Question

What is the relationship between pressure and the area of contact?

Answer 1

Hint: Pressure is a measure of the force exerted on a surface. When the force is more, the pressure is more and when the force is less, the pressure is less. The pressure is also related to the area of contact in such a way that both are inversely proportional to each other. The relationship between pressure and area of contact can be understood from various real-life situations.

Complete step by step answer:
Most of us would have wondered why the flat edge of a knife cannot be used to cut fruit. Some of us would also have wondered why we cannot walk quickly on snow or sand with spiked shoes or heeled sandals. Some of us, in our school days, would have felt that wearing bags with broader straps reduces the pain on our shoulders. The common reason for all these questions is one simple answer, pressure.
The pressure is defined as the force acting perpendicular to a unit surface area. It is represented by
$P=\dfrac{F}{A}$
where
$P$ are the pressure
$F$ is the normal force
$A$ is the area of the surface
Let this be equation 1.

As the definition says, if $A=1,P=F$.
This means that pressure is equal to the magnitude of the normal force acting on a unit surface area, in contact with the force. It is a scalar quantity and its SI unit is $pascal(Pa)$.
$1Pa$ is equal to the pressure exerted on a surface area of $1{{m}^{2}}$ due to a force of $1N$.
Sometimes, $pascal(Pa)$ is also represented as $N{{m}^{-2}}$ or $kg{{m}^{-1}}{{s}^{-2}}$.
From equation 1, it is clear that pressure is inversely proportional to the surface area of contact.
$P\propto \dfrac{1}{A}$
Hence, when the area of contact decreases, pressure increases. At the same time, when the area of contact increases, pressure decreases.
This explanation can be used to answer all the examples given above. The flat edge of a knife has a broader area when compared to the sharp edge of the knife. So, it is easy to cut a fruit using the sharp edge of a knife because the area of contact between the knife and the fruit is less and the pressure is more. If heeled sandals or spiked shoes are used to walk on sand or snow, the area of contact between the shoe/sandal and the snow/sand is very less. As pressure is inversely proportional to the area of contact, the pressure is more in this case. Due to high pressure, the shoes/sandal go deep inside the sand/snow and it becomes difficult to walk. In school bags, the straps are broadened so that the area of contact between the straps and the shoulders is more. When the area of contact is more, the pressure is less and children feel it easy to carry their school bags.

Note: Pressure is defined in terms of the normal force acting on an area. This means that the force should be acting perpendicular to the area of contact in order to define pressure. In all the examples mentioned above, it is clear that the forces are acting perpendicular to the surface area of contact.