Estudio te´orico-experimental de la din´amica del movimiento circular con fricci´on
DOI:
https://doi.org/10.31349/RevMexFisE.18.020204Keywords:
Rapidez, fuerza normal, fricción, ecuación de BernoulliAbstract
En este trabajo se presenta un estudio te´orico-experimental de la din´amica del movimiento de una esfera que se mueve en una trayectoria circular vertical con fricci´on. En el estudio te´orico se resuelve una ecuaci´on diferencial de Bernoulli que permite calcular la rapidez en cualquier posici´on angular y la rapidez m´ınima necesaria para que la esfera complete una vuelta en la trayectoria circular. En el estudio experimental se utilizan fotopuertas para medir la posici´on angular de la esfera como funci´on del tiempo; a partir de esto, se obtienen de manera indirecta la rapidez y fuerza normal en cualquier posici´on angular. Al comparar los resultados te´oricos y experimentales obtenidos de forma indirecta para la rapidez y fuerza normal se observa que el modelo te ´orico describe de forma cualitativa el comportamiento experimental cuando ¹ = 0:12. Finalmente, se analiza el comportamiento te´orico de la rapidez y fuerza normal para distintos valores del coeficiente de fricci´on cin´etica, donde se observa que para ¹ ¸ 0:2 la rapidez y fuerza normal final decaen de manera abrupta.
This work presents a theoretical and experimental study of the dynamics of the motion of a sphere that moves in a vertical circular trajectory with friction. In the theoretical study, a Bernoulli differential equation is solved to calculate the velocity at any angular position and the minimum velocity necessary for the sphere to complete one turn in the circular track. In the experimental study, photogates are used to measure the angular position of the sphere as a function of time, from which the velocity and normal force are indirectly obtained in any angular position. When comparing the theoretical and experimental results obtained indirectly for the velocity and the normal force, it is observed that the theoretical model qualitatively describes the experimental behavior when ¹ = 0:12. Finally, the theoretical behavior of the speed and normal force is analyzed for different values of the coefficient of friction kinetic, where it is observed that for ¹ ¸ 0:2 the final normal speed and force decline abruptly.
References
Engineering Physics, Krishna Prakashan.
URL https://books.google.com.mx/books?id=6MH7_FkIgD4C
A. Bettini,A Course in Classical Physics 1—Mechanics, Undergraduate Lecture Notes in Physics, Springer International Publishing, 2016.
URL https://books.google.com.mx/books?id=6TTeCwAAQBAJ
F. d. Simoni,Velocidade m´ınima para completar um loop circular vertical: uma abordagem cinem´atica, Rev.
Bras. Ensino F´ıs. 40 (2018).
URL http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000300403&nrm=iso
I. A. C. Melnik, V. d. A. Oliveira,An´alise do movimento de uma part´ıcula em um loop circular vertical usando no¸c˜oes de limite, Rev. Bras. Ensino F´ıs. 42 (2020).
URL http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100439&nrm=iso
L. P. Franklin, P. I. Kimmel,Dynamics of circular motion with friction, Am. J. Phys. 48 (3) (1980).
URL https://doi.org/10.1119/1.12306
I. Richard Lapidus,Circular motion with sliding friction, Am. J. Phys. 49 (883) (1981).
URL https://doi.org/10.1119/1.12388
P. L. T. Jr.,Trouble on the loop-the-loop, Am. J. Phys. 55 (826) (1987).
URL https://doi.org/10.1119/1.14997
T. Prior, E. J. Mele,A block slipping on a sphere with friction: Exact and perturbative solutions, Am. J. Phys.
(5) (2007).
URL https://doi.org/10.1119/1.2410018
B. B. Asavapibhop, N. Suwonjandee,Loop-the-loop: An easy experiment, a challenging explanation, AIP Conference Proceedings 1263 (249) (2010).
URL https://doi.org/10.1063/1.3479881
N. Suwonjandee, B. Asavapibhop,Loop-the-loop: bringing theory into practice, Phys. Educ. 47 (6) (2012).
URL https://doi.org/10.1088/0031-9120/47/6/751
W. K-lobus,Motion on a vertical loop with friction, Am. J. Phys. 79 (2011).
URL https://doi.org/10.1119/1.3602091
D. Souza, V. Coluci,The motion of a ball moving down a circular path, Am. J. Phys. 85 (2017).
URL https://doi.org/10.1119/1.4972177
O. Bertran, J. Riba,A revised solution for a sphere rolling in a vertical loop, Eur. J. Phys. 42 (015008) (2020).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 RAUL CORTES MALDONADO, MARY CARMEN GÓMEZ CONDE, CARLOS BUENO AVENDAÑO, JOSÉ FEDERICO CASCO VÁSQUEZ
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
