To calculate the pressure exerted on the floor, we use the formula for pressure:

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

Where:

• $P$ is the pressure (in pascals, $Pa$).
• $F$ is the force exerted (in newtons, $N$).
• $A$ is the area (in square meters, $m^2$).

Step 1: Convert mass to force

The force exerted is the weight of the woman, which is calculated as:

$F = m \cdot g$

Where:

• $m = 67.0 \, \text{kg}$ (mass of the woman).
• $g = 9.81 \, \text{m/s}^2$ (acceleration due to gravity).

$F = 67.0 \cdot 9.81 = 656.67 \, \text{N}$

Step 2: Convert area to square meters

The area of the heel is given as $1.59 \, \text{cm}^2$. Convert this to square meters:

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

$A = 1.59 \cdot 10^{-4} \, \text{m}^2$

Step 3: Calculate pressure

Substitute $F$ and $A$ into the pressure formula:

$P = \frac{656.67}{1.59 \cdot 10^{-4}}$

$P = 4,129,559.75 \, \text{Pa}$

Final Answer:

The pressure exerted on the floor is approximately:

$P = 4.13 \, \text{MPa} \, (\text{megapascals})$

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Questions for further exploration:

1. How would the pressure change if the heel's area were halved?
2. What happens to the pressure if the woman's weight increases by 10%?
3. How does the pressure compare to the typical pressure exerted by a car tire on the ground?
4. What role does the material of the heel play in distributing the pressure?
5. How would the calculation differ if the heel's area was irregular?

Tip:

Always ensure unit conversions are consistent when working with physical quantities to avoid calculation errors.