Hooke’s law is basically a rule that shows the relationship between the Force of a spring and the extension of a spring. All springs have a spring constant (measure in Newtons per Metre or N/M) which tells us how many Newtons (or how much force) is needed to extend that spring ( or whatever material it is) by 1 Metre. So a spring with a spring constant of 10N/M will extend by 1 metre for every 10 Newtons of force. Remember that the extension of a spring is not the total final length of the stretched spring, but how many cm/m it has stretched by.

This relationship is shown with a formula of **F=kx **where** F = force applied (Newtons)**, **K = Spring Constant (N/m)**, and** x = the extension** of the spring (m or cm normally)

# F=kx

or rearrange to get

# k=F/x or x=F/k

In an exam question if they ask you to calculate the spring constant of a spring, they will give you a scenario for example:

Spring y is measured to be 2cm. When 2N is added the final measured length is 10cm. What is the spring constant?The extension is the final length minus the normal un-stretched length. So here x = 10 cm – 2 cm = 8cm = x. Using k=F/x k = 2N/8cm = 1/4 =

0.25N/cm(spring constant)

**The bigger the spring constant (k), the stiffer the spring**. This is because a bigger spring constant requires more Newtons/force to stretch the spring by the same amount (1 metre or centimetre).Therefore sometimes the spring constant can be referred to by the stiffness of the spring.