Hooke’s Law

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)


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.


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