--- title: "Elastic Strain Energy and Force-Extension Graphs" description: "The area under a force-extension graph is the work done stretching a sample, held as elastic strain energy while the material stays elastic. A loading curve that does not retrace on unloading shows en" canonical: https://lightmysky.com/learn/science/elastic-strain-energy-and-force-extension-graphs-mt_4WnFUmR13O source: https://lightmysky.com/learn/science/elastic-strain-energy-and-force-extension-graphs-mt_4WnFUmR13O.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Elastic Strain Energy and Force-Extension Graphs The area under a force-extension graph is the work done stretching a sample, held as elastic strain energy while the material stays elastic. A loading curve that does not retrace on unloading shows energy that never came back. Subject: Science · Area: Matter & Materials · Ages 17 to 18 Page: https://lightmysky.com/learn/science/elastic-strain-energy-and-force-extension-graphs-mt_4WnFUmR13O ## Ready when they can - Finds strain energy as the area under a force-extension line, and as half of F times x for a spring - Reads a loading and unloading pair of curves and states how much energy was not returned - Predicts the launch speed of an object fired by a stretched spring from the energy stored ## Lesson: Banking energy in a stretch Stretch a spring and you bank energy in it. The work you do becomes elastic strain energy. A force against extension graph shows it as the area below the curve. While the line runs straight from the origin, the area is a triangle: half the force times the extension. Load a band and unload it, and the curves refuse to match. The unloading line sits lower and encloses a loop. That loop is an energy receipt: its area equals the energy lost as heat each cycle. Gentle pulls on metal show almost no loop and spring fully back. **Example.** A spring pulled with 10 N to 0.2 m stores half times 10 times 0.2, which is 1 J. Let it fire a 0.5 kg ball with no other losses. Set 1 equal to half times 0.5 times v squared to get v equals 2 metres per second. Stored energy becomes launch speed. **Recap.** Read stored energy off the graph area, price the loop as lost heat, and spend the rest as launch speed. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Moments, Pressure & Hooke's Law](https://lightmysky.com/learn/science/moments-pressure-and-hookes-law-mt_vuNjYx3qOy) ## Opens up - [Simple Harmonic Motion: the Defining Relation and Its Graphs](https://lightmysky.com/learn/science/simple-harmonic-motion-the-defining-relation-and-its-graphs-mt_NTDayHkdfh) - [Stress, Strain and the Young Modulus](https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y)