(a) the tension of each thread and the angular acceleration of the
cylinder;
(b) the time dependence of the instantaneous power developed by
the gravitational force.
1.254. Thin threads are tightly wound on the ends of a uniform
solid cylinder of m ass m. The free ends of the threads are attached to
Fig. 1.59.
Fig. 1.60.
the ceiling of an elevator car. The car starts going up with an acceleration wo. Find the acceleration w' of the cylinder relative to the car and
the force F exerted by the cylinder on the ceiling (through the threads).
1.255. A spool with a thread wound on it is placed on an inclined
smooth plane set at an angle a = 30° to the horizontal. The free end
of the thread is attached to the wall as shown in Fig. 1.61. The mass
of the spool is m = 200 g, its moment of inertia relative to its own
axis I = 0.45 g • m2, the radius of the wound thread layer r = 3.0 cm.
Find the acceleration of the spool axis.
1.256. A uniform solid cylinder of mass m rests on two horizontal
planks. A thread is wound on the cylinder. The hanging end of the
thread is pulled vertically down with a constant force F (Fig. 1.62).
Find the maximum magnitude of the force F which still does not
bring about any sliding of the cylinder, if the coefficient of friction
between the cylinder and the planks is equal to k. What is the ac4*