Final answer:
The extension of a spring is directly proportional to the force applied, as established by Hooke's law, until the limit of proportionality is reached.
Step-by-step explanation:
The extension of a spring is directly proportional to the force applied to it, up to the limit of proportionality. This linear relationship is described by Hooke's law, which states that the force (F) applied to stretch or compress a spring is directly proportional to the displacement (Δx) the spring undergoes.
This can be represented mathematically as F = kΔx, where k is the spring's force constant or stiffness coefficient. The proportionality constant k uniquely characterizes a spring's stiffness, and its value determines how much the spring will stretch or compress under a given force.
It's important to note that this direct proportionality holds true as long as the deformation remains within the elastic limit of the spring material. Once the force exceeds this limit, the spring may not return to its original shape (permanent deformation), and Hooke's law will no longer apply.