Hooke's law and springs — Physics, 14–17 years
For a spring or elastic material, stretching usually grows in step with the applied force—up to a limit. This gives a way to measure force and to predict when a material will stop returning to its shape.
Force and extension
Hooke's law says that, within the elastic limit, extension is proportional to force: F = kx. Here x is the change in length and k describes how stiff the spring is. A large k means more force is needed for each metre of extension.
Why springs need a law
Inventors needed reliable ways to make scales, clocks and suspension systems behave predictably. Testing showed that many springs respond in a straight-line pattern at first, but not forever. Hooke's law captures that useful region and also warns us that a spring can be stretched too far.
Finding the extension
A spring has k = 80 N/m and a 12 N force is attached. Start with F = kx. Rearrange: x = F/k = 12/80 = 0.15 m, or 15 cm. This answer is trustworthy only if 12 N lies within the spring's proportional, elastic range.
The common trap
The tempting mistake is to assume that doubling the force always doubles the extension. It is reasonable because the first measurements often do exactly that, but the spring eventually becomes permanently deformed or breaks. Check the graph or stated limit before using F = kx.
Where it is used
A spring balance measures weight because a known force produces a measurable extension. Car suspensions use springs to support the vehicle while allowing controlled movement, and some sensors turn tiny extensions into readings. These designs must stay within safe limits, since real materials are not perfectly ideal.
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