Irodov – Problems in General Physics

Fig. 1.63.

celeration w„,„„ of the axis of the cylinder rolling down the inclined

plane?

1.257. A spool with thread wound on it, of mass m, rests on a rough

horizontal surface. Its moment of inertia relative to its own axis is

equal to I = TmR 2 , where y is a numerical factor, and R is the out-

side radius of the spool. The radius of the wound thread layer is equal

to r. The spool is pulled without sliding by the thread with a constant

force F directed at an angle a to the horizontal (Fig. 1.63). Find:

(a) the projection of the acceleration vector of the spool axis on the

x-axis;

(b) the work performed by the force F during the first t seconds af-

ter the beginning of motion.

1.258. The arrangement shown in Fig. 1.64 consists of two identical

uniform solid cylinders, each of mass m, on which two light threads

Fig. 1.64. Fig. 1.65.

are wound symmetrically. Find the tension of each thread in the pro-
cess of motion. The friction in the axle of the upper cylinder is as-
sumed to be absent.
1.259. In the arrangement shown in Fig. 1.65 a weight A possesses
mass m, a pulley B possesses mass M. Also known are the moment of
inertia I of the pulley relative to its axis and the radii of the pulley

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