Certainly! Let's solve the problem step-by-step.
Step 1: Understanding the given values
- The pressure is initially given as [tex]\( 28.0 \frac{\text{pounds}}{\text{inch}^2}\)[/tex].
- We need to convert this pressure into [tex]\(\frac{\text{newtons}}{\text{centimeter}^2}\)[/tex].
- The conversion factors are:
- [tex]\(1 \text{ pound} = 4.45 \text{ newtons}\)[/tex]
- [tex]\(1 \text{ inch}^2 = 6.45 \text{ centimeters}^2\)[/tex]
Step 2: Convert pounds to newtons
Since 1 pound is equivalent to 4.45 newtons, we convert the pressure from pounds to newtons:
[tex]\[
\text{Pressure in newtons per inch}^2 = 28.0 \frac{\text{pounds}}{\text{inch}^2} \times 4.45 \frac{\text{newtons}}{\text{pound}} \\
= 124.6 \frac{\text{newtons}}{\text{inch}^2}
\][/tex]
Step 3: Convert inch[tex]\(^2\)[/tex] to centimeter[tex]\(^2\)[/tex]
Since 1 inch[tex]\(^2\)[/tex] is equivalent to 6.45 centimeters[tex]\(^2\)[/tex], we convert the area from inch[tex]\(^2\)[/tex] to centimeter[tex]\(^2\)[/tex]:
[tex]\[
\text{Pressure in newtons per centimeter}^2 = \frac{124.6 \frac{\text{newtons}}{\text{inch}^2}}{6.45 \frac{\text{centimeter}^2}{\text{inch}^2}} \\
= 19.318 \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
Step 4: Express the answer with the correct number of significant figures
The given pressure [tex]\(28.0 \frac{\text{pounds}}{\text{inch}^2}\)[/tex] has three significant figures, so we express our final answer in three significant figures:
[tex]\[
= 19.3 \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
The pressure is [tex]\( 19.3 \frac{\text{newtons}}{\text{centimeter}^2} \)[/tex].
