# Force is determined by pressure and area

Physics Narrative for 11-14

## Calculating the force

So, if you hold your head under water you can detect the pressure of the surrounding water with your ears. (Your eardrum acts as a difference in pressure

detector. The bombarding water molecules exert a force on the exposed area of your ear drums. The air particles in your ear bombard the inside and also exert a force. The resultant of these two forces is what you feel.) The size of this force is given by a simple relationship: force = pressure × area.

You can always equalise the pressure

by holding your nose, keeping your mouth shut and exhaling, resulting in more particles bombarding the inside. You can probably adjust the pressure so the force acting on the inside and the force acting on the outside are identical, at least within the swimming pool.

Here's a precise way of writing it out, so that every term is just a number:

forcenewton = pressurenewton / metre^{2} × areametre^{2}

You can also write (making notes to yourself about the units) as force in newton = pressure in newton / metre^{2} × area in metre^{2}

The first form is more concise and precise, as each term reduces to just a number: number × unit divide by unit leaves just number.

(Remember that a physical quantity is a number × a unit.)

## Rearrangements

You can rearrange this to make pressure the subject of the formula, but the relationship is the same. You can write, rather fully, (making notes to yourself about the units):

pressure in newton / metre^{2} = force in newtonarea in metre^{2}

Or even express it rather concisely as:

pressure = forcearea

Most concisely, you could write:

*P* = *F**A*

You'll need to match the representation you choose to the classes you have, so as to allow them to understand the relationship.

In other words, a *big* pressure in the water will produce a *big* force acting over the exposed area of your ear drum. If the pressure is too big you may suffer a perforated ear drum due to the force acting.