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Chapter 10: Problem 15

A person weighing \(75 \mathrm{~kg}\) is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is \(5.0 \mathrm{~cm}^{2}\), calculate the pressure exerted on the underlying surface in (a) bars, \((\mathbf{b})\) atmospheres, and \((\mathbf{c})\) pounds per square inch.

Short Answer

Expert verified
The pressure exerted on the surface by the person weighing 75 kg standing on one foot of a three-legged stool is approximately \(14.715\) bars, \(14.52\) atmospheres, and \(213.37\) pounds per square inch.

Step by step solution

01

(Step 1: Calculate the weight of the person in Newtons)

The weight of the person is given in kg, so we will first need to convert it into a force in Newtons using the gravitational acceleration, g = 9.81 m/s². Weight (force) = mass × gravitational acceleration Weight (force) = 75 kg × 9.81 m/s² = 735.75 N
02

(Step 2: Calculate the contact area in square meters)

The contact area is given in square centimeters. To calculate pressure, we need this area in square meters: Area = 5.0 cm² × 1 m² / 10000 cm² = 5.0 × 10⁻⁴ m²
03

(Step 3: Calculate the pressure exerted on the surface)

We can now calculate the pressure exerted on the surface using the formula: Pressure = Force / Area Pressure = 735.75 N / 5.0 × 10⁻⁴ m² = 1.4715 × 10⁶ N/m² or Pa
04

(Step 4: Convert the pressure into bars)

To convert the pressure in Pascals (Pa) to bars, we can use the following conversion factor: 1 bar = 10⁵ Pa Pressure (bars) = Pressure (Pa) / 10⁵ Pressure (bars) = 1.4715 × 10⁶ Pa / 10⁵ = 14.715 bars
05

(Step 5: Convert the pressure into atmospheres)

To convert the pressure in Pascals (Pa) to atmospheres (atm), we can use the following conversion factor: 1 atm = 101325 Pa Pressure (atm) = Pressure (Pa) / 101325 Pressure (atm) = 1.4715 × 10⁶ Pa / 101325 = 14.52 atm
06

(Step 6: Convert the pressure into pounds per square inch (psi))

To convert the pressure in Pascals (Pa) to pounds per square inch (psi), we can use the following conversion factor: 1 psi = 6895 Pa Pressure (psi) = Pressure (Pa) / 6895 Pressure (psi) = 1.4715 × 10⁶ Pa / 6895 = 213.37 psi As a result, the pressure exerted on the surface by the person weighing 75 kg standing on one foot of a three-legged stool is (a) approximately 14.715 bars, (b) approximately 14.52 atmospheres, and (c) approximately 213.37 pounds per square inch.

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