Answer to Question #192523 in Physics for arjel

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

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

      equilibrium. CALCULATE the Resultant, and Resultant Angle.

Answer 1

Draw the diagram:

From the diagram, we see that for the weight to remain in equilibrium, two conditions are important: the sum of horizontal components of all forces must zero, the sum of vertical components of all forces must be equal:

$$-T_1\cos50°+T_2\cos40°=0,\\ -W+T_1\sin50°+T_2\sin40°=0.\\\space\\ T_1=T_2\frac{\cos40°}{\cos50°},\\\space\\ -W+T_2\frac{\cos40°}{\cos50°}\sin50°+T_2\sin40°=0,\\\space\\ T_2=\frac{W}{\cos40°·\tan50°+\sin40°}=3857\text{ N},\\\space\\ T_1=\frac{W\cos40°}{\cos50°(\cos40°·\tan50°+\sin40°)}=4596\text{ N}.$$

The angle between the ropes is

$$\theta=180°-50°-40°=90°.$$