Match each closed hydraulic system scenario to its calculated unknown value. Assume the fl… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each closed hydraulic system scenario to its calculated unknown value. Assume the fluid is incompressible, there is no friction, and conditions are ideal.

Input: $A = 2 \text{ in}^2$ , $F = 50 \text{ lbs}$ $\rightarrow$ Output: $A = 10 \text{ in}^2$ (Find Output Force) $250 \text{ lbs}$
Input: $A = 3 \text{ in}^2$ , $F = 30 \text{ lbs}$ $\rightarrow$ Output: $F = 150 \text{ lbs}$ (Find Output Area) $15 \text{ in}^2$
Input: $A = 10 \text{ in}^2$ $\rightarrow$ Output: $A = 20 \text{ in}^2$ , $F = 100 \text{ lbs}$ (Find Input Force) $50 \text{ lbs}$
Input: $F = 40 \text{ lbs}$ , moves $5 \text{ in}$ $\rightarrow$ Output: $F = 200 \text{ lbs}$ (Find Output Distance) $1 \text{ in}$

Cevap

The correct matches are based on applying Pascal's Principle and the conservation of work. Output Force is 250 lbs, Output Area is 15 in², Input Force is 50 lbs, and Output Distance is 1 in.

Each matching pair applies either Pascal's Principle (

P = \frac{F_1}{A_1} = \frac{F_2}{A_2}

) or the conservation of work (

F_1 \cdot d_1 = F_2 \cdot d_2

) to solve for the missing variable in the hydraulic system.

Adım Adım Çözüm

Calculate the Output Force for the first scenario.

250 lbs

Using Pascal's Principle (

F_1/A_1 = F_2/A_2

), the system pressure is 50 lbs / 2 in² = 25 psi. The output force is 25 psi * 10 in² = 250 lbs.

Calculate the Output Area for the second scenario.

15 in²

The system pressure is 30 lbs / 3 in² = 10 psi. Rearranging the formula for area (

A = F/P

), the output area is 150 lbs / 10 psi = 15 in².

Calculate the Input Force for the third scenario.

50 lbs

System pressure is determined by the output side: 100 lbs / 20 in² = 5 psi. The required input force is 5 psi * 10 in² = 50 lbs.

Calculate the Output Distance for the fourth scenario.

1 in

By conservation of work (

F_1 \times d_1 = F_2 \times d_2

), the input work is 40 lbs * 5 in = 200 in-lbs. Thus, the output distance is 200 in-lbs / 200 lbs = 1 in.

Anahtar Kavram

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted undiminished. The work done on the input piston equals the work done by the output piston.

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