Mechanical Snell's Law
Classical Physics
2020-12-16 v1
Abstract
We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the vertex horizontally, we find the least-time path. We define the angles of incidence and refraction similar to the refraction of a light ray. It is remarkable that the ratio of the sines of these angles is identical to the ratio of the average speeds on the two partial paths as long as the horizontal component of the conservative force vanishes.
Cite
@article{arxiv.2012.08062,
title = {Mechanical Snell's Law},
author = {KyungTae Kim and June-Haak Ee and Kyounghoon Kim and U-Rae Kim and Jungil Lee},
journal= {arXiv preprint arXiv:2012.08062},
year = {2020}
}
Comments
10 pages, 1 figure, Version published in J. Korean Phys. Soc