Force needed to support Suspension of a Vehicle

[Alison A.]

Homework Statement

A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N/mm and an unstreched length of 347 mm.

http://imgur.com/1dTVs12

Determine the value P and the force supported by member AB so that the suspension has the equilibrium position shown where member AB is horizontal.

Homework Equations

ΣF=0
ΣF_xi+ΣF_yj=0,
ΣF_x=0, and ΣF_y=0.
Spring Law: F_s=kδ=k(L-L₀)

The Attempt at a Solution

I started by trying to find the force of the spring
F_s= 178 N/mm (R_CA-347mm)

Finding R_CA I took the pythagorean theorem (141)²+(229)²=R_CA, R_CA=268

However when I put that number back into the equation it's a negative number... I don't understand why or what I'm doing wrong.

 

[BvU]

I think I saw this in another thread too ? Anyway, the force the spring exercises being negative says something about the direction it is working in. That's perfectly fine. Your problem statement says nothing about it, but I suppose the picture has AB horizontal and the car in a steady state equilibrium. Then your equations come in useful.