A mechanical engineer is testing a hydraulic actuation system. The standard baseline confi… — Armed Services Vocational Aptitude Battery (ASVAB)

A mechanical engineer is testing a hydraulic actuation system. The standard baseline configuration features an input piston with an area of $2 \text{ in}^2$ , an output piston with an area of $20 \text{ in}^2$ , an applied input force of $50 \text{ lbs}$ , and an input stroke distance of $12 \text{ in}$ . Match each experimental setup below to its resulting output force and output travel distance.

Input area is increased to $4 \text{ in}^2$ (all other baseline parameters unchanged) $250 \text{ lbs}$ output force; $2.4 \text{ in}$ travel distance
Output area is increased to $60 \text{ in}^2$ (all other baseline parameters unchanged) $1500 \text{ lbs}$ output force; $0.4 \text{ in}$ travel distance
Input force is increased to $100 \text{ lbs}$ and input stroke is reduced to $6 \text{ in}$ (areas unchanged) $1000 \text{ lbs}$ output force; $0.6 \text{ in}$ travel distance
Both input and output areas are tripled to $6 \text{ in}^2$ and $60 \text{ in}^2$ respectively $500 \text{ lbs}$ output force; $1.2 \text{ in}$ travel distance

Cevap

Each setup modifies the mechanical advantage or the input parameters, requiring independent calculations for output force (

F_{out} = F_{in} \times \text{MA}

) and output distance (

d_{out} = d_{in} / \text{MA}

Correct pairings are achieved by systematically calculating the ratio of the new areas (MA), multiplying the corresponding input force by this ratio, and dividing the corresponding input stroke by this ratio. This ensures Pascal's Principle and the conservation of volume are strictly followed.

Adım Adım Çözüm

Calculate the Mechanical Advantage (MA) for each experimental setup.

MA is found by dividing the output area by the input area (

A_{out} / A_{in}

). Setup 1:

20/4=5

; Setup 2:

60/2=30

; Setup 3:

20/2=10

; Setup 4:

60/6=10

MA dictates the multiplier for force and the divisor for distance.

Determine the resulting output force for each setup.

Multiply the applied input force by the MA. Setup 1:

50 \times 5 = 250 \text{ lbs}

; Setup 2:

50 \times 30 = 1500 \text{ lbs}

; Setup 3:

100 \times 10 = 1000 \text{ lbs}

; Setup 4:

50 \times 10 = 500 \text{ lbs}

According to Pascal's Principle, pressure is transmitted equally, so force scales proportionally with area.

Determine the resulting output travel distance for each setup.

Divide the input stroke distance by the MA. Setup 1:

12 / 5 = 2.4 \text{ in}

; Setup 2:

12 / 30 = 0.4 \text{ in}

; Setup 3:

6 / 10 = 0.6 \text{ in}

; Setup 4:

12 / 10 = 1.2 \text{ in}

Because the fluid is incompressible, work and volume are conserved; travel distance scales inversely to force.

Anahtar Kavram

In hydraulics, Mechanical Advantage (MA) equals the ratio of output to input areas. Output force is multiplied by MA, while output travel distance is divided by MA to conserve work.

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