Calculate the force in a spring and the stored elastic potential energy, based on the spring constant and displacement.
Hooke's law states that the force (F) needed to stretch or compress a spring is directly proportional to the displacement (x) from its rest length, as long as the spring isn't loaded beyond its elastic limit. The spring constant (k, measured in N/m) describes how stiff the spring is — the higher k, the more force is needed for the same displacement.
The energy stored in a stretched or compressed spring is called elastic potential energy, and is calculated with:
Yes, Hooke's law applies equally to both stretching and compressing a spring — the displacement x simply represents the distance from the rest length, in either direction.
Then the relationship between force and displacement stops being linear, and the spring can become permanently deformed (plastic deformation) — it no longer returns to its original shape when the force is removed. Hooke's law no longer applies in this region.
Hooke's law is used, among other things, in spring scales, shock absorbers, clock springs, and other mechanical devices that store or release energy elastically. It's also a fundamental principle in materials science for describing elastic deformation in solids generally.