How big was Galileo's impact? Percussion in the Sixth Day of the "Two New Sciences"

TL;DR

This paper examines Galileo's lesser-known work on percussion force, analyzing his experiments and theoretical models to assess his understanding and reporting of the forces involved in motion.

Contribution

It develops a steady-state and transient model of Galileo's experiment, compares it with real data, and clarifies Galileo's conclusions on percussion force.

Findings

Galileo's experiment accurately measures percussion force despite minor imbalances.

Theoretical models align with experimental results, validating Galileo's approach.

Galileo did not account for thrust force, affecting force calculations.

Abstract

The Giornata Sesta about the Force of Percussion is a relatively less known Chapter from the Galileo's masterpiece "Discourse about Two New Sciences". It was first published lately (1718), long after the first edition of the Two New Sciences (1638) and Galileo's death (1642). The Giornata Sesta focuses on how to quantify the percussion force caused by a body in movement, and describes a very interesting experiment known as "the two-bucket experiment". In this paper, we review this experiment reported by Galileo, develop a steady-state theoretical model, and solve its transient form numerically; additionally, we report the results from one real simplified analogous experiment. Finally, we discuss the conclusions drawn by Galileo -- correct, despite a probably unnoticeable imbalance --, showing that he did not report the thrust force component in his setup -- which would be fundamental for the correct calculation of the percussion force.