Question

What force (in N) must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2200 kg car (a large car) resting on the slave cylinder? The master cylinder has a 2.20 cm diameter, while the slave has a 24.0 cm diameter.

Answer 1

Fm =181.16 N

Step-by-step explanation:

Pascal principle

The pressure acting on one side (master cylinder) is transmitted to all the molecules of the liquid ( slave cylinder) 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 cylinder (Pa)

Ps : Pressure on the slave cylinder (Pa)

Fp : Force on the master cylinder (N)

Fs: Force on the slave cylinder ((N)

Am: master cylinder area (m²)

As: slave cylinder area (m²)

Calculation of the weight of the car (W)

W= m*g= 2200 kg*9.8m/s²= 21560 N

W = Fs

Data

Fs= 21560 N

Dm = 2.20 cm : diameter of the master cylinder

Ds = 24 cm : diameter of the master slave

Calculation of the areas

A= π*R²

Where R is the radio of the cylinder, R = D/2

Rm = Dm/2 = 2.2/ 2 = 1.1 cm

Rs = Ds/2 = 24/2 = 12 cm

Am = π*Rm² = π*(1.1)² cm²

As = π*Rs² = π*(12)² cm²

Calculation of the force on the master cylinder

We apply the Formula (1)

Fm / Am= Fs / As

`Fm= (F_(s)*A_(m)  )/(A_(s) )`

`Fm = (21560*\pi *(1.1)^(2)cm^(2)  )/(\pi*(12)^(2)cm^(2)   )`

`Fm = 21560*  ((1.1)^(2) )/((12)^(2) )`

Fm =181.16 N