Identification of Spring Coefficient

The following three diagrams show the process we used to find each spring coefficient.

First, we hang the spring from a support. Then we attach a small mass to the end of the spring. This mass must be large enough so the spring just begins to stretch.

Why do we need to attach an initial mass to the spring?

Adding additional mass to the spring produces additional extension of the spring.

What force causes this extension?

We can relate the additional extension of the spring and the force that causes it by hanging various additional masses and measuring their resulting deflections.

If we perform measurements on a particular spring and plot the force due to weight versus the extension, we get the graph below:

We want to find a straight line approximation passing through the origin that relates the applied force AND the extension. This linear relationship, W=kx (where x is the additional extension), is derived from experiments and is known as Hooke's Law.

How would you find k?

If we plotted total weight versus spring extension (instead of additional weight versus additional extension), what would the graph look like?