Solution D3-84 (Figure D3.8 condition 4 SM Targ 1988)

The mechanical system consists of loads 1 and 2 (coefficient of friction of loads about the plane F = 0.1), a cylindrical continuous homogeneous roller 3 and step pulleys 4 and 5 with radii of steps R4 = 0.3 m, r4 = 0.1 m, R5 = 0.2 m, r5 = 0.1 m (the mass of each pulley is assumed to be uniformly distributed over its outer rim) (Fig. D3.0-D3.9, Table D3). The bodies of the system are connected to one another by threads wound on pulleys; The sections of the filaments are parallel to the corresponding planes. Under the action of the force F = f (x), which depends on the displacement of the point of application of force, the system comes into motion from a state of rest. When the system moves to pulleys 4 and 5, there are constant moments of the resistance forces, equal to M4 and M5, respectively. Determine the value of the sought value at the time when the displacement of the point of application of the force F is equal to s1.