Calculating the Pressure Exerted by Stilettos

To calculate the pressure exerted by the stilettos worn by a woman while walking, we need to use the formula for pressure:

$$ P = \frac{F}{A} $$

where:

P is the pressure exerted (in Pascals, Pa)
F is the force exerted, which is the weight of the person (in Newtons, N)
A is the area of contact of the heel with the ground (in square meters, m²)

Step 1: Calculate the Force (Weight)

Assume an average weight for a woman to be approximately 70 kg. The force exerted due to gravity can be calculated using the formula:

$$ F = m \cdot g $$

where:

m is the mass of the woman (in kilograms, kg)
g is the acceleration due to gravity, approximately 9.8 m/s²

Substituting values:

$$ F = 70 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 686 \, \text{N} $$

Step 2: Estimate the Area of Contact

The contact area of a stiletto heel is typically quite small. For a common stiletto heel, the area is about 1 cm², which we need to convert to square meters:

$$ A = 1 \, \text{cm}^2 = 1 \times 10^{-4} \, \text{m}^2 $$

Step 3: Calculate the Pressure

Using the formula for pressure, we can now substitute the values of F and A:

$$ P = \frac{F}{A} = \frac{686 \, \text{N}}{1 \times 10^{-4} \, \text{m}^2} $$

Calculating this gives:

$$ P = 6,860,000 \, \text{Pa} \quad \text{or} \quad 6.86 \, \text{MPa} $$

Conclusion

The pressure exerted by the stilettos on the ground is approximately 6.86 MPa. This high pressure is why stilettos can easily damage soft surfaces like wood or carpet, as the force is concentrated over a very small area.