In a car lift used in a service station, compressed air exerts a force on a smal
ID: 1459701 • Letter: I
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 = 4.95 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius 15.3 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
A hydraulic lift has pistons with diameters 8.45 cm and 37.0 cm, respectively. If a force of 825 N is exerted at the input (smaller) piston, what maximum mass can be lifted at the output piston?
m = kg
Explanation / Answer
a) Use Pascal’s law,
F1/A1=F2/A2
F1/r1^2 = F2/r2^2
F1/r1^2 = F2/r2^2
F2= (r2^2/R1^2)*F1
F2= (0.153^2/0.0495^2)*13300 = 127064.5 N
b) P= F2/A2 = F2/r2^2 = (127064.5)/(3.14*0.153^2) = 17.3 *10^5 Nm/s^2 = 17.3 Pa
c) r1=8.45/2 = 4.225 cm = 0.04225m , r2= 37/2 = 18.5 cm = 0.185 m , F1=825 N
Use Pascal’s law,
F1/A1=F2/A2
F1/r1^2 = F2/r2^2
F1/r1^2 = F2/r2^2
F2= (r2^2/R1^2)*F1
F2= (0.185^2/0.04225^2)*825 = 15817.7 N