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

Name: Problem 3, Chapter 14: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2021-08-26T00:40:55-08:00
Duration: 3 min 50 s
Channel: Umar Sohail Qureshi
Description: 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 cm. (a) If the woman balances on one heel, what pressure does she exert on the floor? (b) Should the home- owner be concerned? Explain your answer.

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 cm. (a) If the woman balances on one heel, what pressure does she exert on the floor? (b) Should the home- owner be concerned? Explain your answer.

Key Concepts

Pressure

Pressure is defined as the force exerted per unit area. It is the ratio of the force applied to the surface area over which the force is distributed. Understanding pressure allows us to determine how much stress a given force places on a particular area, which is critical in applications ranging from engineering to everyday situations.

Force

Force, in this context, is the weight of the individual and is computed by multiplying her mass by the acceleration due to gravity. This concept is key because the weight (a force) is what causes pressure when it is applied over a small contact area.

Area Calculation

Calculating the area over which the force is applied is crucial. For a circular contact area, the area is computed using the equation ?r². Accurately determining this area is essential in estimating the pressure, especially when the area is very small compared to the force applied.

Unit Conversion

Unit conversion ensures consistency in calculations. When dimensions are given in one unit (such as centimeters), they often need to be converted to SI units (meters) to accurately perform calculations involving physical quantities like area and pressure. This is a fundamental step in many physics and engineering problems.

Material Stress and Damage

This concept involves understanding how much pressure a material or surface can withstand before it deforms or is damaged. In the context of floor materials, comparing the calculated pressure to the material's tolerance helps determine whether the applied stress might cause damage, which is crucial in evaluating safety and durability.

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