To find the area when a pressure of 4 torr is applied with a force of 400 Newtons, we can use the formula for pressure:
Pressure Formula
Pressure (P) is defined as the force (F) applied per unit area (A):
\[ P = \frac{F}{A} \]
Where:
- \( P \) = Pressure in torr
- \( F \) = Force in Newtons
- \( A \) = Area in square meters
Step 1: Convert Pressure to SI Units
Since 1 torr is approximately equal to 133.322 Pa (Pascals), we can convert 4 torr to Pascals:
\[
P = 4 \, \text{torr} \times 133.322 \, \text{Pa/torr} = 533.288 \, \text{Pa}
\]
Step 2: Rearranging the Formula
Now, we can rearrange the pressure formula to find the area:
\[
A = \frac{F}{P}
\]
Step 3: Substitute Values
Substituting the values of force and pressure into the rearranged formula:
\[
A = \frac{400 \, \text{N}}{533.288 \, \text{Pa}} \approx 0.749 \, \text{m}^2
\]
Step 4: Convert Area to cm²
To convert square meters to square centimeters, use the conversion factor \( 1 \, \text{m}^2 = 10,000 \, \text{cm}^2 \):
\[
A \approx 0.749 \, \text{m}^2 \times 10,000 \, \text{cm}^2/\text{m}^2 = 7490 \, \text{cm}^2
\]
Final Answer
Thus, the area is approximately:
7490 cm²