A 100-kg uniform horizontal disk of radius 5.50 m turns without friction at 2.50 rev/s on a vertical axis through its center, as in Figure P11.46, A feedback mechanism senses the angular speed of the disk, and a drive motor at A maintains the angular speed constant while a 1.20 kg block on top of the disk slides outward in a radial slot. The 1.20-kg block starts at the center of the disk at time t = 0 and moves outward with constant speed 1.25 cm/s relative to the disk until it reaches the edge at t = 440 s. The sliding block feels no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block.
(a) Find the torque that the drive motor must provide as a function of time, while the block is sliding.
(b) Find the value of this torque at t = 440 s, just before the sliding block finishes its motion.
(c) Find the power that the drive motor must deliver as a function of time.
(d) Find the value of the power when the sliding block is just reaching the end of the slot.
(e) Find the string tension as a function of time.
(f) Find the work done by the drive motor during the 440-s motion.
(g) Find the work done by the string brake on the sliding block.
(h) Find the total work on the system consisting of the disk and the sliding block.