Question

What force (in N) must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2400 kg car (a large car) resting on the slave cylinder? The master cylinder has a 1.50 cm diameter, while the slave has a 24.0 cm diameter.

Answer 1

Fm= 91.88 N

Step-by-step explanation:

Pascal principle

The pressure acting on one side is transmitted to all the molecules of the liquid because the liquid is incompressible.

The pressure is definited like this:

P=F/A

Where:

P: Pressure in pascals (Pa)

F: Force acting in the area (N)

A : Area where the force acts (m²)

Pascal principle

Pm=Ps

Fm/ Am= Fs/ As Formula (1)

Where :

Pm : Pressure on the master piston

Ps : Pressure on the slave piston

Fm : Force on the master piston (N)

Fs: Force on the slave piston ((N)

Am: master piston area (m²)

As: slave piston area (m²)

Area Formula (A)

A= π*R²

R : piston radius

Calculation of the weight of the car (W)

W= m*g= 2400 kg*9.8m/s²= 23520 N

W = Fs

Data

Fs = 23520 N

Dm = 1.5 cm

Ds = 24 cm

Rm = 0.75 cm

Rs = 12 cm

Am = π*Rm² = π*(0.75)²

As = π*Rs² = π*(12)²

Force exerted on the master cylinder

We replace data in the formula (1)

`(F_(m) )/(A_(m) ) = (F_(s) )/(A_(s) )`

`F_(m)  = (F_(s)*A_(m)  )/(A_(s))`

`F_(m) = ((23520 N)*(\pi *(0.75)^(2))(cm^(2)))/((\pi *(12)^(2))(cm^(2)))`

`F_(m) = (23520 N)*((0.75)^(2) )/((12)^(2) )`

Fm= 91.88 N