I am currently doing some Hooke's Law problems. While I do not have any trouble with any exercise in particular, I do have trouble with the sign in the equation. Let's say I have a vertical spring and I attached a hanging mass m to it. The string will then stretch a distance Δy. I choose downward as positive.
Therefore, applying Newton's Second Law gives: Fnet = mg - Fk (Fk is the restored force given by Hooke's Law).
Since the vertical spring is at equilibrium, Fnet = 0. Therefore, mg - Fk = 0, or mg = Fk
But Fk also equals -kΔy, where k is the spring constant and Δy is the positive displacement (I chose downward as positive).
So Fk = mg, which is a positive value. But Fk = -ky, which is negative??? I know I must have done something wrong somewhere, but I couldn't figure out where. Could someone please help explaining this for me? Thank you very much. Any help is greatly appreciated.
Fk = -ky (Hooke's Law)
The Attempt at a Solution
I was able to solve most of the problems by "forcing" myself to choose the correct sign; however, I still don't understand what I'm doing and why I got the correct result in the first place. I understand why there is a negative sign in the Hooke's Law equation, since it's a restored force and it must be inversely proportional to the displacement. Having said that, I still don't understand why my attempt above gave Fk both a positive, and a negative value. Please shed some light for me, thanks a lot.
Also, I apologize for the inconvenient notation. I don't know Latex or any other mathematical convention used in forum and typing documents, so please don't delete this thread. Thanks again.