Hooke's Law
Overview
A spring force is proportional to extension: F = kx (restoring form: F = −kx). k = spring constant (N/m), x = extension from natural length. Stiffer springs have larger k. Hooke's Law holds only in the elastic region (below elastic limit). Beyond the elastic limit, the spring deforms permanently. Combining springs: in series — 1/k_total = 1/k₁ + 1/k₂ (k_total < either k); in parallel — k_total = k₁ + k₂ (k_total > either k). Hooke's Law leads directly to SHM (see oscillations).
Hooke's Law: the spring force
Hooke's Law: the force exerted by a spring is proportional to its extension (or compression): F = kx, where k is the spring constant (N/m) — a measure of stiffness — and x is the extension from the natural length. The graph of F vs x is a straight line through the origin with slope k. This is valid only up to the elastic limit; beyond that, the spring deforms permanently.
Springs in series and parallel
Springs in parallel (side by side, sharing the same extension): k_total = k₁ + k₂ (stiffer — they share the load). Springs in series (end to end, sharing the same force): 1/k_total = 1/k₁ + 1/k₂ (more flexible — each extends). A spring extends more when springs are in series and less when in parallel.
- ⚠Using extension in cm instead of metres in F = kx
- ⚠Confusing the restoring force (spring pulls back) with the applied force (weight pulls down) — they are equal and opposite at equilibrium
- ⚠Using Hooke's Law beyond the elastic limit