How do you know when k in Hooke's law is positive or negativ

[Derek Marusarz]

Homework Statement

A 7.2-kg mass is hanging from the ceiling of an elevator by a spring of spring constant 150N/m whose unstretched length is 80 cm. What is the overall length of the spring when the elevator: (a) starts moving upward with acceleration 0.95m/s2 ; (b) moves upward at a steady 14m/s ; (c) comes to a stop while moving upward at 14 m/s , taking 9.0 s to do so? (d) If the elevator measures 3.2 m from floor to ceiling, what is the maximum acceleration it could undergo without the 7.2-kg mass hitting the f loor?

In part (a), the professor used the equation ma = kx - mg, with the solution being 80 + x. I have seen both equations as F = kx and F = -kx. Now, I realize one must analyze every siruation, but there must beva way to resolve which way the spring is moving. Thank you.

Homework Equations

The Attempt at a Solution

 

[berkeman]

Welcome to the PF.

AFAIK, "k" is always a positive coefficient. Whether the "Force" is "positive" or "negative" depends on the directions of the forces and the directions of the unit vectors in the coordinate systems. Spring force is always restorative to the equilibrium position of the spring when it is neither extended nor compressed. Does that make sense?

 

[haruspex]

I have seen both equations as F = kx and F = -kx.

Further to berkeman's comments, if you are consistent with regard to signs for the displacement and the force, the correct equation is F=-kx. The other would be better written as |F|=k|x|.