Answer:
Fm= 91.88 N
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)
[tex]\frac{F_{m} }{A_{m} } = \frac{F_{s} }{A_{s} }[/tex]
[tex]F_{m} = \frac{F_{s}*A_{m} }{A_{s}}[/tex]
[tex]F_{m} = \frac{(23520 N)*(\pi *(0.75)^{2})(cm^{2})}{(\pi *(12)^{2})(cm^{2})}[/tex]
[tex]F_{m} = (23520 N)*\frac{(0.75)^{2} }{(12)^{2} }[/tex]
Fm= 91.88 N
