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 ?

Question

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $ 7 \times 10^6 $ Pa, would be ________________________ mm$^3$. (Given bulk modulus of copper = $ 1.4 \times 10^{11} $ N m$^{-2}$)

Answer 1

Given Data

Parameter	Value
Girl's mass	50 kg
Heel diameter	1.0 cm = 0.01 m
$g$	9.8 m/s² (or 10 m/s² approx)

Pressure Formula

Pressure = force per unit area:

$$P = \frac{F}{A} = \frac{mg}{\text{heel area}}$$

Step-by-Step Calculation

Step 1: Force (weight)
$$F = mg = 50 \times 9.8 = 490 \, \text{N}$$

Step 2: Heel area (circular)
$$r = \frac{d}{2} = 0.005 \, \text{m}$$
$$A = \pi r^2 = 3.14 \times (0.005)^2 = 7.85 \times 10^{-5} \, \text{m}^2$$

Step 3: Pressure
$$P = \frac{490}{7.85 \times 10^{-5}} = 6.24 \times 10^6 \, \text{Pa}$$

Pressure on Floor

$P = \textbf{6.24 × 10⁶ Pa} = 6.24 \, \text{MPa}$

Comparisons

Situation	Pressure (MPa)
High heel (1 cm²)	6.24
Flat shoe (~200 cm²)	~0.025
Elephant foot	~0.5
Car tire	~0.2

Why High Heels Damage Floors

Tiny contact area → enormous pressure
6 MPa exceeds wood strength (~5 MPa)
Local deformation/crushing occurs