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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
Read stored energy off the graph area, price the loop as lost heat, and spend the rest as launch speed.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.