A box contains a uniform disk of mass M and radius R that is pivoted on a low-friction axle through its center (Figure
12.58). A block of mass m is pressed against the disk by a spring, so that the block acts like a brake, making the disk hard
to turn. The box and the spring have negligible mass. Astring is wrapped around the disk (out of the way of the brake) and
passes through a hole in the box. A force of constant magnitude F acts on the end of the string. The motion takes place in
outer space. At time ti the speed of the box is vi, and the rotational speed of the disk is ωi. At time tf the box has moved a
distance x, and the end of the string has moved a longer distance d, as shown.
(a) At time tf, what is the speed vf of the box?
(b) During this process, the brake exerts a tangential friction force of magnitude f. At time tf, what is the angular speed
ωf of the disk?
(c) At time tf, assume that you know (from part b) the rotational speed ωf of the disk. From time ti to time tf, what is
the increase in thermal energy of the apparatus?
(d) Suppose that the increase in thermal energy in part (c) is 8 × 104 J. The disk and brake are made of iron, and their
total mass is 1.2 kg. At time ti their temperature was 350 K. At time tf, what is their approximate temperature?