The sole of a man's size-10 shoe is around 11.0 in. by 4.00...

The sole of a man's size-10 shoe is around $11.0$ in. by $4.00$ in. Determine the gauge pressure under the feet of a 200-lb man standing upright. Give your answer in both lb/in. $^{2}$ and Pa. [Hint: $1.00 \mathrm{lb} / \mathrm{in}^{2}=6895 \mathrm{~Pa}$. Check your work using $1.00 \mathrm{in} .^{2}=6.45 \times$ $10^{-4} \mathrm{~m}^{2}$ and $\left.1.00 \mathrm{lb}=4.448 \mathrm{~N} .\right]$

The sole of a man's size-10 shoe is around $11.0$ in. by $4.00$ in. Determine the gauge pressure under the feet of a 200-lb man standing upright. Give your answer in both lb/in. $^{2}$ and Pa. [Hint:
$1.00 \mathrm{lb} / \mathrm{in}^{2}=6895 \mathrm{~Pa}$. Check your work using $1.00 \mathrm{in} .^{2}=6.45 \times$
$10^{-4} \mathrm{~m}^{2}$ and $\left.1.00 \mathrm{lb}=4.448 \mathrm{~N} .\right]$

Key Concepts

Pressure

Pressure is a measure of force exerted per unit area. In mechanics and fluid dynamics, it is defined as the force (in units such as pounds or newtons) distributed over an area (in square inches or square meters). This concept is central in understanding how forces act on surfaces, such as how a person’s weight is distributed over the soles of their shoes.

Gauge Pressure

Gauge pressure refers to the pressure measured relative to the ambient atmospheric pressure. Unlike absolute pressure, which includes atmospheric pressure, gauge pressure indicates how much the pressure in a system exceeds or falls below the atmospheric pressure, making it crucial in contexts where only the excess pressure is of interest, such as the pressure on the soles of shoes when standing.

Area Calculation

Area calculation involves determining the surface area over which a force is distributed. For rectangular shapes, the area is found by multiplying the length by the width. This concept is applied when calculating the pressure under a shoe by determining the contact area between the shoe sole and the ground.

Unit Conversion

Unit conversion is the process of converting quantities from one set of units to another, ensuring consistency and accuracy in calculations. In problems involving pressure, it is important to convert measurements from non-SI units (such as lb/in²) to SI units (such as Pascals) using appropriate conversion factors, which allows for standardized comparisons and calculations.

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