Question

Problem 31 mi ma Two blocks ma = 4 kg and m2 = 9 kg are initially arranged as shown in the figure. They are tied to a massless rope going around the pulley. The pulley has a form of a cylinder e with a mass of M = 8 kg and radius of R = 40 cm. Both the incline and the horizontal surface have a coefficient of kinetic friction uk = 0.15. The incline is at the angle 8 = 55° with respect to horizontal. The blocks are released from rest and begin to accelerate such that mz is moving down the incline and m. moves horizontally. Find: (a) the tension (in N) in the rope on the left side of the pulley; (b) the tension (in N) in the rope on the right side of the pulley; (c) the acceleration (in m/s) of the block m.; (d) the angular acceleration (in rad/sec) of the pulley; (e) the speed (in m/s) of the block m: after it moves for At = 2 sec.

Answer 1

m, Tz f f 13 0-55% V= utat = 0+ 3.46 X2 = 6.92 m/s. Ti MIR Ra=a x =) T2-T, = ma T- Mix 0 +2 +6 C) a = g/m₂ sino - lik m₂ W5o - lam) 1m, tm2 + M12) d) 2- 9 3.46 = 8.65 rad/2 7 .40 m₂ g sino - Ta - MK M₂g uso = m₂ a 0 (T2 - Ti) R = I2 = MR? ima - Mx mig = mia - 3.46 m/s2 e

from ein ③ a Tizmi [atlxg] 4[3.46+ 0-159.81] = 19,726N T2 = Tit +ma/ = 19.726+ 8x 3.46 2 33.566 N