10.5 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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Vishal Baghel | Contributor-Level 10

5 months ago

Mass of the girl, m = 50 kg

Diameter of the heel, d = 1.0 cm = 0.01 m, Radius of the heel, r = d/2 = 0.005m

Area of the heel, $π r^{2}$ = 7.85 $\times 10^{- 5}$ $m^{2}$

Force exerted by heel on the floor, F = mg = 50 $\times 9.8$ N = 490 N

Pressure exerted by heel on the ground, p = F/A = 490/ (7.85 $\times 10^{- 5})$ N/ $m^{2}$

= 6.24 $\times 10^{6}$ N/ $m^{2}$

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Since velocity does not change, so acceleration will be zero.

mg = FB + Fv $\Rightarrow \frac{4 π}{3} r^{3} ρ g = \frac{4 π}{3} r^{3} σ g + 6 π η r v$

$\Rightarrow v = \frac{2 r^{2} (ρ - σ) g}{9 η} = \frac{2 \times 0.1 \times 0.1 \times 1 0^{- 6} \times (1 0^{4} - 1 0^{3}) \times 10}{9 \times 1.0 \times 1 0^{- 5}}$

$\Rightarrow h = \frac{400}{2 g} = 20 m$

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10.5 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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