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Question 14.2: The Car Lift In a car lift used in a service station, compre...

The Car Lift

In a car lift used in a service station, compressed air exerts a force on a small piston that has a circular cross section of radius 5.00 cm. This pressure is transmitted by a liquid to a piston that has a radius of 15.0 cm.

(A) What force must the compressed air exert to lift a car weighing 13 300 N?

(B) What air pressure produces this force?

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(A) Conceptualize Review the material just discussed about Pascal’s law to understand the operation of a car lift.

Categorize This example is a substitution problem.

Solve F_1 / A_1=F_2 / A_2 for F_1 :

\begin{aligned}F_1 & =\left(\frac{A_1}{A_2}\right) F_2=\frac{\pi\left(5.00 \times 10^{-2}  m\right)^2}{\pi\left(15.0 \times 10^{-2}  m\right)^2}\left(1.33 \times 10^4  N\right) \\& =1.48 \times 10^3  N\end{aligned}

(B) Use Equation 14.1 to find the air pressure that produces this force:

P \equiv \frac{F}{A}     (14.1)

\begin{aligned}P & =\frac{F_1}{A_1}=\frac{1.48 \times 10^3  N}{\pi\left(5.00 \times 10^{-2}  m\right)^2} \\& =1.88 \times 10^5  Pa\end{aligned}

This pressure is approximately twice atmospheric pressure.

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