Problem

Pressures inside the funnel of a tornado can be as low as 150 torr. If the pressure inside a house is 760 torr and the pressure outside is 150 torr, what is the net force on a $1.2 \mathrm{~m} \times 1.5 \mathrm{~m}$ window? i $\times 10^{4} \mathrm{~N}$

Solution

Step 1 :Given that the pressure inside the house is 760 torr and the pressure outside is 150 torr, we can calculate the pressure difference as \(760 \mathrm{~torr} - 150 \mathrm{~torr} = 610 \mathrm{~torr}\).

Step 2 :The area of the window is given as \(1.2 \mathrm{~m} \times 1.5 \mathrm{~m} = 1.8 \mathrm{~m}^2\).

Step 3 :However, the pressure is given in torr and needs to be converted to Pascals (Pa) for the calculation, since 1 torr = 133.322 Pa. Therefore, the pressure inside the house in Pa is \(760 \mathrm{~torr} \times 133.322 \mathrm{~Pa/torr} = 101324.72 \mathrm{~Pa}\) and the pressure outside in Pa is \(150 \mathrm{~torr} \times 133.322 \mathrm{~Pa/torr} = 19998.3 \mathrm{~Pa}\).

Step 4 :The pressure difference in Pa is therefore \(101324.72 \mathrm{~Pa} - 19998.3 \mathrm{~Pa} = 81326.42 \mathrm{~Pa}\).

Step 5 :We can now calculate the net force on the window using the formula for pressure difference, which is Force = Pressure difference * Area. Therefore, the net force is \(81326.42 \mathrm{~Pa} \times 1.8 \mathrm{~m}^2 = 146387.56 \mathrm{~N}\).

Step 6 :However, the question asks for the answer in the format of i × 10^4 N. Therefore, we need to convert this result to the required format. The net force on the window is therefore \(146387.56 \mathrm{~N} / 10^4 = 14.64 \times 10^4 \mathrm{~N}\).

Step 7 :Final Answer: The net force on the window is approximately \(\boxed{14.64 \times 10^{4} \mathrm{~N}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/16383/

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