Deformation

Elastic materials, and objects such as springs, change shape when a force is exerted on them:

  • stretching happens when the material or object is pulled
  • compression happens when the material or object is squashed

A change in shape like this is called deformation. In general, the greater the force exerted, the greater the amount of deformation. This is why an elastic band gets longer the harder you pull it, and why a rubber ball squashes more the harder you squeeze it.

Remember that if you pull or squeeze too hard, the object may not return to its original size and shape afterwards, and it may even snap. Until you reach this point, a special case called Hooke’s Law applies.

Hooke's Law

The extension of a material or a spring is its increase in length when pulled. Hooke’s Law says that the extension of an elastic object is directly proportional to the force applied to it. In other words:

  • if the force applied is doubled, the extension doubles
  • if no force is applied, there is no extension

You can investigate Hooke’s Law using a spring:

  1. hang the spring from a stand and clamp
  2. measure its length with a ruler
  3. hang an empty slotted mass carrier from the lower end and measure the new length of the spring
  4. keep adding more slotted masses, measuring the new length each time

For mass added, calculate the extension (new length – length at start). You can then plot a force-extension graph:

  • plot force on the vertical (y) axis
  • plot extension on the horizontal (x) axis

The graph should be a straight line that passes through the origin (0,0). The diagram shows an example of this.

Force-extension graph demonstrating Hooke's law. A straight line passes through the origin (0,0).A force-extension graph for a spring

Using Hooke's Law

In a force-extension graph:

  • the steeper the line, the stiffer the spring
  • the area under the line is the work done (energy needed) to stretch the spring.

Example

Question

Using the graph, calculate the work done to extend the spring from 0 m to 0.10 m.

The area under the line is a triangle:

area = ½ × base × height

= ½ × 0.10 × 5 = 0.25 J