Spring Constant

It is useful if we can predict the how much a rod of a certain material stretches, when there is a force. This knowledge is important if we want to make something. If we build a tall building, we need to know much the concrete gets compressed, when someone stands on it. It also tells us something about the nature of the solid. If the rod hardly stretches when we pull it, then the rod could be quite strong.

To see how or what we can predict, consider a material shaped into a long, thin cylinder. Imagine hanging this at one end, and fixing a weight to the other end. The rod stretches by a certain amount. If I use a rod of a different material, it is likely to stretch by a difference amount. So this tells us something about the material.

To make it easy to talk about the experiment, we should learn some names for the different parts of the setup. We call the weight the "load." If, instead of hanging a weight, I pull at the rod with my fingers, then we can still call this force a load. So the term "load" can be used for any kind of force.

When there is a load, the rod would become a bit longer. This happens to any material - some becomes longer, some shorter. The change in length is called the "extension."

We can measure the extension with a ruler. If we do this for a few different loads and record the numbers, we can plot a graph of load against extension. Most likely, we would find that the graph is a straight line.

For most materials, we would get a straight line, if the extension is not too big. This means that the extension is proportional to the force. This relation is called the Hooke's law. This law allows us to predict the extension e of the rod, if we know the force F. The relation is

F = ke.
(If we use x to denote the extension, then it is written as F = kx, which is quite common.)

The constant k is called the spring constant. Rearranging, we get k = F/e. So the spring constant is the force per unit extension. It is a number that depends on the material. If rods of the same size and shape are made from different materials, the spring constants are likely to be different, for different rods.

Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 2 October 2010.