the end of the process, when all the water contained in this bucket has drained to the lower bucket. In the development of the theoretical model, we shall use the conservation equations of fluid mechanics in unsteady state, in the so-called integral form: continuity, in the form of conservation of the volume flux; energy, in the form provided by Torricelli’s law; and Newton’s 2nd law, best known in fluid mechanics as the linear momentum equation
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