Consider the pulley system depicted in the figure. The block is prevented from moving by the applied force F. Assume the pulleys are massless and frictionless. An illustration shows a rectangular block of mass M suspended from a horizontal surface by a complex pulley system comprised of one large pulley, one small pulley, two short ropes, and one long rope. The pulleys are drawn such that the small pulley is some vertical distance below the large pulley and their axles are perpendicular to the page. The left side of the small pulley aligns vertically with the center of the large pulley. One of the short ropes suspends the block of mass M from the bottom of the small pulley's harness and has tension T5. The remaining short rope and the long rope are, respectively, anchored to the top and bottom of the large pulley's harness. This short rope has tension T4 and suspends the large pulley from the horizontal surface. The long rope extends from the large pulley and cradles the small pulley below, first passing along its left edge with tension T2 and then along its right edge with tension T3. The segment of tension T3 continues upward and passes over the large pulley from its right edge. The remaining segment of the long rope has tension T1 along the large pulley's left edge and is pulled with a downward force vector F. (a) Determine the tension in each section of rope. (Use the following as necessary: M and g.) T1= T2= T3= T4= T5= (b) Find the magnitude of F. (Use the following as necessary: M and g.) F = (c) What If? What should the magnitude of the force F be if the mass M is to have an upward acceleration of magnitude a? (Use the following as necessary: M, g, and a.)

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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Consider the pulley system depicted in the figure. The block is prevented from moving by the applied force F.

Assume the pulleys are massless and frictionless.

An illustration shows a rectangular block of mass M suspended from a horizontal surface by a complex pulley system comprised of one large pulley, one small pulley, two short ropes, and one long rope.

The pulleys are drawn such that the small pulley is some vertical distance below the large pulley and their axles are perpendicular to the page. The left side of the small pulley aligns vertically with the center of the large pulley.
One of the short ropes suspends the block of mass M from the bottom of the small pulley's harness and has tension T₅.
The remaining short rope and the long rope are, respectively, anchored to the top and bottom of the large pulley's harness. This short rope has tension T₄ and suspends the large pulley from the horizontal surface.
The long rope extends from the large pulley and cradles the small pulley below, first passing along its left edge with tension T₂ and then along its right edge with tension T_3. The segment of tension T₃ continues upward and passes over the large pulley from its right edge. The remaining segment of the long rope has tension T₁ along the large pulley's left edge and is pulled with a downward force vector F.

(a) Determine the tension in each section of rope. (Use the following as necessary: M and g.)

T₁=

T₂=

T₃=

T₄=

T₅=

(b) Find the magnitude of F. (Use the following as necessary: M and g.)

F =

(c) What If? What should the magnitude of the force F be if the mass M is to have an upward acceleration of magnitude a? (Use the following as necessary: M, g, and a.)

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