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Hooke's Law

Elastic responseForce and extension remain proportional.
SPRING EXPERIMENTF = kx0102030cmnatural length0.0 cm1.0 kgspring forceweight, mgFORCE–EXTENSION GRAPHgradient = k = 50 N/mFx (0.5 m)Current point: 9.8 NELASTIC ENERGY STORED0.96 J
Hooke’s law
F=kx⇒x=mgk=0.2 mF = kx \Rightarrow x = \frac{mg}{k} = 0.2\,\text{m}
Extension19.6 cm
Load force9.8 N
Spring stiffness50 N/m
Energy stored0.96 J
Compare spring setups

The two arrows are equal at rest: the spring pulls upward with the same force that gravity pulls downward. The graph’s gradient is the spring constant, k. This is an ideal spring within its elastic limit; the settling animation is illustrative, not time-calibrated.

  • Produce an extension of about 10 cm
  • Keep the extension under 3 cm
  • Stretch the spring to about 20 cm
  • Reach a 15 cm extension using a spring constant of 120 N/m