Answer:
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
[tex]Fm= \frac{F_{s}*A_{m} }{A_{s} }[/tex]
[tex]Fm = \frac{21560*\pi *(1.1)^{2}cm^{2} }{\pi*(12)^{2}cm^{2} }[/tex]
[tex]Fm = 21560* \frac{(1.1)^{2} }{(12)^{2} }[/tex]
Fm =181.16 N
