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Effects of variable friction force on the sliding movement of a block

Haiduke Sarafian
Organization: The Pennsylvania State University
Department: Department of Physics
Journal / Anthology

Mathematica in Education and Research
Year: 2006
Volume: 11
Issue: 1

We consider a real-life mechanical setting where a solid block is dragged on a leveled, rough board by a slanted thread. The setting is such that the motion of the block increases the slant angle. Consequently, the change in the angle changes the kinematics and dynamics of the problem. For instance, the tension in the thread becomes a function of the slant angle. The latter changes the kinetic friction force and affects the kinematics of the sliding block. To understand the interplay of the various parameters relevant to the problem at hand, we use the symbolic, numeric, and graphic approaches. For instance, we attempt to solve the relevant differential and integro-differential equations symbolically; in certain cases, we apply approximations. We also choose a set of practical parameters such as mass and the friction coefficient, deploy the symbolic solutions, and deduce the numeric values and plots of the quantities of interest. The paper is pedagogical in nature; however it still poses several challenges. The application of the physics principles and the techniques used to analyze the problem can be used as a teaching resource in honors physics and mechanical engineering courses.

*Engineering > Mechanical and Structural Engineering
*Science > Physics