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Chapter 2: Problem 190

The recommended tire pressure in a bicycle is 125 pounds \(/ \mathrm{in}^{2}\). What is this tire pressure in atmospheres? \(\left(1 \mathrm{~atm}=14.70\right.\) pounds \(\left./ \mathrm{in} .^{2}\right)\)

Short Answer

Expert verified
The recommended tire pressure in the bicycle is 125 psi. To convert this to atmospheres, use the conversion factor: \(1~\text{atm} = 14.7~\text{psi}\). The tire pressure in atmospheres can be found using the equation: \(\text{Pressure (atm)} = \frac{\text{Pressure (psi)}}{\text{Conversion factor (1 atm in psi)}} = \frac{125}{14.7} = 8.50~\text{atm}\).

Step by step solution

01

Write the given information

The recommended tire pressure in the bicycle is given in psi and is 125 psi. The conversion factor is 1 atm = 14.7 psi.
02

Write the conversion equation

In order to convert tire pressure from psi to atm, we can use the equation: \[ \text{Pressure (atm)} = \frac{\text{Pressure (psi)}}{\text{Conversion factor (1 atm in psi)}} \]
03

Substitute the given values

Replace Pressure (psi) with 125 and the Conversion factor with 14.7 in the equation from Step 2: \[ \text{Pressure (atm)} = \frac{125}{14.7} \]
04

Calculate the tire pressure in atm

Divide 125 by 14.7: \[ \text{Pressure (atm)} = 8.50 \]
05

Write the final answer

The tire pressure in atmospheres is 8.50 atm.

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