# Hooke's Law

#### Back to Different Types of Forces

## Description

This is a basic physics tutorial that is targeted at GCSE (grade 9 and grade 10) standard reviewing Hooke's Law and Springs. The video for this written tutorial is on its way.

## What is Hooke's Law?

Robert Hooke was an English physicist who first described elasticity. He identified that there is a relationship between force size (magnitude) and the amount of resultant deformation. Hooke's law tells us that the elastic deformation of a substance is proportional to the force that's applied to it. That is, the greater the force, the greater the elastic deformation.

Up until the elastic limit (or yield strength), this relationship is linear (as seen below).

Because the relationship is linear, we can say that the extension of the spring is proportional to the force applied to it.

### extension α force

Mathematically we can describe this as:

### F = k *x* e

Where:

**F**is the force measured in newtons (N),**k**is the spring constant, measured in Newtons per meter (N/m), and**e**is the extension, measured in metres (m).

The *spring constant* varies between different springs. It can be calculated by the gradient of Force-Extension graphs, as shown below. Just make sure you're always working with the right units and that *force* is on the *y*-axis and *extension* is on the *x*-axis.

Knowing this, have a look at the below graph, and work out the spring constant for each line - then roll your mouse over the graph for the answer.

##### The spring constants are 667 N/m, 454 N/m and 200 N/m.

## Hooke's Law and compression

Hooke's Law also applies to the compression of an elastic object; you simply need to change *e* to refer to the compression of the spring. NB: Some texts will use *x* instead of *e*. This is demonstrated with the hanging spring below.

The spring constant is calculated in the same fashion as above, however compression is measured instead of extension (mouse over the graph below for calculations).

##### The spring constant is 231 N/m.

Varying Forces The elastic deformation of a substance is proportional to the force that's applied to it. That is, the greater the force, the greater the elastic deformation (up until its yield or ultimate strength). As you roll your mouse over the image below, you'll note that a doubling in the forces applied in either direction (from +/- 10 N to +/- 20 N) results in a doubling in deformation (from 0.75 cm to 1.5 cm). img src="/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law1.png" onmouseover="this.src='/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law.png'" onmouseout="this.src='/content/1-physics/1-grade-9-10-gcse-hsc/2-forces/5-different-types-of-forces/1-contact-forces/3-deforming-forces/2-hooke-s-law/Hooke%27s-Law1.png'" br h2What is Hooke's Law?/h2 Robert Hooke was an English physicist who first described elasticity and the relationship described above between force magnitude and amount of deformation. You'll often hear this relationship described in terms of a spring. One of the most common ways to explore tension and compression is to study how these forces affect a spring. This is covered in the next tutorial.