To determine the area of the cross-section of a body in both square meters (m²) and square centimeters (cm²) when it exerts a force of 50 N and produces a pressure of 2000 Pa, we can follow these steps:
1. Understand the Given Values:
- Force (F) = 50 N (newtons)
- Pressure (P) = 2000 Pa (pascals)
2. Recall the Formula for Pressure:
The relationship between force, pressure, and area is given by:
[tex]\[
P = \frac{F}{A}
\][/tex]
Where:
- [tex]\(P\)[/tex] is the pressure in pascals (Pa)
- [tex]\(F\)[/tex] is the force in newtons (N)
- [tex]\(A\)[/tex] is the area in square meters (m²)
3. Rearrange the Formula to Solve for Area:
To find the area ([tex]\(A\)[/tex]), rearrange the formula:
[tex]\[
A = \frac{F}{P}
\][/tex]
4. Calculate the Area in Square Meters:
Substitute the given force and pressure values into the formula:
[tex]\[
A = \frac{50 \, \text{N}}{2000 \, \text{Pa}}
\][/tex]
Simplifying this gives:
[tex]\[
A = 0.025 \, \text{m}^2
\][/tex]
5. Convert the Area to Square Centimeters:
To convert the area from square meters to square centimeters, recall that:
[tex]\[
1 \, \text{m}^2 = 10,000 \, \text{cm}^2
\][/tex]
Therefore:
[tex]\[
A_{\text{cm}^2} = 0.025 \, \text{m}^2 \times 10,000 \, \text{cm}^2/\text{m}^2
\][/tex]
Simplifying this gives:
[tex]\[
A_{\text{cm}^2} = 250 \, \text{cm}^2
\][/tex]
6. Summary:
- The area of cross-section in square meters: [tex]\(0.025 \, \text{m}^2\)[/tex]
- The area of cross-section in square centimeters: [tex]\(250 \, \text{cm}^2\)[/tex]
These calculations show that the area of the cross-section of the body is 0.025 square meters or 250 square centimeters when exerting a force of 50 newtons and producing a pressure of 2000 pascals.
