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Difficulty: EasyPascal's Principle and Hydraulics

A mechanic uses a hydraulic floor jack to lift a heavy vehicle transmission. The jack's pump (input) piston has an area of 3 in23 \text{ in}^2, and the lifting (output) piston has an area of 15 in215 \text{ in}^2. If the mechanic applies a downward force of 60 lbs60 \text{ lbs} on the input piston, what is the resulting upward force exerted by the lifting piston?

  1. 300 lbs300 \text{ lbs}Answer
  2. B
    12 lbs12 \text{ lbs}
  3. C
    60 lbs60 \text{ lbs}
  4. D
    900 lbs900 \text{ lbs}

Answer

The lifting piston exerts an upward force of 300 lbs300 \text{ lbs}.
According to Pascal's Principle, the fluid pressure is equal throughout the system. The output piston has an area 55 times larger than the input piston (15/3=515 / 3 = 5). Therefore, to maintain the same pressure, it will output a force 55 times greater than the input force (60×5=30060 \times 5 = 300).

Step-by-Step Solution

1
Determine the area ratio between the output and input pistons.
Area Ratio=15 in23 in2=5\text{Area Ratio} = \frac{15 \text{ in}^2}{3 \text{ in}^2} = 5
This ratio represents the mechanical advantage of the hydraulic system.
2
Multiply the input force by the mechanical advantage to find the output force.
Output Force=60 lbs×5=300 lbs\text{Output Force} = 60 \text{ lbs} \times 5 = 300 \text{ lbs}
Because fluid pressure (P=FAP = \frac{F}{A}) is transmitted equally, a piston with 55 times the area will output 55 times the force.

Key Concept

Pascal's Principle states that pressure is transmitted equally throughout a confined fluid, allowing hydraulic systems to multiply force proportionally to the ratio of their piston areas.
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Topics

Pascal's Principle and Hydraulics

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