Finding the relaxed length of a sping

[sheiky989]

Homework Statement

A ball of mass 560 g hangs from a spring whose stiffness is 185 Newtons per meter. A string is attached to the ball and you are pulling the string to the right, so that the ball hangs motionless. In this situation the spring is stretched, and its length is 15 cm.

What would be the relaxed length of the spring, if it were detached from the ball and laid on a table?

Homework Equations

Force of spring = -ks(stretch length)
arccosθ=adj/hyp
Net force=0
Force of spring + weight + tension = 0

The Attempt at a Solution

Force of spring = -185(.15)
Force of spring = -27.75 N
arccosθ=8/15
θ=57.77

Force of spring vector = <14.8, -24.47, 0> N
Weight = <0, -5.488,0> N

I don't know what to do from here

 

[Mindscrape]

Your spring vector actually needs to be reversed. Gravity is trying to pull the mass down, and the spring force is keeping the mass up, so they need to be opposite. Anyway, if you equate the y component of the spring with the force of gravity (since this is equilibrium and there is no acceleration so the forces have to cancel) you can figure out how much the springs has been displaced from it's rest length (the x in F=-kx).