Answer:
370 N
Explanation:
We can solve this problem by applying Pascal's principle, which states that the pressure in the liquid under the pistons is transmitted equally to every part of the liquid.
This means that the pressure on the two pistons is the same. Therefore, we can write:
[tex]p_1=p_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}[/tex] (1)
where
[tex]F_1, F_2[/tex] are the forces on piston 1 and 2
[tex]A_1,A_2[/tex] is the cross-sectional area of piston 1 and 2
In this problem, we have:
[tex]F_2=mg=(911)(9.8)=8928 N[/tex] is the force on piston 2, where
m = 911 kg is the mass on the piston
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
The diameter of piston 2 is d = 9.76 cm = 0.0976 m, so its area is
[tex]A_2=\pi (\frac{d}{2})^2=\pi(\frac{0.0976}{2})^2=7.48\cdot 10^{-3} m^2[/tex]
The diameter of piston 1 is d = 1.99 cm = 0.0199 m, so its area is
[tex]A_1=\pi(\frac{d}{2})^2=\pi (\frac{0.0199}{2})^2=0.31\cdot 10^{-3} m^2[/tex]
So, solving eq.(1), we find the pressure on piston 1:
[tex]F_1=\frac{F_2A_1}{A_2}=\frac{(8928)(0.31\cdot 10^{-3})}{7.48\cdot 10^{-3}}=370 N[/tex]
