A hydraulic rescue tool, often used by emergency responders to pry open crushed vehicles, … — Armed Services Vocational Aptitude Battery (ASVAB)

A hydraulic rescue tool, often used by emergency responders to pry open crushed vehicles, operates based on Pascal's Principle. The tool's pump applies $200\text{ lbs}$ of force to an input piston that has a cross-sectional area of $0.5\text{ in}^2$ . In order to generate $4,000\text{ lbs}$ of spreading force at the output piston, what must be the cross-sectional area of the output piston?

$10\text{ in}^2$ Cevap
B
$20\text{ in}^2$
C
$40\text{ in}^2$
D
$0.025\text{ in}^2$

Cevap

The cross-sectional area of the output piston must be

10\text{ in}^2

In a hydraulic system, pressure is transmitted equally in all directions based on Pascal's Principle. First, determine the system pressure generated by the input piston by dividing the applied force by the area:

200\text{ lbs} / 0.5\text{ in}^2 = 400\text{ psi}

. Since this same pressure acts on the output piston, the required area to produce

4,000\text{ lbs}

of lifting force is found by dividing the output force by the pressure:

4,000\text{ lbs} / 400\text{ psi} = 10\text{ in}^2

. Alternatively, you can identify that the output force is 20 times the input force, meaning the output area must be 20 times the input area:

0.5\text{ in}^2 \times 20 = 10\text{ in}^2

Adım Adım Çözüm

Calculate the fluid pressure generated by the input piston using the formula Pressure = Force / Area.

P = \frac{200\text{ lbs}}{0.5\text{ in}^2} = 400\text{ psi}

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid, so the output piston experiences this same pressure.

Use the calculated pressure to find the required area of the output piston using the rearranged formula Area = Force / Pressure.

A_2 = \frac{4,000\text{ lbs}}{400\text{ psi}} = 10\text{ in}^2

Dividing the desired output force by the uniform system pressure yields the necessary cross-sectional area to achieve that force.

Anahtar Kavram

Pascal's Principle (Hydraulic Multiplication)

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