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A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.55 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 = 360 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 = 360 s, just before the sliding block finishes its motion. 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. 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 360 s motion. Hint: The work is given by W == motor mv² w²x². KJ (g) Find the work done by the string brake on the sliding block. Hint: The work is given by W block = 1 ½ mv² w²², which is negative since the string applies a force in the opposite direction of the motion. KJ (h) Find the total work on the system consisting of the disk and the sliding block. KJ

A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.55 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 = 360 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 = 360 s, just before the sliding block finishes its motion. 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. 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 360 s motion. Hint: The work is given by W == motor mv² w²x². KJ (g) Find the work done by the string brake on the sliding block. Hint: The work is given by W block = 1 ½ mv² w²², which is negative since the string applies a force in the opposite direction of the motion. KJ (h) Find the total work on the system consisting of the disk and the sliding block. KJ

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter12: Rotation I: Kinematics And Dynamics
Section: Chapter Questions
Problem 35PQ: In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m...
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A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.55 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 = 360 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 = 360 s, just before the sliding block finishes its motion. 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. 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 360 s motion. Hint: The work is given by W == motor mv² w²x². KJ (g) Find the work done by the string brake on the sliding block. Hint: The work is given by W block = 1 ½ mv² w²², which is negative since the string applies a force in the opposite direction of the motion. KJ (h) Find the total work on the system consisting of the disk and the sliding block. KJ
Transcribed Image Text:A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.55 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 = 360 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 = 360 s, just before the sliding block finishes its motion. 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. 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 360 s motion. Hint: The work is given by W == motor mv² w²x². KJ (g) Find the work done by the string brake on the sliding block. Hint: The work is given by W block = 1 ½ mv² w²², which is negative since the string applies a force in the opposite direction of the motion. KJ (h) Find the total work on the system consisting of the disk and the sliding block. KJ
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