In a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm. This pressure is transmitted to a second piston with a radius of 15.0 cm.

a. How large a force must the compressed air exert to lift a 1.33 * 10^4 N car?

b. what pressure produces this force? Neglect the weight of pistons.

### 1 Answer

In a hydraulic lift, the pressure in equals the pressure out.

P1 = P2

Pressure is force over area

P = F/A

a.

F2, the force out is 1.33e4 N

F1/A1 = F2/A2

F1 = (A1/A2)F2

A = (pi)r^2

(A1/A2) = 5^2 / 15^2 = 1/9

F1 = (1/9)F2 = (1.33e4)/9 = 1.48e3 N

b.

P1 = F1/A1 = 1.48e8 / ((pi)(0.05^2)) = 1.88e5 N/m^2 = 1.88e5 Pa

This pressure is approximately twice atmospheric pressure.