Which of the following formulas
correctly shows the relationship between an applied force, the pressure that the
force produces, and the area on which the force acts?
Okay, so let’s first imagine that
we’ve got this surface which has an area, which we’ll call 𝐴. And on this surface with area 𝐴,
we exert a force, which we will call 𝐹. Now, in a situation like this, the
pressure exerted by this force on this area is defined as the force exerted per unit
area. Or in other words, the pressure
exerted is equal to the force exerted on the area divided by the area itself. This is because the equation then
gives us the amount of force exerted for every single unit of area that we have.
In other words, if a force 𝐹 is
exerted over the total area 𝐴 and is distributed over the entire area, then that’s
equivalent to, let’s say, this being a unit of area and having a smaller force
exerted on that area. And that same smaller force is
exerted on every single unit of area, which is equivalent to this large force 𝐹
being exerted on the whole area 𝐴. So this equation gives us the
definition of pressure. And out of all the options A to E,
we can say that it matches with option E.
Therefore, our final answer is that
the pressure produced by the force is equal to that force divided by the area over
which that force is distributed.