Elastic Potential Energy

Teaching Notes

Hooke's Law

Within the elastic limit, the extension of a spring is proportional to the applied force:

F = ke

F = force (N) · k = spring constant (N/m) · e = extension (m)

Elastic Potential Energy

Work done stretching the spring stores elastic PE. The area under the F–e graph (a triangle) gives the energy:

E_e = ½ke²

E_e = elastic PE (J) · k = spring constant (N/m) · e = extension (m)

AQA notation: use e for extension, not x. This formula appears on the AQA equation sheet.

Quadratic Relationship (e²)

Extension	e² factor	Energy
×2	2² = 4	4× energy
×3	3² = 9	9× energy
×4	4² = 16	16× energy

Elastic Limit

Beyond the elastic limit the spring is permanently deformed and does not return to its natural length. Hooke's Law and E_e = ½ke² only apply within the elastic limit.

Force–Extension Graph

The F–e graph is a straight line through the origin (gradient = k). The triangular area beneath it = ½ × e × ke = ½ke².

💡 AQA GCSE: Use e for extension (not x). E_e = ½ke² is on the equation sheet. g = 10 N/kg. Double extension → four times the energy.