Example 15.1 The Car Lift Problem A car lift is used in a service station, compr

Question

Example 15.1 The Car Lift ProblemA car lift is used in a service station, compressed air exerts a force on a small piston of circular cross-section having a radius of5.92cm. This pressure is transmitted by an incompressible liquid to a second piston of radius13.8cm.

What force must the compressed air exert to lift a car weighing12900N?

What air pressure will produce this force?

Consider the lift as a nonisolated system and show that the input energy transfer is equal in magnitude to the output energy transfer. StrategyThis problem is an application of Pascal's law -- the pressure on each piston is the same.
Solution Because the pressure exerted by the compressed air is transmitted undiminished throughout the liquid, we have the following expression.
F1=N


The air pressure that will produce this force is found below.
P=Pa


Consider the lift as a nonisolated system and show that the input energy transfer is equal in magnitude to the output energy transfer. (Do this on paper. Your instructor may ask you to turn in this work.)

You can investigate this situation further withInteractive Example 15.1.

Explanation / Answer

P1 = 3.6 atm = 3.6 * 1.01325 *10^5 Pa
=> F1 = P1* A1 = 3.6 * 1.01325 *10^5 * * (5.92*10^-2)2

=> F1 = 4350 .85 N

=> F2 = F1*A2/A1 = 4350.85 * * (13.8*10^-2)2/ * (5.92*10^-2)2 = 23642. 28 N

Height lifted = 1.52 m

=> displacement * * (5.92*10^-2)2 = 1.52 * * (13.8*10^-2)2

=> Displacement = 8.26 m

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