# Collection of Problems in Theoretical Mechanics by Ivan, V. Meshchersky, N.M. Sinelnikova

By Ivan, V. Meshchersky, N.M. Sinelnikova

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**Example text**

Zzz \r 2% °’ -——--—— Fig. 61 is 15 m taken from the point A. The hoisting capacity of the crane is P=20,000 kgf. The weight of the truss is Q= =l2,000 kgf. Determine_ the reactions of the supports, and the tension T in the screw when the crane is in the position described. Ans. XA=26,000 kgf; YA=77,000 kgf; T=52,000 kgf. 74. An arch truss has a fixed hinged support A and a roller ·support B on a smooth plate inclined at 30° to the horizontal (Fig. 60). The span AB-:20 m. The weight of the truss is Q=l0,000 kgf.

145); 22 v U;= -9- =4OO m/SQC2. R 173. 5 m. 1 m lower than the track. The car rolls along a straight track with velocity v=l0 m/sec. Find also the instants when the particle M passes its bottom and top positions and also the projections of its` velocity on the axes Ox, Oy at these instants. The axis Ox coincides with the direction of the track and the axis Oy passes through the starting bottom position of the particle. Ans. -:22 m/sec, vy=0, where k=0, l, 2, 3, 12. Acceleration of a Particle 174.

ZA=ZB=1506 kgf; ZC=—1212 kgf; XA=XB=0. 131. A uniform rectangular lamina with sides cz and b and weight P rests horizontally on three point supports at the vertices of the rectangle A and B and at some point E (Fig. 116). The force exerted on the supports at the points A and B are {P andg, respectively. Compute the force NE acting on the support at the point E, andthe coordinates of this point. ‘L· =£b_ ns E zoP’x11a’y 11 4-1843 49 132. A round weightless lamina rests in a horizontal position with its centre on the spike O (Fig.