Question

The weight of a man is $750\,N$. The total area of the soles of his shoes is \[250{\text{ }}c{m^2}\]. Find the pressure he applies on the floor
A. 30000 Pa
B. 150 Pa
C. 300 Pa
D. $3 \times {10^6}Pa$

Answer 1

Hint:We use a pressure formula to solve the problem here. The weight of an item is defined as the force exerted on it by gravity in science and engineering. The gravitational force exerted on the item is defined as a vector quantity in certain mainstream textbooks. Others describe weight as a scalar quantity, the gravitational force's magnitude.

Formula used:
${\text{Pressure = }}\dfrac{{{\text{Force}}}}{{{\text{Area}}}}$

Complete step by step answer:
The physical force exerted on an item is known as pressure. The force applied per unit area is perpendicular to the surface of the objects. F/A is the basic formula for pressure (Force per unit area). Pascals is the unit of pressure (Pa). Absolute, atmospheric, differential, and gauge pressures are examples of pressure types.

A finger may be pressed against a wall without leaving a permanent mark; nevertheless, the same finger pressing a thumbtack into the wall can readily harm the wall. Despite the fact that the force delivered to the surface is the same, the thumbtack exerts higher pressure due to the point's concentration of that force into a smaller area.

At every location, pressure is transferred to solid barriers or through arbitrary portions of fluid that are parallel to these limits or sections. Pressure, unlike stress, is defined as a scalar quantity. The force density is the negative gradient of pressure. Given, Force =750 N and area = $ = 250\;{\text{c}}{{\text{m}}^2} = 250 \times {10^{ - 4}}\;{{\text{m}}^2}$.
$\text{Pressure} = \dfrac{{{\text{ Force }}}}{{{\text{ Area }}}} \\
\text{Pressure} = \dfrac{{750}}{{250}} \times {10^4}\dfrac{{\text{N}}}{{{{\text{m}}^2}}}$
$\therefore P = 30,000\;{\text{Pa}}.$

Hence option A is correct.

Note: Here we have to convert cm to m for easy calculation. A knife is another example. When we try to cut with the flat edge, the force is dispersed across a wider surface area, resulting in less pressure and a failure to cut. Using the sharp edge, which has a smaller surface area, results in more pressure and hence a smoother cut. This is an illustration of how pressure may be used in the real world.