Question

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

Answer 1

Pressure

1. The force operating perpendicular to a unit surface area is known as pressure.
2. It is a scalar quantity and its SI unit is pascal $\left(Pa\right)$.
3. $1Pa$ is equal to the pressure exerted on a surface area of $1m^2$ due to a force of $1N$.
4. Sometimes, pascal $\left(Pa\right)$ is also represented as $N{m}^{-2}orkg{m}^{-1}{s}^{-2}$.
5. It is symbolized by $P=\frac{F}{A}.......\left(i\right)[whereP=pressure,F=normalforce,A=area]$

Relation between force and contact of area

From equation (i), it is clear that pressure is inversely proportional to the surface area of contact.

$P\propto \frac{1}{A}$

When the area of contact decreases, pressure increases. At the same time, when the area of contact increases, pressure decreases.

Applying this explanation to some of the situations

1. When compared to a knife's sharp edge, the flat edge has a larger surface area. Because the area of contact between the knife and the fruit is smaller and the pressure is higher, cutting fruit with the sharp edge of a knife is simple.
2. When walking on sand or snow in heeled sandals or spiked shoes, the area of contact between the shoe/sandal and the snow/sand is quite small. The pressure is higher in this scenario because the pressure is inversely proportional to the area of contact. Because of the tremendous pressure, the shoes/sandals sink deep into the sand/snow, making walking difficult.

Hence, when the area of contact decreases, pressure increases. At the same time, when the area of contact increases, pressure decreases.