Question

2. The pulley (disk) has a radius "R" and a mass "m". The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the surface is "u. The system is released from rest and block B descends. Block A has a mass "2m" and block B has a mass "m Write out the forces and torque equations. Given [R, m, h, ], Determine: a. The acceleration of the system and the tension of the rope on either side of the pulley. ".

Answer 1

Considering the forces and torques on A, B and the pulley independently in x and the z directions we can write the force and torque equations Force on A Force on B; Torque on Pulley; B-mg = ma (14-5) R la Where T.Ts are the tension in A and B respectively. I is the moment of inertia of the pulley considering it as a solid disc of radius R. α is the angular acceleration of the pulley and a is the acceleration of the two block system comprising of blocks A and B Torque on Pulley; (7,-5)R-1α =-mR- (Z-1, )=-ma Combining all the three equations into one, we obtain, ma - 2/mg mg -ma Acceleration a-2(1-2%)g Tension on the pulley 14 = m(a + g)