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why is it 123.7? isnt it in third quadrant so 180+(90-56.3)=213.7

why is it 123.7? isnt it in third quadrant so 180+(90-56.3)=213.7

Elements Of Electromagnetics
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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Question

why is it 123.7?

isnt it in third quadrant so 180+(90-56.3)=213.7

 

Take moment about point A. EMA =0 MA =-F, x6+ F, x(5+4) Substitute F cos a for F, and Fsina for F,. M, =-F cosax6+F sin a x(5+4) . (1) ...... Differentiate the above equation with respect to angle. dM, d-F cosax6+Fsina×(5+4) da da = 6F sin a +9F cos a For the maximum moment, 6Fsin α + 9F cos α = 0 9 tan a = a =-56.3 Calculate the angle from positive x direction. a = 180– 56.3 = 123.7° Therefore, the allowable angle for the required force is 123.7°
Transcribed Image Text:Take moment about point A. EMA =0 MA =-F, x6+ F, x(5+4) Substitute F cos a for F, and Fsina for F,. M, =-F cosax6+F sin a x(5+4) . (1) ...... Differentiate the above equation with respect to angle. dM, d-F cosax6+Fsina×(5+4) da da = 6F sin a +9F cos a For the maximum moment, 6Fsin α + 9F cos α = 0 9 tan a = a =-56.3 Calculate the angle from positive x direction. a = 180– 56.3 = 123.7° Therefore, the allowable angle for the required force is 123.7°
The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Fabout point A reaches 10.000 in.-lb. determine the largest value F may have and specify the value of a for which the moment about .A is the largest. Note that the value of Fyou determine must not produce a moment about, A that exceeds 10.000 in.-Ib for any possible value of a. - 5 in. --- 4 in. - HAO 6 in. F Figure P4.7
Transcribed Image Text:The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Fabout point A reaches 10.000 in.-lb. determine the largest value F may have and specify the value of a for which the moment about .A is the largest. Note that the value of Fyou determine must not produce a moment about, A that exceeds 10.000 in.-Ib for any possible value of a. - 5 in. --- 4 in. - HAO 6 in. F Figure P4.7
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