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?

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Solution

## Step 1: Given DataMass 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 UsedForce 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 PressureUpon substituting the values we get,$P=\frac{4mg}{{\mathrm{\pi d}}^{2}}$ $=\frac{4×50×9.8}{3.14×0.{01}^{2}}$ $=6.24×{10}^{6}Pa$Hence, the pressure exerted by the heel on the horizontal floor is $6.24×{10}^{6}Pa$.

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