Answer to Question #262535 in Complex Analysis for luka

Question

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.  

Answer 1

Resultant force

$$R=F_A+F_B+F_C=5\angle 0\degree+ 9\angle 135\degree+12\angle 240\degree$$

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

$$\approx-7.364-4.028j$$

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

$$\tan \theta=\dfrac{-4.028}{-7.364}, 180\degree<\theta<270\degree$$

$$\theta\approx208.678\degree$$

$$R=8.394\angle208.678\degree$$

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).