Cilindrii unei piese hidraulice au dimetrele 15cm și 150cm. De câte ori va fi multiplicată forța ce acționează asupra pistonului cu diametrul mai mic?

100 times

Explanation:

Question:

The cylinders of a hydraulic part are 15cm and 150cm in diameter. How many times will the force acting on the piston with the smaller diameter be multiplied?

Solution:

Smaller diameter = 15cm

Bigger diameter = 150cm

Using Pascal's principle

F/A = f/a

Pressure = Force/Area

Pressure on piston with bigger diameter = pressure on piston with smaller diameter

Let Pressure on piston with bigger diameter = P

P =F/A

pressure on piston with smaller diameter = p

p = f/a

F/A = f/a

F×a = f×A

F/f = A/a

Area = πr^2

F/f = [π×(150)^2]/ [π×(15)^2]

F/f = (150)^2/ (15)^2

F/f = 100

F = 100f

The force acting on the piston with the smaller diameter will be multiplied 100 times.