Targ S.M. 1988 D3 option 67

The mechanical system consists of weights 1 and 2 (coefficient of friction of weights on the plane f=0.1); solid cylindrical roller 3 and stepped pulleys 4 and 5 with radii R₄=0.3m; r₄=0.1m; R₅=0.2m; r₅=0.1m (the mass of each pulley is considered to be uniformly distributed along its outer rim). Under the action of force F; depending on the displacement of the point of application of force, the system comes into motion from a state of rest. When the system moves, pulleys 4 and 5 are acted upon by constant moments of resistance forces; equal to M₄ and M₅, respectively. Determine the value of the desired quantity at the time when the displacement of the point of application of the force F is equal to S₁.