In a car lift used in a service station, compressed air exerts a force on a smal

Question

In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross section having a radius of r1 = 5.45 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius 13.6 cm.

(a) What force must the compressed air exert on the small piston in order to lift a car weighing 13,300 N? Neglect the weights of the pistons.
? N

(b) What air pressure will produce a force of that magnitude?
? Pa

(c) Show that the work done by the input and output pistons is the same.

Please explain clearly, show your work, & include a free body diagram

Explanation / Answer

Here ,

r1 = 5.45 cm

r2 = 13.6 cm

a) force , F = 13300 N

let the force on second F2

F2/(pi * r1^2) = F1/(pi * r2^2)

F2/(pi * 5.45^2) = 13300/(pi * 13.6^2)

F2 = 2135 N

the force must the compressed air exerting os 2135 N

b)

let the air pressure is P

P * pi * (0.136)^2 = force

P * pi * (0.136)^2 = 2135

P = 36763 Pa

the pressure needed is 36763 Pa

c)

as the energy is conserved ,

the work done by input and output piston is the same

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