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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

Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotation Of A Rigid Object About A Fixed Axis
Section: Chapter Questions
Problem 10.3OQ: A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different...
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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
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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