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

Question

Example 15.1 The Car Lift
Problem A car lift is used in a service station, compressed air exerts a force on a small piston of circular cross-section having a radius of 5.92 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius 13.8 cm.

What force must the compressed air exert to lift a car weighing 12900 N?
F1= 2373.96 N

What air pressure will produce this force?
F2=215616 Pa

What If? What if the maximum force that the compressed gas can produce is equivalent to 3.60 atm?
(a) What is the maximum weight of the car it can lift up?
W = N

(b) At this maximum output, if the vehicle needs to be lifted up 1.52 m, through what distance the small piston will be displaced?
y = m

Explanation / Answer

max pressure of the compressed air = 3.6 atm
1 atm = 101.3 Pa
=> max pressure = 364.68 Pa
( wt of car X g ) / 0.138^2 = 364.68

=> max wt of the car = 2.2 kg ( taking g = 9.8 m/s^2 )

vol of liquid falling from in one limb = vol of liq raising in the other

13.8 ^2 X 1.52 = 5.92^2 X height

height = 8.26 mts

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