Question

Q1.B) In a car lift used in a service station, compressed air exerts a force on a small piston that has a circular cross section and a diameter of 8.00 cm. This pressure is transmitted by a liquid to a piston that has a diameter of 16.0 cm. What force must the compressed air exert to lift a car weighing 1960 N? What is the air pressure produces this force?

Answer 1

Given:

(d1)diameter of small piston = 8cm

(d2)diameter of larger piston = 16cm

force due to car (F2)= 1960N

To Find:

force must be exerted to lift the car =?

air pressure produced this force =?

Solution:

From the given information, we can draw a rough diagram of the situation as shown below,

According to Pascal's law, pressure is equally transmitted through a fluid thus we lead to the conclusion

that P1 = P2

   $\dfrac{f1}{a1} = \dfrac{f2}{a2}$

f1  $= \dfrac{f2 \times a1}{a2}$

thus, (a1) area of small piston = π(r1)² = 3.14 × 0.08  × 0.08 = 0.020m²

(a2) area of larger piston = π(r2)² = 3.14 × 0.16  × 0.16 = 0.080m²

on putting values in above equation

f1 = $f1 = \dfrac{1960 \times 0.02}{0.08}$ = 490N

similarly, the pressure produces this force = F1/a1

= 490/0.02 = 24500 Pa

thus, force must be exerted to lift the car = 490 N

air pressure produced this force = 24500 Pa