Springs and Hooke’s law · Grade 12
When you stretch a spring, the extension is proportional to the force, up to a point called the limit of proportionality. This is Hooke’s law. Stretching or squashing something elastically stores energy in its elastic potential store.
Key facts
- Extension = stretched length − original length.
- Hooke’s law: F = kx, where k is the spring constant (N/m) and x is the extension in metres.
- Elastic deformation: returns to its original shape. Plastic (inelastic): stays deformed.
- On a force–extension graph, the straight part has gradient k (if force is on the y-axis).
- Elastic potential energy: E = ½kx² (= area under the force–extension line).
- Springs in series: 1/k = 1/(k₁) + 1/(k₂). In parallel: k = k₁ + k₂.