Question

The cross-sectional area of the output piston in a hydraulic device is 3.0 times the area of the input piston. For each 1.5 cm the input piston moves, how far does the output piston move

Answer 1

For each 1.5 cm the input piston moves, then output piston will move 0.5 cm

Step-by-step explanation:

Let cross-sectional area of the input piston = A

Let cross-sectional area of the output piston = 3A

pressure (P) = Force (F) / Area (A)

F = PA

For a constant gravitational force on the inlet and outlet piston;

P₁A₁ = P₂A₂

But pressure = ρgh

where;

ρ is density of water

g is acceleration due to gravity

h is the distance or height moved by the piston

(ρg)h₁A₁ = (ρg)h₂A₂

h₁A₁ = h₂A₂

Area of output piston = 3 times area of input piston

h₁A₁ = h₂(3A₁)

For each 1.5 cm the input piston moves, then output piston will move;

1.5A₁ = h₂(3A₁)

1.5 = 3h₂

h₂ = 1.5 / 3

h₂ = 0.5 cm

Thus, for each 1.5 cm the input piston moves, then output piston will move 0.5 cm