Question

Explain the relation between the area of contact and pressure exerted on a body.

Answer 1

Hint: Think of why it is more comfortable to sleep on a mattress than on bare floor in terms of pressure exerted and the area of contact between your body and the mattress. How would you justify being able to lie flat on sand without sinking whereas standing on your feet would make you sink faster? Is it just your weight, or your area of contact, or both?

Complete answer:
The interdependency between area and pressure can be easily understood using everyday practical applications.
For example, a sharp knife has a lesser surface area but cuts better than a blunt knife. This is because the sharp knife exerts more pressure on the object due to less area of contact between them. However, the area of contact between a blunt knife and the object is larger and the weight(pressure) that we exert on the knife will get evened out over this area and will be less impacting.
Another example, it is difficult for us to walk in desert sand because our feet sinks into it whereas a camel, which is much heavier than us, is able to walk through easily. This is because camels have broader feet. The body weight exerted by the camel gets distributed over the contact area, reducing the pressure of the camel’s weight on the sand.
Therefore, from just the examples, we can establish that pressure exerted on a body and its area of contact follow an inverse relation. And the pressure applied on a body is directly proportional to the force exerted on the body.
Physically, pressure can be defined as the force exerted by a body per unit area, i.e.,
$P = \dfrac{F}{A}$
Therefore, more pressure = more force and less contact area, and less pressure = less force and more contact area.

Note:
Remember that the magnitude of pressure depends on the “area of contact” with the object and not just the area of the object. Also, the force exerted contributes to the pressure incident on the object.