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Chapter 9: Problem 1

Someone steps on your toe, exerting a force of \(500 \mathrm{N}\) on an area of \(1.0 \mathrm{cm}^{2} .\) What is the average pressure on that area in atm?

Short Answer

Expert verified
Express your answer in atmospheres (atm). Answer: The average pressure on the toe area is about 49.3 atm.

Step by step solution

01

Convert area to SI units (square meters, m²)

We need all values in SI units to perform calculations. Given area is in \(\mathrm{cm}^2\), let's convert it to \(\mathrm{m}^2\). We know that 1m = 100cm. Area in \(\mathrm{m}^2\) = Area in \(\mathrm{cm}^2\) × \((\frac{0.01\,\mathrm{m}}{1\,\mathrm{cm}})^2\) Area in \(\mathrm{m}^2\) = \(1.0\,\mathrm{cm}^2\) × \((\frac{0.01\,\mathrm{m}}{1\,\mathrm{cm}})^2\) = \(1.0 \times 10^{-4} \,\mathrm{m}^2\)
02

Calculate the pressure in Pascals (Pa)

Pressure (P) = Force (F) / Area (A) P = \(\frac{500\,\mathrm{N}}{1.0 \times 10^{-4}\,\mathrm{m}^2}\) = \(5000000\,\mathrm{Pa}\) or \(5 \times 10^6\,\mathrm{Pa}\)
03

Convert pressure from Pascals to atmospheres (atm)

To convert pressure from Pascals to atmospheres, we will use the following conversion factor: 1 atm = 101325 Pa. Pressure in atm = Pressure in Pa / 101325 Pressure in atm = \(\frac{5\times10^{6}\,\mathrm{Pa}}{101325\,\mathrm{Pa/atm}} \approx 49.3\,\mathrm{atm}\) So, the average pressure on that area is about 49.3 atm.

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