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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, m虏)

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 \(\mathrm{cm}^2\) 脳 \((\frac{0.01\,\mathrm{m}}{1\,\mathrm{cm}})^2\) Area in \(\mathrm{m}^2\) = \(1.0\,\mathrm{cm}^2\) 脳 \((\frac{0.01\,\mathrm{m}}{1\,\mathrm{cm}})^2\) = \(1.0 \times 10^{-4} \,\mathrm{m}^2\)
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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