Solution D2-61 (Figure D2.6 condition 1 SM Targ 1988)

Solution D2-61 (Figure D2.6 condition 1 SM Targ 1988)

The mechanical system consists of a rectangular vertical plate 1 with a mass m1 = 24 kg and a load D with a mass m2 = 8 kg; plate or moves around the horizontal guide (Fig. D2.0-D2.4), or rotates around the vertical axis z, lying in the plane of the plate (Fig. D2.5-D2.9). At time t0 = 0, the load begins to move under the action of internal forces along the trough existing on the plate; the law of its motion s = AD = F (t) is given in Table. D2, where s is expressed in meters, t - in seconds. The shape of the gutter in Fig. D2.0, D2.1, D2.8, D2.9 - rectilinear (trough KE), in Fig. A2.2-D2.7 is a circle of radius R = 0.8 m centered at the center of mass C1 of the slab (s = AD in figure D2.2 - D2.7 is counted along the arc of the circle). The plate (Figures D2.0-D2.4) has a velocity v0 = 0 at the instant t0 = 0. The plate (Fig. D2.5-D2.9) has an angular velocity ω0 = 8 s-1 at time t0 = 0, and at this moment the rotational moment M (the moment relative to the axis) given in the table in newtonometers and directed as ω0 for M> 0 and in the opposite direction for M <0 begins to act on it. The z axis passes from the center C1 of the plate at a distance b; the dimensions of the slab are shown in the figures. Assuming the cargo to be a material point and neglecting all the resistances, determine the indicated in the table in columns 4 and 9, where it is indicated: in column 4 (refers to Figures D2.0-D2.4) x1 - displacement of the plate in time from t0 = 0 to t1 = 1 s, v is the plate speed at time t1 = 1 s, N is the total normal plate pressure on the guides at time t = 1 s (indicate where the force is directed); in column 9 (refer to Figures 5-9) ω1 is the angular velocity of the plate at time t1 = 1 s, ω = f (t) is the angular velocity of the plate as a function of time. In all figures, the load is shown in the position at which s = AD> 0; For x <0, the cargo is on the other side of point A.