Answer:
a. = 93 N
b. = 94.9 N
Explanation:
Answer:
Explanation:
from the question we were given the following:
density of oil (ρ) = 8.3 x [tex]10^{2}[/tex] [tex]\frac{kg}{m^{3} }[/tex]
radius of the output plunger (R) = 0.125 m
radius of the input piston (r) = 7.70 x [tex]10^{-3}[/tex] m = 0.0077 m
output force (F2) = 24500 N
input force (F1) = ?
acceleration due to gravity (g) = 9.8 [tex]\frac{m}{s^{2} }[/tex]
difference in height of the plunger and piston (h) = 1.3 m
[tex]\frac{F2}{A2}[/tex] = [tex]\frac{F1}{A1 }[/tex]
F1 = ( [tex]\frac{F2}{A2 }[/tex] ) x A1
where A1 is the area of the input piston and A2 is the area of the output plunger
Area = π x [tex]radius^{2}[/tex]
A2 = π x [tex]0.125^{2}[/tex] = 0.049
A1 = π x [tex]0.0077^{2}[/tex] = 0.000186
recall that from above F1 = ( [tex]\frac{F2}{A2 }[/tex] ) x A1
F1 = ( [tex]\frac{24500}{0.049 }[/tex] ) x 0.000186
F1 = 93 N
P2 = P1 + ρgh
where P = pressure = [tex]\frac{F}{ A }[/tex]
therefore the equation above now becomes
[tex]\frac{F2}{ A2 }[/tex] = [tex]\frac{F1}{ A1 }[/tex] + ρgh
F2 = ( [tex]\frac{F1}{ A1 }[/tex] + ρgh ) x A2
F2 = ( [tex]\frac{24500}{ 0.000186 }[/tex] + ( 8.3 x [tex]10^{2}[/tex] [tex] x 9.8 x 1.3 ) ) x 0.049
F2 = 94.9 N
