Question

Q2: Fig. 2 is system comprising of 4 masses and 3 pulleys. Take the pulleys as massless and with the cord wrap angles of π. The coefficient of friction between the cord and Pulley B is taken as 0.2 whereas pulleys A and C are both frictionless. The lengths of each of the 3 cords are 1.5m, respectively. Stating all your assumptions, determine the acceleration of the 4 masses shown. Hint: Tt = Tse μθ , where Tt and Ts are the tensions of the tight and slack sides of pulley with friction coefficient, μ, and angle ofwrap, θ. Ha = 0.2 Ha=0 3kg 5kg 4kg 6kg Fig. 2: Pulley system

to find the acceleration in each of the four masses and the 3 pulleys.

the length of each chord is 1.5m.

Answer 1

T_1 = 2 T_4, T_2 = 2 T_3, T_2 = T_1 e^mu pi, T_3 = T_2 /2 = T_1 e^mu pi /2, T_4 = T_1 /2 \r\n For 6 kg: 6g - T_3 = 6 A_1 + 6a implies 12g - 2 T_3 = 12 a_1 + 12a T_3 = 24 a_1 - (3) For 4 kg: T_3 - 4 g = 4 a_1 - 4a implies 3 T_3 - 12g = 12 a_1 - 12a For 3 kg: T_4 - 3g = 3 a_2 + 3a implies 5 T_4 - 15g = 15 a_2 + 15a T_4 = 15 a_2 - (4) For 5 kg 5g - T_4 = 5 a_2 - 5a 15g - 3 T_4 = 15 a_2 - 15a 6g = 6a + 30 a_1 implies g = a + 5 a_1 - (1) 5g = 20 a_2 - 5a implies g = 4 a_2 - a - (2) we already T_2 = T_1 e^pi mu T_3 = T_1 /2 e^pi mu - (5)