MEASUREMENT OF THE ANGLE OF DEPARTURE OF BODIES DURING THEIR MOTION ON A SPHERICAL SURFACE
DOI:
https://doi.org/10.31110/fmo2024.v39i3-07Keywords:
physical experiment, angle of separation, , spherical surface, movement of ball, puckAbstract
The method of conducting a physical experiment, which uses a homemade research installation to determine the separation angle of a ball and a puck during their movement on a spherical surface, is considered.
Formulation of the problem. In the problems of classical mechanics, related to the movement of a sphere on the surface under the influence of the gravitational force of a material point or ball, it is proposed to find the angle at which they break away from the surface. This task is relatively easy to solve for most students. However, the same problems with the friction force cause difficulties during their solution for many knowledgeable students. It is impossible to verify the results of the theoretical consideration of the problem in an experiment, especially remotely, due to the lack of research installations of this type and methodological recommendations for them.
Materials and methods. Theoretically, with and without friction, all possible options for the movement of a material point and a ball on the surface of the sphere are considered. Based on these considerations, the level of difficulty of obtaining the solution of this kind of task for students of bachelor's and master's level is determined. The optimal variant of setting the task for the bachelor's level with experimental verification of the conclusions of the theory was determined. The goal: to determine the separation angle of a flat body and a ball during their movement on a spherical surface - was solved with the help of a developed research installation in the form of two protractors separated by sheets of paper to form a rail spherical road. Students' smartphones in slow-motion mode were used as a digital measurement laboratory during their remote performance of a school physics experiment.
Results. The angle of separation from the surface of the sphere of a flat body (puck) was experimentally determined, which is equal to 520, and the ball - 570. The technique of measuring separation angles and a research facility were developed.
Conclusions. The values of the separation angles predicted by the theory of the movement of bodies in the presence of friction - 520 for the puck and 570 for the ball - have been confirmed in experiments. The invariance of the separation angle from the spherical surface of the ball is proven, regardless of its mass and radius. These results prove the fact that the developed technique and cheap research equipment allow undergraduates to measure ball separation angles and their speed with high accuracy even in remote mode.
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References
Irodov, I. E. (1988). Problems in General Physics. Mir Publishers.
Phan-Budd, S. (2020). Finger paint and physics: a simple demonstration of circular motion and conservation of Energy. The Physics Teacher, 58, 66-67. https://doi.org/10.1119/1.5141979
Flores, J., del Rio, A. G., Calles, A. & Riveros, H. (1972). A simple problem in mechanics: a qualitative approach. The American Journal of Physics, 40, 595–598.
Jayanth, V., Raghunadan, C., & Biswas, A. (2009). A sphere moving down the surface of a static sphere and a simple phase diagram, https://arxiv.org/abs/0808.3531. https://doi.org/10.48550/arXiv.0808.3531
Symon, K. R. (1961). Mechanics, 2nd ed. Addison-Wesley, Reading, MA.
McDaniel, Terry W. (2021). Analysis of the motion of a mass sliding on a sphere with friction. American Journal of Physics. 89, 921–926. https://doi.org/10.1119/10.0005071
McDaniel, Terry W. (2021). Solutions for the motion of a mass sliding on a sphere with friction. Model Physics, Volcano, CA 95689 USA
González-Cataldo, F., Gutiérrez G; Yáñez J. (2017). Sliding down an arbitrary curve in the presence of friction. American Journal of Physics. 85, 108–114. https://doi.org/10.1119/1.4966628
Prior, T, Mele, E. A. (2007). A block slipping on a sphere with friction: Exact and perturbative solutions. American Journal of Physics. 75, 423–426. https://doi.org/10.1119/1.2410018
Mungan, C. E. (2003). Sliding on the surface of a rough sphere. The Physics Teacher. 41, 326–328. https://doi.org/10.1119/1.1607801
de Souza, D. C, Coluci, V. R. (2017). The motion of a ball moving down a circular path. American Journal of Physics. 85, 124. https://doi.org/10.1119/1.4972177.
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Copyright (c) 2024 Валерій Здещиц, Анастасія Здещиц, Карина Пирховка
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