Questions: A bicycle tire pump has a piston with area 0.46 in^2. If a person exerts a force of 27 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump? psi

A bicycle tire pump has a piston with area 0.46 in^2. If a person exerts a force of 27 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump? psi
Transcript text: A bicycle tire pump has a piston with area $0.46 \mathrm{in}^{2}$. If a person exerts a force of 27 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump? $\square$ psi Need Help? Read it Submit Answer
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Solution

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Solution Steps

Step 1: Identify the Given Values

We are given:

  • The area of the piston, \( A = 0.46 \, \text{in}^2 \)
  • The force exerted on the piston, \( F = 27 \, \text{lb} \)
Step 2: Use the Pressure Formula

Pressure \( P \) is defined as the force \( F \) applied per unit area \( A \). The formula for pressure is: \[ P = \frac{F}{A} \]

Step 3: Substitute the Given Values into the Formula

Substitute \( F = 27 \, \text{lb} \) and \( A = 0.46 \, \text{in}^2 \) into the formula: \[ P = \frac{27 \, \text{lb}}{0.46 \, \text{in}^2} \]

Step 4: Calculate the Pressure

Perform the division to find the pressure: \[ P = \frac{27}{0.46} \approx 58.6957 \, \text{psi} \]

Step 5: Round to Four Significant Digits

Round the result to four significant digits: \[ P \approx 58.70 \, \text{psi} \]

Final Answer

\(\boxed{58.70 \, \text{psi}}\)

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