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Hang a load on a spring and watch Hooke’s law in action: set the spring constant and the force, choose a single, series or parallel arrangement, and see the spring stretch to its extension next to a live force–extension graph — a straight line whose gradient is k and whose shaded area is the stored energy. It makes the relationships concrete: x = F⁄k, E = ½kx² = ½Fx, series springs are softer and parallel springs stiffer. Ideal Hooke’s-law model within the limit of proportionality.
Model: Hooke’s law F = k·x within the limit of proportionality, elastic PE E = ½kx² = ½Fx, with series (1/k = 1/k₁ + 1/k₂) and parallel (k = k₁ + k₂) spring combinations (CAIE 0625 §1.5 / IB A.2–A.3). Full stress–strain curves and material-specific data are out of scope. Values are computed in full precision and rounded for display. Educational tool — a guide for understanding, not a substitute for exam practice.
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Last updated: July 2026
Hooke’s law, the spring constant, elastic energy, and series vs parallel springs.
Hooke’s law states that the force applied to a spring is directly proportional to its extension, provided the limit of proportionality is not exceeded: F = k·x, where F is the force, x is the extension and k is the spring constant. On a force–extension graph this gives a straight line through the origin, and the simulator draws exactly that line as you change the load.
The spring constant k is the force needed to produce one metre of extension, measured in newtons per metre (N/m). It is the gradient of the force–extension line: a stiffer spring has a larger k and a steeper line, so it extends less for the same load. Rearranging Hooke’s law, the extension for a given force is x = F/k.
The elastic potential energy stored in a stretched spring is E = ½k·x², which is equal to ½F·x. Graphically it is the area under the force–extension line (a triangle of base x and height F), and the simulator shades that area so you can see the stored energy grow as the square of the extension. Doubling the extension therefore stores four times the energy.
Two springs in series (end to end) make a softer combination: the effective constant is k_eff = 1/(1/k₁ + 1/k₂), which is smaller than either spring, so the same load produces more extension. Two springs in parallel (side by side) make a stiffer combination: k_eff = k₁ + k₂, larger than either spring, so the load produces less extension. The mode selector lets you compare all three arrangements directly.
Up to the limit of proportionality the extension is proportional to the force and Hooke’s law holds. Beyond it the force–extension line curves — the spring extends more per unit force and may be permanently (plastically) deformed. The optional elastic-limit demo shows this non-linear region clearly. Full stress–strain curves and material-specific data are deliberately out of scope; the tool keeps to the clean, examinable Hooke’s-law region.
Spring questions reward a clear method — read the gradient off a force–extension graph for k, use x = F/k for extensions, and ½k·x² for stored energy. A GetYourTutors physics specialist who comes to your home in Dubai can work through past-paper force–extension and energy questions with your child, connect the graph to the equations, and clear up the common mix-up between force, extension and stored energy.