Solution D1-53 (Figure D1.5 condition 3 SM Targ 1988)

A load D of mass m, having received at initial point speed v0, moves in the curved pipe ABC, located in the vertical plane; sections of the pipe or both inclined, or one horizontal, and the other inclined (Figure D1.0-D1.9 of Table D1). In the figure AB, the load, in addition to the gravity, is acted upon by a constant force Q (its direction is shown in the figures) and the resistance force of the medium R, depends on the speed of the load v (opposite to the motion). At point B, the load, without changing its speed, passes to the section of the aircraft's pipe, where, in addition to gravity, the variable force F acts on it, the projection of which Fx on the x axis is given in the table. Considering the cargo as a material point and knowing the distance AB = l or the time t1 of the cargo movement from point A to point B. Find the law of cargo movement on the aircraft section, i.e. x = f (t), where x = BD. Friction of the load on the pipe is neglected.