Question

A $50kg$ girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of $1.0cm$. What is the pressure exerted by the heel on the horizontal floor?

Answer 1

Step 1: Given Data

Mass of the girl $m=50kg$

Diameter of the heel $d=1.0cm=0.01m$

Let the acceleration due to gravity $g=9.8m/s^2$

Step 2: Formula Used

Force exerted by the girl on the heel must be equal to her weight.

$\therefore F=mg$

We know that radius $r=\frac{d}{2}$

$\therefore$Area of the heel $a={\mathrm{\pi r}}^2=\mathrm{\pi }{\left(\frac{\mathrm{d}}{2}\right)}^2$

Hence, the pressure is given as

$P=\frac{F}{A}$

Step 3: Calculate the Pressure

Upon substituting the values we get,

$P=\frac{4mg}{{\mathrm{\pi d}}^2}$

$=\frac{4\times 50\times 9.8}{3.14\times 0.{01}^2}$

$=6.24\times {10}^{6}Pa$

Hence, the pressure exerted by the heel on the horizontal floor is $6.24\times {10}^{6}Pa$.