Questions: Convert the pressure 578 N / km^2 to pascals (Pa). Recall that 1 Pa=1 N / m^2.

Transcript text: Convert the pressure $578 \mathrm{~N} / \mathrm{km}^{2}$ to pascals (Pa). Recall that $1 \mathrm{~Pa}=1 \mathrm{~N} / \mathrm{m}^{2}$.

Solution

Solution Steps

Step 1: Understand the Units

Identify the given units and the units to which you need to convert. The given pressure is in $ \mathrm{N} / \mathrm{km}^{2} $ and needs to be converted to pascals ($ \mathrm{Pa} $), where $ 1 \, \mathrm{Pa} = 1 \, \mathrm{N} / \mathrm{m}^{2} $.

Step 2: Convert Square Kilometers to Square Meters

Recognize that $ 1 \, \mathrm{km} = 1000 \, \mathrm{m} $. Therefore, $ 1 \, \mathrm{km}^{2} = (1000 \, \mathrm{m})^2 = 1,000,000 \, \mathrm{m}^{2} $.

Step 3: Apply the Conversion Factor

Use the conversion factor to convert the pressure from $ \mathrm{N} / \mathrm{km}^{2} $ to $ \mathrm{N} / \mathrm{m}^{2} $ (pascals). Multiply the given pressure by the conversion factor: \[ 578 \, \mathrm{N} / \mathrm{km}^{2} \times \frac{1 \, \mathrm{km}^{2}}{1,000,000 \, \mathrm{m}^{2}} = 578 \times 10^{-6} \, \mathrm{N} / \mathrm{m}^{2} \]

Step 4: Simplify the Expression

Calculate the result: \[ 578 \times 10^{-6} = 0.000578 \, \mathrm{Pa} \]