Question

A hanging weight, with a mass of me = 0.350 kg, is attached by a rope to a block with mass m2 = 0.820 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 R2 = 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 4k = 0.250. At the instant shown, the block is moving with a velocity of v; = 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. R2R Mg (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. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s

Answer 1

(a) moment of martia of the pulley I = 1 m R " the ) 140.35 0.022 0.03'y = 2.28x10-4 kg m? from consenation of energy [kg + Kq tik net + Ug ; - fox = [kat ke trood jo * * 0,3570,82 + LHS = * *0.82X0.82" + +*2,280x1014) *(0,82%0,03) +0,82% 9.870.7 -0.25%0,35% 9,8 x 0,7 [since ki = 1 min2, k = 1 m, v told u= mq gh and fr Box = ungh J → LHSE 0.1176 +0,2756 + 0,0851 + 5,625 - 0,6002 5,5031J and RH3= 140.35 V? + 170, 8242 +4% 2,287/04 X10+966) 2 = 0.7116 V2 LHS RHS 5,5031 = 07116V? V = 7.73 mis 17.73 1257,67 radis (6) wa 213 =

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