Question

Two springs have different spring constants. How could you identify the spring with the greater spring constant value?

Answer 1

You could attach both springs to the ceiling and hang the same mass from both. The one that stretches less has the larger spring constant value.

Explanation:

Let `m` be the mass that you hang from both springs, in kg. The force of gravity on the mass has magnitude `mg` in Newtons, where `g=9.8\ m/s^{2}` is the acceleration due to gravity near the surface of the earth.

By Hooke's Law, the magnitude of the restoring force is equal to `ky`, where `y` is the downward displacement, in meters, from the original equilibrium position of the bottom of the spring (distance of the stretching amount) and `k>0` is the spring constant.

Therefore, equating the magnitudes of the two forces (which are opposite in direction), we can say that `ky=mg` so that `k=(mg)/y`.

This means that `k` is inversely proportional to the displacement `y`. The smaller `y` is, the bigger `k` will be. In fact, for a given mass, when `y` is half as big (for one spring compared to another) that means `k` is twice as big (for that new spring).