A mechanic uses a simple hydraulic lift to raise a motorcycle. The system's input piston h… — Armed Services Vocational Aptitude Battery (ASVAB)

A mechanic uses a simple hydraulic lift to raise a motorcycle. The system's input piston has a cross-sectional area of $5 \text{ in}^2$ , and the output (lifting) piston has a cross-sectional area of $50 \text{ in}^2$ . If the mechanic applies a downward force of $40 \text{ lbs}$ on the input piston, what is the upward force exerted by the output piston?

A
$4 \text{ lbs}$
B
$40 \text{ lbs}$
C
$200 \text{ lbs}$
$400 \text{ lbs}$ Cevap

Cevap

The upward force exerted by the output piston is

400 \text{ lbs}

According to Pascal's Principle, pressure is transmitted equally throughout a confined fluid. The pressure generated at the input piston is

40 \text{ lbs} / 5 \text{ in}^2 = 8 \text{ psi}

. This exact same pressure acts on the larger

50 \text{ in}^2

output piston, resulting in an upward force of

8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

. Alternatively, using the mechanical advantage ratio:

50 / 5 = 10

, so the output force is

10 \times 40 = 400 \text{ lbs}

Adım Adım Çözüm

Calculate the pressure exerted by the input piston.

P = \frac{F_{in}}{A_{in}} = \frac{40 \text{ lbs}}{5 \text{ in}^2} = 8 \text{ psi}

Pascal's Principle states that pressure applied to an enclosed fluid is transmitted equally in all directions.

Calculate the output force by applying the pressure to the output piston's area.

F_{out} = P \times A_{out} = 8 \text{ psi} \times 50 \text{ in}^2 = 400 \text{ lbs}

The output force is the product of the constant fluid pressure and the area of the output piston.

Anahtar Kavram

Pascal's Principle and Hydraulic Multiplication

Tahmini Süre:45s

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