Question

A $60\text{kg}$ girl wearing high heel shoes balances on a single heel. The heel is circular with a radius 1 cm. What will be the pressure exerted by the heel on the horizontal floor?

• A. $1.87\times {10}^3$ pascal
• B. $1.78\times {10}^3$ pascal
• C. $1.87\times {10}^6$ pascal
• D. $1.78\times {10}^6$ pascal

Answer 1

Answer: (C)

Step 1: Given that:

The mass($m$ ) of the girl= $60kg$

The radius($r$ ) of the circular heel of the girl= $1cm=\frac{1}{100}cm=0.01m$

Step 2: Calculation of pressure exerted by the heel on the horizontal floor:

Pressure= $\frac{Force\left(F\right)}{Area\left(A\right)}$

Force applied by girl on the floor= Weight of the girl

Thus,

$F=mg$ =$60kg\times 9.8m{s}^{-2}=588N$

Where $g$ is the acceleration due to gravity.

Now,

Area of the heel of the girl= $\pi \times {\left(0.01m\right)}^2=0.0001\pi m^2$

$A=0.0001\times \frac{22}{7}{m}^2$

$A=\frac{0.0022}{7}{m}^2$

$A=\frac{22\times {10}^{-4}}{7}{m}^2$

Hence,

The pressure applied by the heel of the girl will be;

$P=\frac{588N}{\frac{22\times {10}^{-4}}{7}{m}^2}$

$P=\frac{588\times 7}{22\times {10}^{-4}}$

$P=\frac{4116}{22}\times {10}^4$

$P=187.1\times {10}^4$

$P=1.87\times {10}^{6}Pa$

Thus,

The pressure applied by the heel of the girl on the floor will be $1.87\times {10}^{6}Pa$