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24 August, 02:29

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the

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  1. 24 August, 02:37
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    F₂ = 925.92 N

    Explanation:

    In a hydraulic lift the normal stress applied to one arm must be equally transmitted to the other arm. Therefore,

    σ₁ = σ₂

    F₁/A₁ = F₂/A₂

    F₂ = F₁ A₂/A₁

    where,

    F₂ = Initial force that must be applied to narrow arm = ?

    F₁ = Load on Wider Arm to be raised = 12000 N

    A₁ = Area of wider arm = πr₁² = π (18 cm) ² = 324π cm²

    A₂ = Area of narrow arm = πr₂² = π (5 cm) ² = 25π cm²

    Therefore,

    F₂ = (12000 N) (25π cm²) / (324π cm²)

    F₂ = 925.92 N
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