A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences 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 as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by T 2mrvw. = t N.m (b) Find the value of this torque at t = 465 s, just before the sliding block finishes its motion. 2.52 N-m (c) Find the power which the drive motor must deliver as a function of time. t W/s (d) Find the value of the power when the sliding block is just reaching the end of the slot. 18.2 x w (e) Find the string tension as a function of time. ]t N/s
A uniform horizontal disk of radius 5.50 m turns without friction at = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences 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 as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by T 2mrvw. = t N.m (b) Find the value of this torque at t = 465 s, just before the sliding block finishes its motion. 2.52 N-m (c) Find the power which the drive motor must deliver as a function of time. t W/s (d) Find the value of the power when the sliding block is just reaching the end of the slot. 18.2 x w (e) Find the string tension as a function of time. ]t N/s
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Transcribed Image Text:A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.30 rev/s on a vertical axis through its center, as in the figure
below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant
while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and
moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences
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 as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by
= 2mrvw.
t N-m
(b) Find the value of this torque at t= 465 s, just before the sliding block finishes its motion.
N.m
2.52
(c) Find the power which the drive motor must deliver as a function of time.
t W/s
(d) Find the value of the power when the sliding block is just reaching the end of the slot.
18.2
x w
(e) Find the string tension as a function of time.
t N/s
(f) Find the work done by the drive motor during the 465 s motion. Hint: The work is given by W
8.47
motor
kJ
(g) Find the work done by the string brake on the sliding block. Hint: The work is given by W =-—-—-mv² w²t², 1
block
since the string applies a force in the opposite direction of the motion.
-4.23
kJ
=
= mv² w²t².
(h) Find the total work on the system consisting of the disk and the sliding block.
4.24
kJ
which is negative
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