Answer:
The force to be applied on the primary piston is 140.63 N.
Explanation:
To solve this problem we apply the following formulas:
Pascal principle: F=P*A Â Formula (1)
F=Force applied to the piston
P: Pressure
A= Piston area
[tex]A=\frac{\pi*d^{2} }{4}[/tex] Formula (2)
d= piston diameter
Nomenclature:
Fp= Force on the primary piston
Fs= Force on the secondary piston
Ap= Primary piston area
As= Secondary piston area
W= car weight
Calculation of the force Fp necessary to support the weight of the car.
Pascal principle: Fp=P*Ap (Equation1)
In (Equation1) we know Ap and we don't know P.
Pressure calculation:
We apply Newton's first law for a balanced Secondary piston -automobile system
Newton's first law: ∑F=0
W-Fs=0
W=Fs
W=P*As
[tex]P=\frac{W}{As}[/tex]
We replace [tex]P=\frac{W}{As}[/tex]in equation 1:
[tex]Fp=\frac{W}{As} *Ap[/tex]
[tex]Fp=\frac{W}{\frac{\pi*d_{s}^{2} Â }{4} } *\pi *\frac{d_{p^{2} } }{4}[/tex]
[tex]Fp=W*\frac{d_{p}^{2} Â }{d_{s}^{2} Â }[/tex]
[tex]Fp=2200*\frac{2,1^{2} }{26^{2} }[/tex]
[tex]Fp=2200*\frac{4.41}{676}[/tex]
[tex]Fp=14.35kg[/tex]
Calculation of Fp in Newtons (N):
[tex]1kg=9.8N[/tex]
[tex]Fp=14.35kg*\frac{9.8N}{kg}[/tex]
Fp=140.63N
The force that must be exerted on the primary cylinder to support the weight of car resting on the secondary cylinder is is 140.65 N.
The force that must be exerted on the primary cylinder to support the weight of a 2200-kg car (a large car) resting on the secondary cylinder is determined by appling Pascal priciple as shown below;
F = PA
P = F/A
[tex]\frac{F_s}{d_s^2} = \frac{F_p}{d_p^2} \\\\F_p = \frac{F_sd_p^2}{d_s^2}[/tex]
Substitute the given values and solve for the primary force,
[tex]F_p = \frac{(2200\times 9.8) \times (0.021)^2}{(0.26)^2} \\\\F_p = 140.65 \ N[/tex]
Thus, the force that must be exerted on the primary cylinder to support the weight of car resting on the secondary cylinder is is 140.65 N.
Learn more about pascal principle here: https://brainly.com/question/4262025
