A 50.0 -kg woman wearing high-heeled shoes is invited into a...

A 50.0 -kg woman wearing high-heeled shoes is invited into a home in which the kitchen has vinyl floor covering. The heel on each shoe is circular and has a radius of $0.500 \mathrm{cm} .$ (a) If the woman balances on one heel, what pressure does she exert on the floor? (b) Should the homeowner be concerned? Explain your answer.

Key Concepts

Material Strength and Stress Concentration

Understanding the pressure exerted on a surface helps in evaluating whether the material can withstand the applied force without damage. High pressure due to a small contact area can lead to stress concentration, potentially exceeding the strength of the material, which is a critical consideration in assessing safety and material durability.

Unit Conversion

Unit conversion plays a key role in ensuring that all measurements are in consistent units, especially in physics problems. For instance, converting the radius from centimeters to meters is important when calculating the area in square meters, which is required for standard SI units in pressure calculations.

Area Calculation for Circular Surfaces

When the contact area is circular, its area is calculated using the formula A = ?r^2, where r is the radius of the circle. This calculation is crucial because it determines how the force is spread out across the surface, which in turn affects the pressure exerted on that surface.

Pressure

Pressure is defined as the force applied per unit area. It represents how the force is distributed over the contact surface. In physics, pressure is calculated as the force (often weight) divided by the area over which the force is applied. This concept is essential for understanding how even a relatively small force can create a high pressure if applied over a small area.

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