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The pressure inside a tire is measured as [tex]\( 28.0 \, \text{pounds/inch}^2 \)[/tex]. What is its pressure in [tex]\(\text{newtons/centimeter}^2\)[/tex]?

1 pound [tex]\( = 4.45 \, \text{newtons} \)[/tex]
1 inch[tex]\(^2 = 6.45 \, \text{centimeters}^2\)[/tex]

Express the answer to the correct number of significant figures.

The pressure is [tex]\(\boxed{\,}\)[/tex] [tex]\(\frac{\text{newtons}}{\text{centimeter}^2}\)[/tex].



Answer :

GinnyAnswer
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].