Question

What is the pressure exerted by weight of \[80{\text{ N}}\] on an area of $1.6{\text{ }}{{\text{m}}^2}$?

Answer 1

Hint: Pressure is the measure of force exerted on a unit area of a given body. Its unit is given as Newton per unit square meter. So, on substituting the given values of force and area in the formula, we can get the answer.

Formula used:
In this solution we will use the following formula for pressure. The pressure $P$ exerted by a force of $F$ units on an area of $A$ square units is given by $P = \dfrac{F}{A}$.

Complete step by step answer:
During some dynamic or static analysis, especially areas like fluid mechanics, hydrodynamics and aerodynamics, when we are not interested in the force exerted on the entire surface upon, we use the concept of pressure as a measure of the force on a unit area of that surface.

We will say that the pressure exerted on the surface is $x$ Pa or $x{\text{ N}}{{\text{m}}^{ - 2}}$ if the force which is assumed to be exerted uniformly throughout the surface per unit square meter, that is, the force exerted on $1{\text{ }}{{\text{m}}^2}$ of the surface is $x{\text{ N}}$. In cases where the force dos not encompass an area up to $1{\text{ }}{{\text{m}}^2}$, it is a measure of the how much force needed to make the same effect as the force has done to the smaller area.

The mathematical expression for the force is given as $P = \dfrac{F}{A}$ where $P$ is the pressure exerted on the surface of a body by the force, $F$ is the force exerted on the body and $A$ is the area of surface on which the force acts. In the question we have $F = 80{\text{ N}}$ and $A = 1.6{\text{ }}{{\text{m}}^2}$ so the pressure exerted by the weight is $P = \dfrac{{80{\text{ N}}}}{{1.6{\text{ }}{{\text{m}}^2}}}$
$\therefore P = 50{\text{ N}}{{\text{m}}^{ - 2}}$

Hence, the pressure exerted by a weight of \[80{\text{ N}}\] on an area of $1.6{\text{ }}{{\text{m}}^2}$ is $50{\text{ N}}{{\text{m}}^{ - 2}}$.

Note:It is common to get confused when the areas of both the weight and the body on which the weight exerts a pressure. Remember that by Newton’s third law, both the objects exert pressure on each other. We will use the area of that object on which the force causing the pressure is exerted rather than the area of the object which is exerting the pressure.