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

Solution Steps

We are given:

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

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

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

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

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

Final Answer