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Difficulty: MediumPascal's Principle and Hydraulics

A mechanic uses a hydraulic floor jack to lift the front axle of a delivery truck. The jack's output piston has a cross-sectional area of 25 in225 \text{ in}^2 and must support a load of 5,000 lbs5,000 \text{ lbs}. If the input piston has a cross-sectional area of 0.5 in20.5 \text{ in}^2, what is the minimum input force the mechanic must apply to lift the truck? (Assume a frictionless, ideal system)

  1. 100 lbs100 \text{ lbs}Answer
  2. B
    200 lbs200 \text{ lbs}
  3. C
    10,000 lbs10,000 \text{ lbs}
  4. D
    250,000 lbs250,000 \text{ lbs}

Answer

100 lbs100 \text{ lbs}
In a closed hydraulic system, pressure is uniform. The pressure created by the load on the output piston is its force divided by its area (5,000/25=200 psi5,000 / 25 = 200 \text{ psi}). To produce this same pressure at the input piston, you multiply the pressure by the input piston's area (200×0.5200 \times 0.5), which equals an input force of 100 lbs100 \text{ lbs}.

Step-by-Step Solution

1
Calculate the fluid pressure required at the output piston using the formula P = F/A.
5,000 lbs/25 in2=200 psi5,000 \text{ lbs} / 25 \text{ in}^2 = 200 \text{ psi}
Pascal's Principle states that pressure applied to a confined fluid is transmitted equally in all directions.
2
Apply the calculated pressure to the input piston to find the required input force using F = P × A.
200 psi×0.5 in2=100 lbs200 \text{ psi} \times 0.5 \text{ in}^2 = 100 \text{ lbs}
The input piston must generate the identical system pressure to balance and lift the load.

Key Concept

Pascal's Principle (Hydraulic Mechanical Advantage)
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Topics

Pascal's Principle and Hydraulics

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