A maintenance crew is selecting a hydraulic jack to lift a heavy machinery component. The … — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance crew is selecting a hydraulic jack to lift a heavy machinery component. The load must be lifted exactly $2 \text{ inches}$ . Different jacks have different input (pump) and output (lifting) cylinder areas.

Match each hydraulic jack's specifications to the distance its input piston must be pushed down to achieve the $2 \text{-inch}$ output lift.

Jack Alpha: Input Area = $2 \text{ in}^2$ , Output Area = $10 \text{ in}^2$ $10 \text{ inches}$
Jack Beta: Input Area = $3 \text{ in}^2$ , Output Area = $12 \text{ in}^2$ $8 \text{ inches}$
Jack Gamma: Input Area = $4 \text{ in}^2$ , Output Area = $24 \text{ in}^2$ $12 \text{ inches}$
Jack Delta: Input Area = $5 \text{ in}^2$ , Output Area = $10 \text{ in}^2$ $4 \text{ inches}$

Cevap

To find the input distance, calculate the mechanical advantage (Output Area / Input Area) and multiply it by the desired output distance (

2 \text{ inches}

). Jack Alpha requires

10 \text{ inches}

, Jack Beta requires

8 \text{ inches}

, Jack Gamma requires

12 \text{ inches}

, and Jack Delta requires

4 \text{ inches}

Each correct match is found by calculating the mechanical advantage (Output Area divided by Input Area) and multiplying that ratio by the desired

2\text{-inch}

output lift. This ensures the volume of fluid pushed by the pump equals the volume required to lift the load.

Adım Adım Çözüm

Determine the mathematical relationship for distance in a closed hydraulic system.

\text{Input Area} \times \text{Input Distance} = \text{Output Area} \times \text{Output Distance}

Because liquids are essentially incompressible, the volume of fluid displaced by the input piston must equal the volume of fluid pushing up the output piston.

Rearrange the formula to solve for the required Input Distance.

\text{Input Distance} = \text{Output Distance} \times (\frac{\text{Output Area}}{\text{Input Area}})

This isolates the unknown variable, making it easier to plug in the given values for each jack.

Calculate the required input distance for Jack Alpha.

2 \text{ inches} \times (\frac{10}{2}) = 2 \times 5 = 10 \text{ inches}

Applying the specific area measurements of Jack Alpha to the derived formula.

Apply the same formula to the remaining jacks to find their respective input distances.

Beta:

2 \times (\frac{12}{3}) = 8 \text{ inches}

. Gamma:

2 \times (\frac{24}{4}) = 12 \text{ inches}

. Delta:

2 \times (\frac{10}{5}) = 4 \text{ inches}

Completing the required calculations to find all corresponding values.

Anahtar Kavram

In a hydraulic system, the distance an input piston must travel is proportional to the ratio of the output area to the input area. A larger mechanical advantage requires a proportionally larger input distance to conserve the total volume of displaced fluid.

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