Respuesta :
Answer:
a) 1: 100 F₂ = 100 F₁, b) P₁ = P₂ 1:1
Explanation:
The pressure in a system is the same for a given horizontal line, therefore
P₁ = P₂
where subscript 1 is for small piston and index 2 is for large piston 2
a) they ask the relation of the forces
pressure is defined by
P = F / A
for the small piston
P₁ = F₁ / A₁
the area of the piston is
A₁ =π r₁²
P₁ = F₁ /π r₁²
for big piston
P₂ = F₂ / A₂
in the exercise indicates that the diameter of the large piston is 10 times the diameter of the small piston
A = π r₂²
r₂ = 10 r₁
r₂ = π 10² r₁²
we substitute
P₂ = [tex]\frac{F_2}{ \pi \ 100 \ r_1^2}[/tex]
we equalize the pressures
[tex]\frac{F_1 }{ \pi \ r_1^2 } = \frac{F_2}{ \pi \ 100 r_1^2}[/tex]
F₁ = F₂ / 100
F₂ / F₁ = 100
therefore the force ratio is
1: 100
b) according to Pascal's principle for the same height the pressure is the same regardless of the shape of the container, therefore the pressure of the two pistons is the same
P1 = P2
1: 1
