Question

In a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm. The pressure is transmitted to a second piston with a diameter of 30.0 cm.

(A) How large of a force must the compressed air exert to lift a 1.33x10^4 N car?

(B) How much pressure is exerted by the compressed air?

Answer 1

A)

Using Pascals law,

F1/A1 = F2/A2

Given:

Radius of the piston in the compressed air side, r1 = 5 cm = 0.05 m

Area, A1 = πr12

Diameter of second piston, d2 = 30 cm = 0.30 m

Area, A1 = πr22

F2 = 1.33 x 104 N

F1/ πr12 = 1.33 x 104 / πr22

F1/0.052 = 1.33 x 104 /0.32

F1 = 3.69 x 102 N

The force that must the compressed air exert to lift the car, F1 = 3.69 x 102 N

B)

Pressure exerted by the compressed air, P = F1/A1 = F1/ πr12= 3.69 x 100/ 3.14 x 0.05x0.05

                                                                        P = 47006.4Pa

Pressure exerted by the compressed air, P = 47006.4 Pa