Answer to Question #262535 in Complex Analysis for luka

Question #262535

Determine, using complex numbers, the magnitude and direction of the resultant of the coplanar forces given below, which are acting at a point. Force A , 5N acting horizontally, Force B , 9N acting at an angle of 1350 to force A, Force C , 12N acting at an angle of 2400 to force A.  


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Expert's answer
2021-11-08T19:41:42-0500

Resultant force


R=FA+FB+FC=50°+9135°+12240°R=F_A+F_B+F_C=5\angle 0\degree+ 9\angle 135\degree+12\angle 240\degree

=(5+0j)+(922+922j)+(663j)=(5+0j)+(-\dfrac{9\sqrt{2}}{2}+\dfrac{9\sqrt{2}}{2}j)+(-6-6\sqrt{3}j)

7.3644.028j\approx-7.364-4.028j

R=(7.364)2+(4.028)28.394|R|=\sqrt{(-7.364)^2+(-4.028)^2}\approx8.394

tanθ=4.0287.364,180°<θ<270°\tan \theta=\dfrac{-4.028}{-7.364}, 180\degree<\theta<270\degree

θ208.678°\theta\approx208.678\degree

R=8.394208.678°R=8.394\angle208.678\degree

Hence, the magnitude of the force that has the same effect as the three forces acting separately is: 8.394 N and its direction is 208.678° to the horizontal (i.e. from Force A).


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