First pulley ley
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:First pulley
Second pulley
FIGURE 2
FIGURE 2 shows a block of mass m, is hung from the double pulley system.
Each pulley has the same mass m, and same radius R. When a downward
pulling force of F is exerted, first pulley and second pulley rotate with angular
accelerations of a1 and a2, the block accelerates upwards with linear
acceleration of a. The rotating second pulley also in the same time accelerates
upwards with linear acceleration of a. The rope does not slip over the pulley.
(a) Draw free body diagrams separately for the first pulley, the second pulley
and the block.
(b) By treating the pulleys as uniform discs, state the required equation to
determine the moment of inertia of the pulley.
(c) State the equations if you are going to determine the magnitude of the
downward pulling force F. The equations must be related to Newtn's
second law for rotational motion and Newton's second law for linear
motion.
Expert Solution
Step 1
The tensions in the rope on the sides of pulley will be different due to rotational inertia.
Three FBD will be drawn , of pulley 1 and pulley 2 and of block
The pulley '1' will be subjected to angular acceleration
The pulley 2 will be subjected to angular as well as linear acceleration
The block will be subjected to linear acceleration only.
Applying newton's second law of motion, we can frame equations which can be used to find moment of inertia and also force F
The complete solution is attached.
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