Forces and extension

Extension happens when an object increases in length, and compression happens when it decreases in length. The extension of an elastic object, such as a spring, is described by Hooke's law:

force exerted by a spring = extension × spring constant

This is when:

  • force is measured in newtons (N)
  • spring constant is measured in newtons per metre (N/m)
  • extension is measured in metres (m)

Example

A force of 3 N is applied to a spring. The spring stretches reversibly (elastic deformation) by 0.15 m. Calculate the spring constant.

First, rearrange force = spring constant × extension to find spring constant:

spring~constant = \frac{force}{extension}

spring~constant = 20~N/m

Elastic limit

The spring constant is different for different elastic objects. For a given spring and other elastic objects, the extension is directly proportional to the force applied. For example, if the force is doubled, the extension doubles.

This works until the elastic limit is exceeded. When an elastic object is stretched beyond its elastic limit, the object does not return to its original length when the force is removed. In this instance, the relationship between force and extension changes from being linear to being non-linear.

Non-linear extension occurs more in some materials than others. Materials like clay or putty usually show non-linear extension.

Force-extension graphs

Linear extension and elastic deformation can be seen below the elastic limit.

Non-linear extension and plastic deformation can be seen above the elastic limit. The gradient of a force-extension graph before the elastic limit is equal to the spring constant.

A force extension graph. Linear section drawn from origin to occupy half of graph area. Non linear section has decreasing gradient. Change from linear to non-linear is marked and labelled.