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Difficulty: HardPascal's Principle and Hydraulics

An industrial hydraulic press uses two pistons connected by an enclosed, incompressible fluid. The input piston has a cross-sectional area of 3 in23 \text{ in}^2, and the output piston has a cross-sectional area of 30 in230 \text{ in}^2. If an operator applies a constant force of 50 lbs50 \text{ lbs} to the input piston, what is the maximum weight the press can lift, and how far must the input piston travel in total to raise that weight by exactly 5 inches5 \text{ inches}?

  1. 500 lbs500 \text{ lbs} maximum weight; 50 inches50 \text{ inches} of input travelAnswer
  2. B
    5 lbs5 \text{ lbs} maximum weight; 50 inches50 \text{ inches} of input travel
  3. C
    500 lbs500 \text{ lbs} maximum weight; 0.5 inches0.5 \text{ inches} of input travel
  4. D
    5 lbs5 \text{ lbs} maximum weight; 0.5 inches0.5 \text{ inches} of input travel

Answer

The press can lift a maximum weight of 500 lbs, and the input piston must travel 50 inches.
The correct answer correctly applies the area ratio of 10 (30/330/3). The output force is multiplied by this ratio (50×10=500 lbs50 \times 10 = 500 \text{ lbs}), and the input distance must also be 10 times the output distance (5×10=50 inches5 \times 10 = 50 \text{ inches}) to displace enough fluid volume.

Step-by-Step Solution

1
Calculate the area ratio between the output and input pistons.
Area Ratio = 30 in2/3 in2=1030 \text{ in}^2 / 3 \text{ in}^2 = 10.
This ratio represents the mechanical advantage of the hydraulic system.
2
Calculate the maximum weight (output force) the press can lift.
Foutput=50 lbs×10=500 lbsF_{output} = 50 \text{ lbs} \times 10 = 500 \text{ lbs}.
According to Pascal's Principle, pressure is transmitted equally. Therefore, the output force is the input force multiplied by the area ratio.
3
Calculate the required input travel distance.
dinput=5 inches×10=50 inchesd_{input} = 5 \text{ inches} \times 10 = 50 \text{ inches}.
To conserve work and fluid volume, the input piston must move proportionally farther than the output piston by a factor equal to the area ratio.

Key Concept

In a hydraulic system, a larger output piston multiplies the input force by the ratio of their areas, but the input piston must travel proportionally farther to conserve fluid volume and work.
Estimated Time:1m 30s
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Topics

Pascal's Principle and Hydraulics

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