Question

The foot of an elephant has an area of 275 $c{m^2}$. If the mass of the elephant is 2200 kg, find the pressure exerted by the elephant on the ground ( g = 10$m{s^{ - 2}}$). If your answers x finds the value of $\dfrac{x}{{{{10}^5}}}$.

Answer 1

Hint Pressure is defined by us as the force which is perpendicular to the surface of an object per unit area over which the force that is exerted is distributed. With the help of this concept we can solve this question.

Complete step by step answer
We know that the area of one foot = 275 $c{m^2}$.
Now we can write that:
$275 \times {10^{ - 4}}{m^2}(\therefore 1c{m^2} = {10^{ - 4}}{m^2})$
But the total force is acting through the four legs. So, total area of the four feet (A), which is equal to: $4 \times 275 \times {10^{ - 4}}{m^2}$
The mass of the elephant (m) = 2200 kg
The value of g is given as 10 $m{s^{ - 2}}$.
The force exerted by the elephant is equal to the weight of the elephant.
$P = \dfrac{{mg}}{A}(\therefore F = W - mg)$
Substituting the values in the above equation, we get:
$P = \dfrac{{2200 \times 10}}{{4 \times 275 \times {{10}^{ - 4}}}} = \dfrac{{22 \times {{10}^3} \times {{10}^4}}}{{1100}}$
$= \dfrac{{22 \times {{10}^7}}}{{11 \times {{10}^2}}}$
P = $2 \times {10^5}Pa$

Therefore, the pressure exerted by the elephant is $2 \times {10^5}Pa$

Note We should know that the formula to find the pressure is Pressure (P) = Force (F) / Area (A). Pressure is also defined as a way to measure the potential system.