The force that must be applied is 261.3 N
Explanation:
According to Pascal's principle, the pressure is transmitted equally in all parts of the fluid: so, the pressure on the narrow cylinder must be equal to the pressure on the wide cylinder.
So we can write:
[tex]p_1 =p_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}[/tex]
where:
[tex]F_1[/tex] is the force applied on the small cylinder
[tex]A_1 = \pi r_1^2[/tex] is the area of the first cylinder, with [tex]r_1 = 4 cm[/tex] being the radius
[tex]F_2[/tex] is the force on the wide cylinder, which is the weight of the car, so:
[tex]F_2 = mg=(1500 kg)(9.8 m/s^2)=14700 N[/tex]
where m = 1500 kg is the mass of the car
[tex]A_2 = \pi r_2^2[/tex] is the area of the wide cylinder, with [tex]r_2=30 cm[/tex] being its radius
Substituting and solving for [tex]F_1[/tex], we find the force on the narrow cylinder:
[tex]F_1 = \frac{F_2 A_1}{A_2}=\frac{(14700)(\pi (4)^2)}{\pi (30)^2}=261.3 N[/tex]
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