Two boxes are connected to a cord, and the cord is hung over a pulley connected to the ceiling, as shown in the figure below. MR The masses of the boxes are m, = 17.0 kg and m, = 11.0 kg, the mass of the pulley is M = 5.00 kg, and the radius of the pulley is R = 0.300 m. Box m, is initially on the floor, and box m, is initially 4.70 m above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the cord is small enough to be ignored, and the cord does not slip on the pulley, nor does it stretch. (a) How much time (in s) does it take box m, to hit the floor after being released? At, = Apply Newton's second law to each box. Consider the forces on each box and be careful of directions and signs of forces and acceleration. Then relate the net torque on the pulley to its angular acceleration. What is the moment of inertia of the pulley? How does the angular acceleration relate to the linear acceleration of the boxes? s (b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m, to hit the floor if the mass of the pulley were neglected.) At, = If you found an expression for acceleration in part (a) in terms of the masses, how will it now change? How will the tensions on each box now be related? s
Two boxes are connected to a cord, and the cord is hung over a pulley connected to the ceiling, as shown in the figure below. MR The masses of the boxes are m, = 17.0 kg and m, = 11.0 kg, the mass of the pulley is M = 5.00 kg, and the radius of the pulley is R = 0.300 m. Box m, is initially on the floor, and box m, is initially 4.70 m above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the cord is small enough to be ignored, and the cord does not slip on the pulley, nor does it stretch. (a) How much time (in s) does it take box m, to hit the floor after being released? At, = Apply Newton's second law to each box. Consider the forces on each box and be careful of directions and signs of forces and acceleration. Then relate the net torque on the pulley to its angular acceleration. What is the moment of inertia of the pulley? How does the angular acceleration relate to the linear acceleration of the boxes? s (b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m, to hit the floor if the mass of the pulley were neglected.) At, = If you found an expression for acceleration in part (a) in terms of the masses, how will it now change? How will the tensions on each box now be related? s
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Two boxes are connected to a cord, and the cord is hung over a pulley connected to the ceiling, as shown in the figure below.
MO R
The masses of the boxes are m
= 17.0 kg and m,
1
= 11.0 kg, the mass of the pulley is M = 5.00 kg, and the radius of the pulley is R = 0.300 m. Box m, is initially on the floor, and box m, is initially 4.70 m
above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the cord is small enough to be ignored, and the cord does not slip on the pulley, nor does it stretch.
(a) How much time (in s) does it take box m, to hit the floor after being released?
At, =
Apply Newton's second law to each box. Consider the forces on each box and be careful of directions and signs of forces and acceleration. Then relate the net torque on the pulley to its angular acceleration.
What is the moment of inertia of the pulley? How does the angular acceleration relate to the linear acceleration of the boxes? s
(b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m,
to hit the floor if the mass of the pulley were neglected.)
At, =
If you found an expression for acceleration in part (a) in terms of the masses, how will it now change? How will the tensions on each box now be related? s
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