Question

A hanging weight, with a mass of m1 = 0.365 kg, is attached by a rope to a block with mass m2 = 0.825 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μk = 0.250. At the instant shown, the block is moving with a velocity of vi = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible.

(a). Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown

(b). What is the angular speed of the pulley (in rad/s) after the block has moved this distance?

Answer 1

(@. The friction force will be f = N f=My (M28) f = 0.250 (0.825 x 9.2) m. = 2.02125 N The friction force will only be exerted on the Sliding block : Calculate moment of Inertia for the hallow cylinder I MER? + R₂²) 0.350 (10.02² +10.03 -) I = 2.275 X10 kg-m? using work energy Theorem. work done by Geoarity & work done by fiction = change in Kinetic energy. -) m ghid) - f(d) = (m, tm2) vf I wf (m, tmav? I w² - 0.36589.880.7-2.02125x0.75 (0.365 +0.825) x 2² 2 + 2.275x104. - 2 - (0.365 +0.825 x 0.82² (0.365 & XV 1.089025 = 0.595 f +0. 126382 +0.126389 Vf + 2.275x70x10821 Vt = 1.395 ml See 0.400078 +0.084983 (6.) The W Angular speed can be found by the relation. = F = 1.395 = 46.5o4 rad/sec