A $50 \;kg$ girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter $1.0 \;cm$. What is the pressure exerted by the heel on the horizontal floor ?
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Mass of the girl, $m=50 kg$
Diameter of the heel, $d=1 cm =0.01 m$ Radius of the heel, $r=d / 2=0.005 m$
Area of the heel $=\pi r^{2}=\pi(0.005)^{2}=7.85 \times 10^{-5} m ^{2}$
Force exerted by the heel on the floor:
$F=m g=50 \times 9.8=490 N$
Pressure exerted by the heel on the floor:
$P=\frac{\text { Force }}{\text { Area }}=\frac{490}{7.85 \times 10^{-5}}$
$=6.24 \times 10^{6} \;N m ^{-2}$
Therefore, the pressure exerted by the heel on the horizontal floor is $6.24 \times 10^{6} \,Nm ^{-2}$
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