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Chapter 10: Problem 15

Suppose that a woman weighing 130 \(\mathrm{lb}\) and wearing high- heeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is \(0.50 \mathrm{in.}^{2},\) calculate the pressure exerted on the underlying surface in (a) pounds per square inch, (b) kilopascals, and (c) atmospheres.

Short Answer

Expert verified
The pressure exerted by the woman wearing high-heeled shoes on the underlying surface is (a) 260 psi, (b) approximately 1793 kPa, and (c) approximately 17.7 atm.

Step by step solution

01

Find Pressure in Pounds per Square Inch (psi)

First, we'll find the pressure in the unit of pounds per square inch (psi). To do so, we use the formula: Pressure = Force / Area Given the woman's weight is 130 pounds, which is the force, and the heel area is 0.50 square inches, we can plug in these values: Pressure (psi) = Force (lbs) / Area (in²) = 130 lbs / 0.50 in² Now, we compute the pressure in psi.
02

Calculate Pressure in psi

Pressure (psi) = 130 lbs / 0.50 in² = 260 psi So, the pressure exerted on the underlying surface in pounds per square inch is 260 psi.
03

Convert Pressure to Kilopascals (kPa)

To convert the pressure from psi to kilopascals (kPa), we can use the conversion factor: 1 psi ≈ 6.895 kPa So, to convert 260 psi to kPa, we can simply multiply the pressure value by the conversion factor: Pressure (kPa) = 260 psi * 6.895 kPa/psi Now, we calculate the resulting pressure in kPa.
04

Calculate Pressure in kPa

Pressure (kPa) = 260 psi * 6.895 kPa/psi ≈ 1793 kPa The pressure exerted on the underlying surface is approximately 1793 kPa.
05

Convert Pressure to Atmospheres (atm)

Finally, we will convert the pressure from psi to atmospheres (atm). To do this, we'll use the conversion factor: 1 psi ≈ 0.06805 atm So, to convert 260 psi to atmospheres, we'll multiply the pressure value by the conversion factor: Pressure (atm) = 260 psi * 0.06805 atm/psi Now, we compute the pressure in atmospheres.
06

Calculate Pressure in atm

Pressure (atm) = 260 psi * 0.06805 atm/psi ≈ 17.7 atm The pressure exerted on the underlying surface is approximately 17.7 atmospheres. In summary, the pressure exerted by the woman wearing high-heeled shoes on the underlying surface is (a) 260 psi, (b) approximately 1793 kPa, and (c) approximately 17.7 atm.

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