Question

Please answer all parts and show all work

11. (50 pts) A 4.0 kg mass is connected by a massless string to the rim of a pulley. You can assume that the pulley is a cylindrical shell has a radius of 0.50 m and a mass of 11.6 kg, as shown in the figure and that the string does not slip on the pulley. The mass is released from rest at a height of 2m above the ground. a. (10 pts) How much torque does the string apply to the wheel? b (10 pts) What is the angular acceleration of the pulley c. (10 pts) What is the linear acceleration of the mass? d. (20 pts) What is the speed of the mass just before it hits the SM ground? Ke 2 M

Answer 1

Mass of pulley, M = 11.6 kg mass of block m = 4 kg radius of pulley R = 0.50 m h = 2 m \r\n Let angular acceleration of pulley is alpha and linear acceleration of block is a. And tension in string is T. As string does not slip over pulley. a = R alpha mg - T = ma torque equation on pulley T. R = I alpha I = moment of inertia of pulley I = MR^2 T = I alpha/R = (MR^2)/R middot a/R T = M a mg - T = ma = mg - Ma - Ma = > a = mg/M + m = 4 times 9.81/11.6 + 4 (c) a = 2.51 m/s^2 (a) torque on pulley = > TR = Ma . R = 11.6 times 0.5 times 2.51 = 14.56 N. m (b) alpha = a/R = 2.51/0.5 = 5.0 = rod/s^2 (d) y = a_y t + 1/2