Question

Aryan whose mass is 70 kg is on a summer trip to goa. The cross-sectional area of Aryan's foot is $70c{m}^2.$
a) What is the pressure under his feet.
b) Find the minimum area of his slippers so that his foot does not sink in the sand. The sand can withstand a pressure up to $25kN/m^2$.

Answer 1

a)
Pressure under Aryan's feet:
$P=\frac{F}{A}$
$P=\frac{mg}{A}$
$P=\frac{70\times 10}{2\times 70\times {10}^{-4}}$
$P=5\times {10}^{4}Pa$

b)
Now, we are given maximum pressure, $P^{\prime }=25kN/m^2$
Mass of slippers will be small and can be ignored.
$P^{\prime }=\frac{F}{A^{\prime }}$
$A^{\prime }=\frac{70\times 10}{25\times {10}^3}$
$A^{\prime }=280\times {10}^{-4}{m}^2=280c{m}^2$

Area of 1 slippers will be half of this,
$A^{\prime \prime }=140c{m}^2$