The cord passing over the two small pegs


The cord passing over the two small pegs A and B of the square board is subjected to a tension of 100 N. Determine the required tension P acting on the cord that passes over pegs C and D so that the resultant couple produced by the two couples is 15 N•m acting clockwise. Take θ = 15°.

The cord passing over the two small pegs

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Let us assume clockwise moments are positive and write an equation as follows:

\circlearrowright^+ 15=100\cos30^0(0.3)+100\sin30^0(0.3)-p\cos15^0(0.3)-p\sin15^0(0.3)

(solve for p)

p=70.7 N

 

When solving this problem, remember that each force was broken into x and y components. These components were then used to calculate the moment.

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 4, question 4-77.

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