Two masses m1 = 10 kg and m2 = 1 kg arc connected by a light rope which passes o

Question

Two masses m1 = 10 kg and m2 = 1 kg arc connected by a light rope which passes over a light, low friction pulley between low friction slopes of 30degree and 10degree as shown in the figure. Approximating the masses of the rope and pulley to be negligible and the friction of both the slopes and the pulley to be negligible, find the acceleration of mass m2 up the slope. (Draw free body diagrams axes and acceleration vectors, and write Newton's second law equations in components independently for both masses.) If both of the slopes have the same static coefficient of friction, what is the minimum coefficient of friction, mu8 , for the masses to remain at rest? (You may continue to neglect the masses of the rope and pulley and friction in the pulley. Draw free body diagrams , axes and accelerations, and write Newton's second law equations in components independently for both masses.)

Explanation / Answer

since the blocks are at rest net acceleration = 0

force equation of block m1

m1g * sin(10) - T - k * m1g * cos(10) = 0

10 * 9.8 * sin(10) - T - k * 10 * 9.8 * cos(10) = 0

force equation of block m1

m2g * sin(30) - T - k * m2g * cos(30) = 0

9.8 * sin(30) - T - k * 9.8 * cos(30) = 0

on solving we'll get

coefficient of static friction k = 0.1376

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