Elastic Potential Energy: Stretching a Spring
Simulation Description
This simulation models elastic potential energy stored in a spring, directly addressing AQA GCSE Physics Paper 1 (Energy topic). It demonstrates the relationship between extension, spring constant, and stored energy through Ee = ½ke², with interactive 3D manipulation and live calculation.
The scene shows a steel-coloured helical spring fixed at the left to a heavy wall mount with four visible bolts. A blue block sits at the right end of the spring, attached at the coil groove. The spring geometry rebuilds every frame — individual coils genuinely spread apart as the extension increases, rather than simply stretching a static mesh. A faint white vertical marker shows the natural length position, giving students a clear visual reference for zero extension.
The simulation has two modes:
In Static mode, students pull the block directly by clicking and dragging it rightward. The spring extends, the coils open out, and the block shifts from blue toward orange-red as energy is stored. A red force arrow appears at the block, scaling in length with the applied force (F = ke). When the block is released, the spring immediately restores to its natural length — showing that elastic potential energy is released when the deforming force is removed. Students can alternatively use the extension slider for precise control.
In Oscillate mode, the current extension is captured as the amplitude and the block is set in continuous simple harmonic motion. The equation card updates live throughout. A second amber energy bar appears alongside the elastic potential energy bar — kinetic energy Ek = ½k(A²−e²) — and students can watch the two bars exchange energy in real time: Ee peaks at maximum displacement (block at extremes), Ek peaks at zero displacement (block passing through the rest position), and the sum remains constant, demonstrating conservation of energy.
The equation card (top-right, always visible) shows all three quantities — Ee in joules, k in N/m, e in metres — and writes out the full calculation live: ½ × 40 × 0.35² = 2.450 J. It updates every frame, so students can read off the stored energy at any extension without doing arithmetic. The spring constant slider covers ten real-world values from 10 N/m (very soft, like a mattress spring) to 300 N/m (stiff, like a car suspension spring).
The energy bar panel (top-left, always visible) shows a green-to-cyan gradient bar for Ee that fills proportionally to the stored energy. Students can see that doubling the extension does not double the energy — it quadruples it — because e is squared in the formula.
Toggling 🏷 Labels adds the five-step GCSE causal chain (force applied → spring extends → energy stored → Ee = ½ke² → energy released when force removed) and shows the live extension value as a canvas overlay. Drag to orbit the scene from any angle; scroll or pinch to zoom.
Suggested Class Activity
“How Does Extension Affect Stored Energy?” — Investigating the ½ke² Relationship Suitable for: GCSE Physics Year 10/11 — Energy, elastic potential energy. 25–30 minutes.
Setup (2 min) Display the simulation with k = 40 N/m, mode = Static, labels off. Tell students: “This spring stores energy when you stretch it. Your job is to find the relationship between how far it stretches and how much energy is stored.”
Stage 1 — Prediction (3 min) Ask students to predict on mini whiteboards: “If I double the extension from 0.20 m to 0.40 m, what happens to the stored energy? Does it double, more than double, or less than double?” Take a show of hands. Most will predict it doubles.
Stage 2 — Data collection (7 min) Use the extension slider to set each extension precisely. Students read the Ee value from the equation card and record results:
| Extension e (m) | Ee (J) | What happened to Ee? |
|---|---|---|
| 0.10 | 0.200 | — |
| 0.20 | 0.800 | × 4 |
| 0.30 | 1.800 | × 9 |
| 0.40 | 3.200 | × 16 |
| 0.50 | 5.000 | × 25 |
Ask: “Extension doubled — what happened to Ee?” Target: it quadrupled. “Extension tripled — what happened?” Target: it multiplied by 9. Establish the pattern: Ee ∝ e². The energy grows with the square of the extension.
Stage 3 — Change the spring constant (5 min) Keep e = 0.30 m fixed. Change k using the slider through three values: 20, 40, 80 N/m. Students record Ee each time.
| k (N/m) | e (m) | Ee (J) |
|---|---|---|
| 20 | 0.30 | 0.900 |
| 40 | 0.30 | 1.800 |
| 80 | 0.30 | 3.600 |
Ask: “What happened to Ee when k doubled?” Target: Ee doubled. Establish: Ee ∝ k. The energy is directly proportional to the spring constant. Ask: “Which spring would be harder to stretch? Which stores more energy at the same extension?” Target: the stiffer spring — it takes more force and stores more energy.
Stage 4 — Oscillation and energy transfer (5 min) Set e = 0.40 m, k = 40 N/m. Switch to Oscillate. Ask students to watch the two energy bars and answer: “At which point in the oscillation is all the energy elastic potential energy? At which point is all the energy kinetic?” Target: all Ee at maximum displacement (extremes); all Ek at zero displacement (passing through rest position). Ask: “Does the total energy change during oscillation?” Target: no — it transfers between Ee and Ek but the total stays constant. This is conservation of energy.
Stage 5 — Written explanation (5 min) Toggle 🏷 Labels on. Use the step chip chain as a writing frame. Students answer: “A spring with a spring constant of 60 N/m is extended by 0.25 m. Calculate the elastic potential energy stored. Show your working.”
Strong answer: Ee = ½ × k × e² = ½ × 60 × 0.25² = ½ × 60 × 0.0625 = 1.875 J.
Adaptation notes
- For lower-confidence learners: leave the equation card visible throughout and work through Stage 2 as a class, reading values together rather than independently. The colour change from blue to orange-red gives a visual cue that more energy is stored without needing to read numbers
- For higher ability: ask why the formula contains e² and not e — connect to the area under a force-extension graph (F = ke, so work done = area of triangle = ½ × F × e = ½ × ke × e = ½ke²). This is the graphical derivation of the formula
- For SEND learners: extra-slow mode in the accessibility panel; the reading ruler supports equation card use; the energy bar gives a visual proxy for stored energy that does not require reading a number; dragging the block directly is more intuitive than using the slider for students who find abstract sliders difficult to interpret