Question

In a car lift used in a service station, compressed air exerts a force on a small piston having a radius of 1.5 cm. This pressure is transmitted to a second piston of radius of 6.75 cm. What force must the compressed air exert in order to lift a car weighing 17,750 Newton’s? What air pressure will produce this force?

Answer 1

The forces and pistons' areas are connected as follows:

$$F_2 = \dfrac{F_1A_2}{A_1}$$

where $F_2, F_1 = 17750N$ are the forces exerted by the second and first pistons respectively, $A_2, A_1$ are their areas. Since areas are proportional to the radii squared ($r_1 = 1.5cm, r_2 = 6.75cm$), obtain:

$$F_2 = \dfrac{F_1r_2^2 }{r_1^2} = \dfrac{17750N\cdot (1.5cm)^2}{(6.45cm)^2} \approx 9.6\times 10^2N$$

Answer. $9.6\times 10^2N$.