A sign weighs 150 N is supported by ropes a and b which make 30° angles with the horizontal. The sign is not moving. What forces do the ropes exert on the sign?

Question

I'm not really sure how to complete this problem or what formula to use, if anyone can help I'd appreciate it, thank you!

Answer 1

The sign must remain in equilibrium, that is, NOT in motion by the 

forces acting on it.  In this problem, only a gravity down force of

150N is acting on it.  It is being resisted by two diagonal ropes.  The

diagonal force in the rope can be resolved into vertical and horizontal

components.  If we were to isolate the sign with the forces acting

on it, commonly referred to as "taking a free-body diagram," we

would have a diagram as illustrated at the following URL...

 

https://www.wyzant.com/resources/files/405784/equilibrium_forces

 

Adding vertical forces "(P)v" must equal to zero, adding horizontal

forces "(P)h" must equal to zero.  

 

Recognize that the resultant force in the rope "(P)resultant" is

simply the hypotenuse of a right triangle at an angle of 30deg from

horizontal with vertical and horizontal force components "(P)v and

(P)h" as its legs.  This value is easily calculated.