Question

The maximum gauge pressure in a hydraulic system is 15 atm. What is the largest mass that could be lifted by this system if the diameter of the piston is 65 cm

Answer 1

The maximum force that can be lifted by this system is 51,478.4 kg

Step-by-step explanation:

Given;

maximum gauge pressure of the hydraulic system, Hp = 15 atm = 1.52 x 10⁶ N/m²

diameter of the piston, d = 65 cm = 0.65 m

The maximum gauge pressure of the piston is given as;

`Hp = (F)/(A)`

Where;

F is the maximum force of the piston

A is the area of the piston

`A = \pi ((0.65)/(2) )^2\\\\A = 0.3319 \ m^2`

F = Hp x A

F = 1.52 x 10⁶N/m² x 0.3319m²

F = 504488 N

Force is given as;

F = mg

m = F/g

m = 504488/9.8

m = 51,478.4 kg

Therefore, the maximum force that can be lifted by this system is 51,478.4 kg