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NOTES AND DISCUSSIONS Comment on “Sliding down an arbitrary curve in the presence of friction” by F. Gonzalez-Cataldo, G. Gutierrez, and J. M. Yanez, Am. J. Phys. 85(2), 108–114 (2017) a) L. A. del Pino and S. Curilef Departamento de Fısica, Universidad Catolica del Norte, Avenida Angamos 0610, Antofagasta, Chile (Received 11 September 2017; accepted 8 December 2017) https://doi.org/10.1119/1.5029480 2 2 Recently, Gonzalez-Cataldo et al. have presented the v ¼ v þ 2gyðÞ ðÞ a R 2lgxðÞ a analysis of the motion of a block slipping on an arbitrary sur- sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 face under the action of gravity, including the effects of fric- dx dy þ 2l v j þ da; (6) tion. Using basic differential geometry, they achieved a da da general expression for determining the speed of the block, an expression depending on the tangential angle to the cross which is a Volterra integral equation of the second kind, section of the surface. However, this analysis is a lengthy with the Kernel way to solve the problem. Here, we present a solution sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi derived from the work-energy theorem. This method, previ- 2 2 dx dy ously used by Prior and Mele, gives an
American Journal of Physics – American Association of Physics Teachers
Published: Jun 11, 2018
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