But what about solids? Pressure and stress

What about solids?

The whole of this section so far has focused on pressure in liquids and gases. What about solids? The simple expression for pressure as force divided by area leads to a bit of a confusion.

Often teaching about pressure in schools starts with one solid resting on another. It might involve camels with big feet walking across the desert or stiletto heels being banned from the school hall. It could be that pupils measure their weight on bathroom scales, find the total area of the soles of their shoes and then calculate the pressure under each foot. These activities (and lots of others) are interesting and offer excellent opportunities for discussion with pupils. Unfortunately:

None of these activities involve pressure!

For camels with big feet, stilettos with sharp heels or snow shoes with big areas the forcearea being measured is not a pressure: It is properly called a stress. The key here is that stress is a vector and that it acts in a particular direction.

Stress is measured as forcearea (exactly the same units as pressure).

So:

• Stiletto heels make a mark on the school hall floor because the gravity force acting on the woman acts on a tiny area giving rise to a big stress.
• The camels' feet do not sink into the sand because the gravity force acting on the camel acts on a big surface area giving rise to a small stress.

In general, if a solid object is placed on a surface and the area of contact between them is small a large stress is produced and since there is a relatively small amount of material supporting the object it makes a deep impression on the surface. If a supporting material is known to be weak then it should be subjected to small stresses, which involves spreading the force over a larger area.

We strongly recommend that you teach these two ideas of pressure and stress separately and furthermore teach them in the order presented here with pressure and hydraulics first (thinking about liquids and gases) and stress very much later (thinking about solids). In fact stress often appears first in post-16 studies in physics.

Why does a drawing pin push into the notice board at the sharp end and not into your finger? This is easily explained in terms of stress: The same force (the same push from your finger) acts on both ends, so where the area is big (at the cap of the pin) the stress is reduced and where the area is tiny (at the point) the stress is much increased.

In similar ways we can also explain the action of stiletto heels and camels' feet.

These stress explanations become much more difficult where one of the surfaces is not a solid. So using large area tyres to move over mud or snowshoes to walk on snow are a little more complex than they seem to explain. A first explanation will be along the same lines as for solid-solid surfaces. But persistent questioning by a class can lead quickly into difficult territory caused by the materials in question (mud, snow, sand) being rather complex in their behaviour. For example, why is it that you can move cautiously over soft sand and mud, but will sink if you stay still for too long or if you try to run? These instances cannot easily be explained simply by talking of force and area.

Here's a more detailed microscopic explanation for what happens to an object (such as a heavy box or a human wearing a snowshoe) when it is placed on the surface of some snow. When the object is first placed on the snow the forces on the object are simple. There is a downwards gravitational force and a negligible upwards force due to the snow. As the object sinks, so it distorts the snow resulting in a net resistive force caused by the cohesive forces in the snow (these are the forces that hold snowballs together). The greater the distortion, the greater is the force. Eventually the resistive force will be equal to the gravitational force at which stage the object will stop accelerating down into the snow and typically stop moving as well. All this means that the more you distort the snow the less you will sink before stopping – so wear snow shoes!