Three strings are attached to an object. If one of the strings is pulled north with a force of 10 N and one of the other strings is pulled west with 15 N, what force must be applied to the third string so that the object does not move?

Question

Please help me with this question! I am ok with vector questions but I don't know what to do with this one. I tried a couple of times and I couldn't get the right answer.

Answer 1

Pull south with 10 N
Pull east with 15 Newtons

If you are doing this on an x y axis system then
Fx = 15
Fy = -10
|F| = sqrt(225 + 100) = sqrt (325) = 18.03
tan theta = Fy/Fx = -10/15

Answer 2

F1+F2 = -15+10i =18N.[-33.7o]=18N.[33.7o] N. of W. = 18N.[146.3o]CCW.

F3 must be equal in magnitude to F1+F2 but opposite in direction:
F3 = 18N.[33.7o] S. of E. = 18N.[146.3+180] = 18N.[326.3o] CCW.

The system is in Equilibrium; therefore, the object does not move,