Hooke’s law — Physical education, 14–17 years
How the extension of a spring changes with the force pulling it, while the spring remains elastic.
The idea
For many springs, doubling the force doubles the extension, as long as the spring has not been stretched too far. This straight-line relationship is written F = kx: F is force, x is extension and k describes how stiff the spring is. A larger k means more force is needed for the same extension.
Why we need it
A spring does not simply feel “hard” or “soft”; its response can be measured and predicted. Hooke’s law grew from the need to design clocks, balances and machines that return to a known position. It turns a pull into a measurable extension, giving engineers a way to calculate forces without seeing them directly.
A worked example
A spring has k = 50 N/m and is stretched by 0.08 m. Use F = kx, so F = 50 × 0.08 = 4 N. If the spring is pulled by 6 N instead, its predicted extension is x = F/k = 6 ÷ 50 = 0.12 m, provided it remains within its elastic range.
The common trap
The usual mistake is to apply Hooke’s law to every stretch, even after the spring has passed its elastic limit. This feels reasonable because the spring still gets longer as the force increases. Beyond the limit, however, the graph is no longer a straight line and the spring may not return to its original length.
Outside school
Spring scales use a known spring to turn weight into a movement that can be read on a scale. Vehicle suspension uses springs to absorb bumps, although real suspension also includes damping. The same force–extension idea appears in some sensors that detect weight, movement or vibration.
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