Stretchiness: for teachers

In general when materials are stretched they first go through a phase when the amount of stretch (the extension) depends on the load and when the load is removed they return to their original length. This is called elastic behaviour. At an atomic level this is explained as follows. Atoms and molecules attract one another and the load pulls them apart against this attraction but when removed, the attraction pulls the material back to its original length. In this phase, the extension depends on the original length of the material; the longer the unstretched length, the greater the extension - and also on the cross sectional area of the material – the greater the area the less the extension.

This can be expressed mathematically by the equation

e = Fl/EA

where e is the extension, F is the load, A is the cross sectional area, l is the unstretched length and E is a constant, called Young’s modulus, that differs for different materials. E is named after the 18^th century scientist, Thomas Young, who, as was common in his day, worked in other fields as well and was instrumental in establishing the wave theory of light.

Young’s modulus measures the stiffness, rather than the stretchiness, of a material. The larger its value, the less a material stretches for a given load. So steel (E = 207 GN/m²) stretches less for a given load than aluminium (E = 69 GN/m²).

As the load is increased, there comes a point where a material becomes permanently stretched; as the load is removed the material shrinks but not back to its original length. The point where this behaviour begins is called the elastic limit of the material. At a molecular level, layers of atoms (or molecules) have slid past one another and no longer slide back to their original positions.

Eventually with further increase in load, the material reaches its breaking load. This depends on the cross sectional area of the sample – the greater the area, the greater the breaking load. This is usually expressed as the breaking strain of the material - the breaking load divided by the cross-sectional area.

Springs, made of coiled wire, behave in a similar way to wires but in general, they require much smaller loads for a given extension (which is why they are often used for experiments on stretchiness in schools). Their properties depend not only on the material they are made from (and its dimensions) but also on how it is coiled.

For the purposes of the virtual laboratory, elastic behaviour only is modelled, ie the materials have been loaded within their elastic limits.

Scientists normally measure the load in Newtons (N), the length in metres, m, and the cross-sectional area in m². This gives units of Young’s modulus as N/m². The data for the material in the Virtual Laboratory are given in the Table.

*the elastic limit of glass is essentially the same as the tensile strength, which in turn is very dependent on the details such as the number of cracks in the surface of the sample.

Note G stands for giga (1 x 10⁹ or 1 billion) and M for mega (1 x 10⁶ or 1 million). 1 newton (1 N) is a unit of force approximately equivalent to a load of 0.1 kg (100 g), about the weight of an apple.

To do the experiment described in the virtual laboratory requires sophisticated apparatus. In order to get measurable extensions, a wire that is both long (perhaps 2 or 3 metres and very thin is required and a load close to the breaking load must be used. Even so the extensions are small and have to be measured with a micrometer. Breaking of the wire is a distinct possibility and can be a safety hazard.

National curriculum references

Click here to visit the National curriculum web site.

Key stage 1

Key stage 2

Key stage 3