3.4.2—Elastic energy

The work done in stretching an elastic string or spring is stored as elastic potential energy: E=∫F dx. For a Hookean region, E=½Fx=½(λ/l)x².

Use the actual force–extension graph when the law changes or the string becomes slack. Extension is measured from natural length, and energy is a scalar even when the force direction changes.

A spring reaches 3.0 N at extension 0.06 m while remaining linear. Its stored energy is ½×3.0×0.06=0.090 J.

The energy is not Fx for a gradually applied load; that would be the rectangle, whereas the linear graph gives a triangle.