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.

Fm =181.16 N

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 =181.16 N

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