Stretching rubber (non-linear extension)

How to find out how a rubber band stretches

Five steps, and the order matters: the very first measurement is the one every other number depends on.

1. 1Measure the original lengthMeasure the band's length with no force stretching it. This is your starting point for everything that follows.+
2. 2Add force in equal stepsIncrease the force in equal-sized steps — for example, by hanging equal masses on the band one at a time.+
3. 3Measure the new lengthAfter each increase in force, measure the band's new, stretched length.
4. 4Calculate the extensionExtension = stretched length − original length. Work it out after every step.+
5. 5Plot the graphPlot extension (up the side) against force in newtons (along the bottom). Then look at the shape: straight line or curve?

Predict, then check

Picture one rubber band's graph: force in newtons along the bottom, extension up the side. The line starts off steep, then gradually flattens.

Section A covers the first few newtons, where the line climbs steeply. Section B comes later, where the line has flattened out. In which section is the band easier to stretch?

What you need to know

• Forces can stretch or squash objects. Force is measured in newtons (N).
• An object is elastic if it returns to its original length when the stretching force is removed. A rubber band is elastic.
• extension = stretched length − original length
• A spring, up to a limit: equal increases in force give equal increases in extension, so its force–extension graph is a straight line through the origin (Hooke's Law).
• A rubber band: equal increases in force give different increases in extension, so its graph curves. Extension is not directly proportional to force for rubber.
• Extra stretch per newton tells you how easy a band is to stretch. Rubber's long, tangled molecular chains explain why it changes.

The big picture

Forces can change the shape of an object, and a rubber band shows this beautifully: pull it and it stretches, let go and it returns to its original length, so it is elastic. Its extension is how much longer it is than its original length. Unlike a spring, a rubber band's extension goes up by different amounts for equal increases in force, so its force–extension graph curves instead of being a straight line. The reason is inside the rubber: its long, tangled molecular chains straighten out first, and once they are nearly straight the band is much harder to stretch.

⚠ Watch out

Calling the stretched length the extension. The extension is only the extra bit, so always take away the original length — and take away the ORIGINAL length every time, not the length from the step before.

Memory hook

Slack first, stiff later. Pulling the tangles out of rubber's chains is easy; stretching chains that are already nearly straight is hard work.

Check yourself

Stretch a rubber band slowly between your fingers. Describe where it feels easy and where it feels hard, and say what the molecular chains are doing at each stage.