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.
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Acknowledgments
As members of the Korea Pragmatist Organization for Physics Education (KPOPℰ), the authors thank to the remaining members of KPOPℰ for useful discussions. We thank Soo-hyeon Nam, Q-Han Park, and Chaehyun Yu for their reading the manuscript and useful comments. This work is supported in part by the National Research Foundation of Korea (NRF) under the BK21+ program at Korea University, Initiative for Creative and Independent Scientists. The work of JHE, URK, and JL is also supported by the NRF under Contract No. NRF-2017R1E1A1A01074699 (JHE, URK, JL), NRF-2018R1A2A3075605 (JHE, URK), NRF-2018R1D1A1B07047812 (URK), NRF-2019R1A6A3A01096460 (URK), and NRF-2017R1A2 B4011946 (JHE).
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Kim, K., Ee, JH., Kim, K. et al. Mechanical Snell’s Law. J. Korean Phys. Soc. 76, 281–285 (2020). https://doi.org/10.3938/jkps.76.281
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DOI: https://doi.org/10.3938/jkps.76.281