Answer:
a) F = 4.9 10⁴ N, b) F₁ = 122.5 N
Explanation:
To solve this problem we use that the pressure is transmitted throughout the entire fluid, being the same for the same height
1) pressure is defined by the relation
P = F / A
to lift the weight of the truck the force of the piston must be equal to the weight of the truck
∑F = 0
F-W = 0
F = W = mg
F = 5000 9.8
F = 4.9 10⁴ N
the area of the pisto is
A = pi r²
A = pi d² / 4
A = pi 1 ^ 2/4
A = 0.7854 m²
pressure is
P = 4.9 104 / 0.7854
P = 3.85 104 Pa
2) Let's find a point with the same height on the two pistons, the pressure is the same
[tex]\frac{F_1}{A_1} = \frac{F_2}{A_2}[/tex]
where subscript 1 is for the small piston and subscript 2 is for the large piston
F₁ = [tex]\frac{A_1}{A_2} \ F_2[/tex]
the force applied must be equal to the weight of the truck
F₁ = [tex]( \frac{d_1}{d_2} )^2\ m g[/tex]
F₁ = (0.05 / 1) ² 5000 9.8
F₁ = 122.5 N
