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Chapter 1: Problem 39

In a user's manual accompanying an American-made automobile, a typical gauge pressure for optimal performance of automobile tires is $32 \mathrm{lb} / \mathrm{in} .^{2} .$ What is this pressure in grams per square centimeter and kilograms per square meter?

Short Answer

Expert verified
The pressure in grams per square cm is 3.22 g/cm^2 and in kilograms per square meter is 322. Tracy kg/m^2 respectively.

Step by step solution

01

Conversion from lb/in^2 to g/cm^2

To convert from lb/in^2 to g/cm^2, First convert lb to g. Multiply the given value 32 lb / in^2 by 453.59237 g/lb. Then, convert in^2 to cm^2. The square of an inch is 6.45 cm^2. Divide the earlier determined value by 6.45 to get the value in g/cm^2.
02

Conversion from g/cm^2 to kg/m^2

We convert g/cm^2 to kg/m^2. First, convert grams to kilograms. Since 1 g is equal to 0.001 kg, Multiply the prior step's result by 0.001. Then convert cm^2 to m^2. Since 1 cm is equal to 0.01 m, we have to square this to convert cm^2 to m^2. So multiply the obtained value in kg/cm^2 by 10000 (since (0.01)^2 is 0.0001, hence the value should be multiplied by 1/0.0001 = 10000 to convert cm^2 to m^2).
03

Final answer

The final answers then are the pressures in grams per square centimeter (g/cm^2) and kilograms per square meter (kg/m^2).

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