Abstract
My paper focuses upon the problem of determining the nature, establishing the proportionality, and measuring the intensity of the force of percussion of a projected or falling body, as treated in the Sixth Day of Galileo’s Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638). This fragment was written around 1638–1639 as part of two additional Days of the Discorsi, which Galileo never finished and remained unpublished until 1718. Galileo’s last works on percussion show a significant step towards a generalization of his own views on uniform and accelerated motion that will later lead to the Newtonian principle of inertia. The experiment with two equal weights hanging on a pulley, performed in Arcetri during the same period, is compared with the Paduan 1604–1608 experience of the “water balance.” Both account for more than three decades of inquiries into what Galileo called forza della percossa, which marked the transition from preclassical to classical mechanics.
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Notes
The Florentine braccio or braccio da panno ("tailor’s arm"), usually adopted by Galileo as the standard measure of length, was equal to 58.4 cm.
Let m b be the mass of the ball, m h that of the hand, v b the velocity of the ball, v h that of the hand, and Δp the shock fully absorbed by the hand, supposing that the hand still maintains its original velocity after catching the ball. The relation between their quantities of motion, before and after the impact, is given by the following expressions: m b v b + m h v h = (m b + m h)v h + Δp and, Δp = m b v b + m h v h – m b v h – m h v h = m b v b – m b v h = m b(v b – v h).
Namely as the ratio between the displacement Δs and the time interval Δt, which becomes the instantaneous velocity v(t 0 ) at a given time t 0 as Δt → 0.
An equivalent formulation is: a body moving with a constant velocity v will cover a space 2s in a given time t, where s is the space covered in the same time by a body moving with a uniformly accelerated motion from v 0 = 0 to v t = v.
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Acknowledgements
Special thanks to Roberto Vergara Caffarelli (Department of Physics, University of Pisa) for his inspiring reconstructions of Galileo’s experiments, as well as for the coinage of the name “Galileo’s machine” itself. I am also very grateful to Massimiliano Badino (Centre d’Història de la Ciència, Universitat Autònoma de Barcelona) for his helpful remarks during the writing of my paper.
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Stefano Salvia, PhD, is a research assistant in History of Science at the Department of Philosophy of the University of Pisa.
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Salvia, S. “Galileo’s Machine”: Late Notes on Free Fall, Projectile Motion, and the Force of Percussion (ca. 1638–1639). Phys. Perspect. 16, 440–460 (2014). https://doi.org/10.1007/s00016-014-0149-1
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DOI: https://doi.org/10.1007/s00016-014-0149-1
Keywords
- Galileo Galilei
- machine
- percussion