Question

Determine the magnitude of the forces F1 and F2 in the given figure, assuming that there is no net force on the object.

Answer 1

I know that I have to put it in the xy-plane doing so I have the drawing:

Answer 2

If I call f1=II F1 II i.e. f1 is the magnitude of F1 and f2=II F2 II (f2 is the magnitude of F2) then I have that F1=f1<cos270,sin270> and F2=f2<cos135,sin135>.But the forces are vectors pointing towards the origin not away from the origin this is what is confusing me.I know I have to solve for f1 & f2 using the equation F1+F2+Fg=0.Do I have F1 & F2 correct? or is it the negative of what I have???and what is Fg?

Answer 3

i think you are over complicating the problem
Forces can be split into horizontal and vertical components
given force F, the vertical component is Fsin(theta), horizontal component is Fcos(theta)


Now set the horizontal components equal, and vertical components equal such that net is zero
\[F_{2}\cos(45) = 20\cos(30)\]
\[F_{1} = F_{2}\sin(45) + 20\sin(30)\]
solve system of equations to find F1 and F2