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Difficulty: EasyPascal's Principle and Hydraulics

A hydraulic press used for stamping metal parts has an input piston with a cross-sectional area of 2 in22 \text{ in}^2 and an output piston with a cross-sectional area of 6 in26 \text{ in}^2. If a downward force of 30 lbs30 \text{ lbs} is applied to the input piston, how much force is exerted by the output piston?

  1. A
    10 lbs10 \text{ lbs}
  2. B
    30 lbs30 \text{ lbs}
  3. 90 lbs90 \text{ lbs}Answer
  4. D
    180 lbs180 \text{ lbs}

Answer

90 lbs90 \text{ lbs}
According to Pascal's Principle, pressure is transmitted equally throughout a confined fluid. The pressure generated at the input is P=F1A1=302=15 psiP = \frac{F_1}{A_1} = \frac{30}{2} = 15 \text{ psi}. This same pressure acts on the output piston. The output force is F2=P×A2=15×6=90 lbsF_2 = P \times A_2 = 15 \times 6 = 90 \text{ lbs}. Alternatively, using the mechanical advantage, since the output area is 33 times larger than the input area, the output force is 33 times the input force.

Step-by-Step Solution

1
Identify the given values from the problem description.
A1=2 in2A_1 = 2 \text{ in}^2, F1=30 lbsF_1 = 30 \text{ lbs}, A2=6 in2A_2 = 6 \text{ in}^2
These variables are required to apply Pascal's Principle.
2
Determine the mechanical advantage by finding the ratio of the output area to the input area.
Ratio = A2A1=62=3\frac{A_2}{A_1} = \frac{6}{2} = 3
The output force is multiplied by the ratio of the piston areas.
3
Calculate the output force (F2F_2).
F2=30×3=90 lbsF_2 = 30 \times 3 = 90 \text{ lbs}
Multiplying the input force by the mechanical advantage gives the total output force.

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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