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15 February, 15:49

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

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  1. 15 February, 19:06
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    For each 1.5 cm the input piston moves, then output piston will move 0.5 cm

    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
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