Spring force

Click, click: you absent-mindedly play with your ballpoint pen. The tip snapping back every time is thanks to a tiny spring. Springs are everywhere: in your mattress, in every car's suspension, in a trampoline. And they all obey a remarkably simple law.

Hooke's law

If you pull on a spring, it stretches. The special thing: the stretch is proportional to the force. Twice the force means twice the stretch, three times the force three times the stretch. As a formula: F = D · s. Here F is the force in newtons, s the stretch, which we usually give in centimetres, and D the spring constant in the matching unit N/cm. If you plot the force upwards and the stretch to the right, you get a straight line through the origin.

The spring constant D

The spring constant D tells you how stiff a spring is. It is exactly the slope of the line in the force-stretch diagram: D = 3 N/cm means every centimetre of stretch takes 3 N. D is often given in N/m instead of N/cm, and then you put the stretch in metres. 3 N/cm becomes 300 N/m that way. A soft ballpoint pen spring has a small D, a stiff suspension spring a huge one. That's exactly what a spring scale is built on: it measures the stretch and uses D to turn it straight into a force.

Where springs hide

In your mattress, dozens of springs catch your weight, each giving way exactly as far as its spring constant allows. In a car's suspension, stiff springs swallow the potholes. And on a trampoline the stretched mat uses the stored energy to fling you back up. By the way, the law only holds up to the elastic limit: pull a spring beyond that limit and it stays deformed, and the nice straight line is gone.