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 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.
Principles of Physics: A Calculus-Based Text
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Chapter10: Rotational Motion
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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 z
= 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
(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.
It N/s
(f) Find the work done by the drive motor during the 465 s motion. Hint: The work is given by W
KJ
motor
(g) Find the work done by the string brake on the sliding block. Hint: The work is given by W
block
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
=
mv² w²t².
= 1/2mv ²2 w²12², 1 which is negative
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Step 1: Determine the given data:
VIEWStep 2: a) Find the torque:
VIEWStep 3: b) Calculate the torque:
VIEWStep 4: c) Calculate the power delivered:
VIEWStep 5: e) Calculate the tension:
VIEWStep 6: f) Calculate the work done by the motor:
VIEWStep 7: g) Calculate the work done by tension:
VIEWStep 8: d) Calculate the power:
VIEWStep 9: h) Calculate the total work done:
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