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

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

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W,,:45O m/sec2; wl:6 m/sec?. 181. The rectilinear motion of a particle is defined by the law; $::1*5,-; (at+e·*"), where a and g are constants.

Derive formulae for the moment M of the couple which should be applied to the rod to keep it in equilibrium, and the tension T in the threads. Ans- M; T": • Vl2——4r2 sin! jg 2 Vl2——4r’ sin? if9. Centre of Gravity 148. Find the position of the centre of gravity C of an area limited by a semicircle AOB of a radius R and two straight lines of equal length AD and DB (Fig. 133). OD=3R. Ans. ocii? 19 R. 3r=+12 149. Find the position of the centre of gravity of a homogeneous disk with a round hole, assuming that the radius of the disk is rl and that of the hole is fg (Fig.

140 Fig. 141 Fig. 142 156. A 30,000-kgf load is transferred at a distance of 60 m from the fore compartment of a ship to the aft one. The displacement of the ship equals 4,500,000 kgf. Calculate the distance by which the centre of gravity of the ship and the load is displaced. Ans. 4 m. 157. Two halves of a round homogeneous cylinder are tied together by a thread wrapped round the cylinder with weights P attached to each end of the thread (Fig. 141). The cylinder weighs Q kgf. The plane of contact of both halves of the cylinder is vertical.

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