In an aircraft's hydraulic braking system, the master cylinder (input) connects to a brake… — Armed Services Vocational Aptitude Battery (ASVAB)

In an aircraft's hydraulic braking system, the master cylinder (input) connects to a brake caliper cylinder (output). The cross-sectional area of the caliper cylinder is $5$ times the area of the master cylinder. If the master cylinder piston is pushed with $40 \text{ lbs}$ of force and travels $5 \text{ inches}$ , what is the resulting force and travel distance of the caliper cylinder piston?

$200 \text{ lbs}$ of force and $1 \text{ inch}$ of travelCevap
B
$200 \text{ lbs}$ of force and $25 \text{ inches}$ of travel
C
$8 \text{ lbs}$ of force and $25 \text{ inches}$ of travel
D
$8 \text{ lbs}$ of force and $1 \text{ inch}$ of travel

Cevap

The caliper cylinder piston will output

200 \text{ lbs}

of force and move

1 \text{ inch}

Based on Pascal's principle and the conservation of energy, the larger output cylinder multiplies the input force by the area ratio (

40 \times 5 = 200 \text{ lbs}

). Correspondingly, the output distance must be divided by that same ratio (

5 \div 5 = 1 \text{ inch}

) to ensure the work input equals the work output.

Adım Adım Çözüm

Determine the area ratio between the input and output cylinders.

Area Ratio = 5.

The problem states the caliper cylinder has an area 5 times larger than the master cylinder.

Calculate the resulting force at the output cylinder.

Output Force = Input Force x Area Ratio =

40 \text{ lbs} \times 5 = 200 \text{ lbs}

According to Pascal's principle, pressure is transmitted equally, so the force is multiplied by the ratio of the piston areas.

Calculate the travel distance of the output cylinder.

Output Distance = Input Distance / Area Ratio =

5 \text{ inches} / 5 = 1 \text{ inch}

Because fluid is incompressible, the volume displaced by the input piston equals the volume displaced by the output piston. A larger area requires proportionally less travel distance.

Anahtar Kavram

In a closed hydraulic system, moving from a smaller to a larger cylinder multiplies the force by the area ratio but decreases the travel distance by that same ratio, conserving the total work done.

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