Answer to Question #233096 in Physics for ceejay

Question

A load W = 6000N is supported by two ropes one of which makes an angle of

     50^o with the horizontal while the other rope makes an angle of 60^o with the

     Horizontal. Calculate the force exerted by each rope so as to provide

      equilibrium. CALCULATE the Resultant, and Resultant Angle.

Answer 1

$\sum F_x=0:\quad T_1\cos50^{\circ}=T_2\cos60^{\circ}$

$T_1=0.778T_2$

$\sum F_y=0:\quad T_1\sin50^{\circ}+T_2\sin60^{\circ}=W$

$0.778T_2+0.866T_2=6000$

$T_2=3628\:{\rm N}, \quad T_1=2822\:\rm N$