Solution D4-96 (Figure D4.9 condition 6 SM Targ 1989)

The mechanical system consists of a rectangular vertical plate 1 with a mass m1 = 18 kg moving along the horizontal guides, and a load D with a mass m2 = 6 kg (Fig. D4.0 - D4.9, table D4). At time t0 = 0, when the plate speed u0 = 2 m / s, the load under the influence of internal forces starts to move along the slab of the plate. In Fig. 0-3, the trough KE is rectilinear and when the load moves the distance s = AD varies according to the law s = f1 (t), and in Fig. 4-9 gutter is a circle of radius R = 0.8 m and when the load moves the angle φ = ∟AC1D varies according to the law φ = f2 (t). In Table. D4, these dependences are given separately for Fig. 0 and 1, for Fig. 2 and 3, etc., where s is expressed in meters, φ - in radians »t - in seconds. Considering the load as a material point and neglecting all the resistances, determine the dependence u = f (t), that is, the velocity of the plate as a function of time.