F=ma 2025 Problem 05

Physics · mechanics

Problem

Question: Three identical cylinders are used in this setup. Two of them are placed side by side on a horizontal surface, with a negligible distance between their surfaces so they do not touch. The third identical cylinder is placed on top of the first two, such that their centers form an equilateral triangle, as shown in the figure below. The coefficients of friction are: μ1\mu_1: the coefficient of friction between the cylinders, and μ2\mu_2: the coefficient of friction between the cylinders and the ground. For which of the following pairs (μ1,μ2)(\mu_1, \mu_2) will the system remain in equilibrium? Pair 1: (12,112)(\frac{1}{2}, \frac{1}{12}). Pair 2: (13,110)(\frac{1}{3}, \frac{1}{10}). Pair 3: (\frac{1}{4}, \frac{1}{8}}). (A) Pair 1 only. (B) Pair 2 only. (C) Pair 3 only. (D) Pairs 1 and 2 only. (E) Pairs 1, Pair 2, and Pair 3. *Note: This problem references figure(s): `image_question/F=MA_2025_05_1.png`*

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