Question

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

Answer 1

Mass of the girl, $m=50kg$
Diameter of the heel, $d=1cm=0.01m$
Radius of the heel, $r=\frac{d}{2}=0.005m$
Area of the heel $=\pi r^2$
$=\pi \times (0.005{)}^2$
$=7.85\times {10}^{-5}{m}^2$
Force exerted by the heel on the floor:
$F=mg$
$=50\times 9.8$
$=490N$
Pressure exerted by the heel on the floor:
$P=\frac{Force}{Area}$
$=490/(7.85\times {10}^{-5})=6.24\times {10}^{6}N/m^2$
Therefore, the pressure exerted by the heel on the horizontal floor is $6.24\times {10}^{6}N/m^2$.