Solution D10-52 (Figure D10.5 condition 2 SM Targ 1989)

The mechanical system consists of homogeneous stepped pulleys 1 and 2, wound with threads, weights 3-6 attached to these threads, and a weightless block (Fig. D10.0-D10.9, Table D10). The system moves in a vertical plane under the action of gravity forces and a pair of forces with a torque M applied to one of the pulleys. The radii of the pulley stages 1 are: R1 = 0.2 m, r1 = 0.1 m, and the pulley 2 - R2 = 0.3 m, r2 = 0.15 m; their radii of inertia relative to the rotation axes are equal respectively to ρ1 = 0.1 m and ρ2 = 0.2 m. Neglecting friction, determine the acceleration of a load having a greater weight; the weights P1, ..., P6 of the pulleys and weights are given in the table in newtons. Loads, whose weights are equal to zero, are not represented in the drawing (the pulleys 1, 2 are always represented as parts of the system).