Hooke's Law — Stretch a Spring and Find Its Stiffness

In 1660 Robert Hooke found how springs behave and hid it in an anagram, later revealed as 'ut tensio, sic vis' — as the extension, so the force. The pull needed to stretch a spring is proportional to how far it stretches. You will measure that straight-line law yourself.

Hang a spring from a firm support with a ruler fixed vertically beside it. Note where the bottom of the unstretched spring sits — that is your zero. (A force meter, which is just a spring in a tube, works too and reads the force directly.)

Hang a known weight on the spring and read how far the bottom has dropped on the ruler — that is the extension. Add more weight, one step at a time, recording the mass and the extension each time. Take four or five readings. Do not overload it: if you stretch a spring too far it never springs back, and Hooke's law stops working (the 'elastic limit').

What your straight line means. (1) The slope of your force-versus-stretch line IS the stiffness k, measured in newtons per metre; a stiff spring gives a steep line. (2) The energy stored in a stretched spring grows as one-half k times the stretch squared — which is why a bow or a catapult stores so much punch at full draw. (3) The law only holds up to the elastic limit; beyond it the material deforms permanently, and this is exactly how engineers test the strength of metals. (4) Springs following Hooke's law are everywhere: bathroom and kitchen scales, car and train suspensions, mattresses and trampolines, the tiny hairspring that keeps a mechanical watch ticking, and — generalised into 'Young's modulus' — the stiffness of every beam and bridge. A mass bouncing on a spring is also the textbook model of every vibration in nature.