Match each hydraulic jack scenario to its correctly calculated parameter based on Pascal's… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each hydraulic jack scenario to its correctly calculated parameter based on Pascal's Principle.

Jack A: Input area is $3 \text{ in}^2$ , Output area is $12 \text{ in}^2$ , Input force is $40 \text{ lbs}$ Produces an output force of $160 \text{ lbs}$
Jack B: Input area is $2 \text{ in}^2$ , Output area is $10 \text{ in}^2$ , Input distance is $15 \text{ inches}$ Moves the output piston a distance of $3 \text{ inches}$
Jack C: Input force is $30 \text{ lbs}$ , Output force is $180 \text{ lbs}$ , Output area is $24 \text{ in}^2$ Requires an input piston area of $4 \text{ in}^2$
Jack D: Input area is $1.5 \text{ in}^2$ , Output area is $15 \text{ in}^2$ , Input force is $45 \text{ lbs}$ Operates at a fluid pressure of $30 \text{ psi}$

Cevap

Jack A matches to 160 lbs output force, Jack B matches to 3 inches output distance, Jack C matches to 4 in² input area, and Jack D matches to 30 psi fluid pressure.

Each hydraulic system operates on Pascal's Principle and the conservation of volume. By applying the formulas for pressure (

P = F/A

) and mechanical advantage (

MA = A_{out}/A_{in}

), the missing parameter for each jack can be calculated and uniquely matched.

Adım Adım Çözüm

Calculate the output force for Jack A.

F_{out} = 160 \text{ lbs}

Using Pascal's principle, mechanical advantage is

12/3 = 4

F_{out} = 40 \times 4

Calculate the output distance for Jack B.

d_{out} = 3 \text{ inches}

Due to volume conservation,

d_{in} \times A_{in} = d_{out} \times A_{out}

15 \times 2 = d_{out} \times 10

Calculate the input area for Jack C.

A_{in} = 4 \text{ in}^2

Since pressure is equal across the system,

P = 180 / 24 = 7.5 \text{ psi}

A_{in} = 30 / 7.5

Calculate the fluid pressure for Jack D.

P = 30 \text{ psi}

Pressure equals force over area,

P = 45 / 1.5

Anahtar Kavram

Pascal's Principle, Fluid Volume Conservation, and Mechanical Advantage

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Cevap

Adım Adım Çözüm

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