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Difficulty: EasyPascal's Principle and Hydraulics

A hydraulic lift system has a small input piston with an area of 2 in22 \text{ in}^2 and a large output piston with an area of 10 in210 \text{ in}^2. If a downward force of 20 lbs20 \text{ lbs} is applied to the small piston, what is the resulting upward force exerted by the large piston?

  1. A
    4 lbs4 \text{ lbs}
  2. B
    40 lbs40 \text{ lbs}
  3. 100 lbs100 \text{ lbs}Answer
  4. D
    200 lbs200 \text{ lbs}

Answer

The upward force exerted by the large piston is 100 lbs100 \text{ lbs}.
According to Pascal's Principle, pressure is uniform throughout a confined fluid system. The pressure at the input piston is 10 psi10 \text{ psi} (20 lbs20 \text{ lbs} divided by 2 in22 \text{ in}^2). When this 10 psi10 \text{ psi} pressure acts upward across the 10 in210 \text{ in}^2 area of the output piston, it generates an output force of 100 lbs100 \text{ lbs} (10×1010 \times 10). Alternatively, you can recognize that the area ratio is 55 to 11 (10÷2=510 \div 2 = 5), which means the input force of 20 lbs20 \text{ lbs} is multiplied by 55 to equal 100 lbs100 \text{ lbs}.

Step-by-Step Solution

1
Calculate the pressure exerted by the small piston.
P=20 lbs2 in2=10 psiP = \frac{20 \text{ lbs}}{2 \text{ in}^2} = 10 \text{ psi}
Pascal's Principle states that pressure applied to a confined fluid is transmitted equally in all directions. Pressure is equal to Force divided by Area.
2
Calculate the output force on the large piston using the uniform pressure.
Foutput=10 psi×10 in2=100 lbsF_{output} = 10 \text{ psi} \times 10 \text{ in}^2 = 100 \text{ lbs}
Force is equal to pressure multiplied by the area of the piston.

Key Concept

Pascal's Principle and Hydraulic Multiplication
Estimated Time:45s
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Topics

Pascal's Principle and Hydraulics

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