Elasticity

📋 Teacher notes

• •Hooke's law: extension is directly proportional to the applied force, e ∝ F, i.e. F = ke — but only up to the ELASTIC LIMIT.
• •Beyond the elastic limit the spring deforms PERMANENTLY: it will not return to its natural length when the load is removed, and F = ke no longer applies.
• •The spring constant k (N/m) measures stiffness: a bigger k means a stiffer spring that stretches less for the same force.
• •Energy stored in a stretched (or compressed) spring: E = ½Fe = ½ke² — the area under a force–extension graph, used in catapults, archery bows, and pogo sticks.
• •Springs in series share the load but each stretches independently (softer overall); springs in parallel share the extension (stiffer overall) — a nice follow-up demonstration.