Question

a mass of 8kg is resting on a horizontal table with coeffficient of kinetic friction 0.35. the mass is connected to a cable that passes over pulley of mass 3.5kg and radius 21 cm. other end of cable is attached to a mass of 15kg. system is released from rest.

a) calc the acceleration of system.

b) how many times does pulley rotate in 2 sec?

Answer 1

you didn't mentioned figure, but no need of figure as i am familiar with these types of problem

Net force on m_2 m_2 g - T_2 = m_2 a T_2 = m_2 9g - a) rightarrow (1) rightarrow net force acting on the m_1 T_1 - mu m_1 g = m_1 a T_1 = m_1 a + mu m_1 g rightarrow (2) Torque on pulley: T_1 - T_1 = I r T_1 - T_1 = 1/2 , r^2 (a/r) = 1/2 mar = 1/2 (3.5) 91) (0.21) T_1 - T_1 = 0.3675 a I = moment of inertia = 1/2 mr^2 alpha = angular acceleration alpha = a/r plug the value of T_1 - T_1 from (1) and (2) rightarrow m_2 g - m_2 a - m_1 a + mu m_1 g = 0.3675 a rightarrow a = m_2 g + mu m_1 g/(0.36 + 5 + m_1 + m_2) = (3.5) (9.8) + (0.35 times 8 times 9.8)/0.3675 + 8 + 3.5 a = 4.83 m/s^2 angular acceleration alpha = a/r = 4.83 m/s^2/0.21 m = 23 rad/s^2 angular displacement theta = 1/2 at^2 theta = 46 rad