Which is it?
If it is an application of Hooke's law, where is it wrong?
Hooke's Law, as I attempted to explain in my previous post:
F = -kx
where
F is the force exerted by the spring
k is the spring constant
x is the elongation of the spring
What you've written is ambiguous, and can be read several way (none of which are correct).
Possible reading 1:
x = k
where
x is the elongation of the spring in mm
k is a constant force in Newtons
You can't directly equate length and force, so this doesn't work (that's the purpose of the spring constant). Also, it implies that the force doesn't change no matter how far the spring is stretched, which is easily disproved with a simple experiment.
Possible reading 2:
x = F
where
x is the elongation of the spring in mm
F is a force in Newtons
This doesn't work because you can't directly compare length and force.
This reading assumes that by "constant force" you mean that the force does not change as long as the elongation does not change, which would be redundant, as the above equation already implies this.
Possible reading 3:
x = kF
where
F is the force exerted by the spring in Newtons
k is the spring constant in mm/Newton
x is the elongation of the spring in mm
This would work, but you'd have to use different spring constants from the way the equation is normally read. This reading of your equation also requires assuming that by "constant force" you actually mean "
aconstant
times force," which is something of a stretch (no pun intended).