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Difficulty: EasyPascal's Principle and Hydraulics

A dentist adjusts a patient's hydraulic examination chair. The system's input piston has a cross-sectional area of 8 in28 \text{ in}^2, and the lifting piston beneath the chair has an area of 64 in264 \text{ in}^2. If the dentist applies 35 lbs35 \text{ lbs} of force to the input piston, how much upward force is generated by the lifting piston?

Answer: 280 lbs

Answer

280
The hydraulic system provides a mechanical advantage equal to the ratio of the two piston areas (64/8=864 / 8 = 8). Multiplying the input force of 35 lbs35 \text{ lbs} by this mechanical advantage yields a total lifting force of 280 lbs280 \text{ lbs}.

Step-by-Step Solution

1
Identify the given variables.
Input area A1=8 in2A_1 = 8 \text{ in}^2, output area A2=64 in2A_2 = 64 \text{ in}^2, and input force F1=35 lbsF_1 = 35 \text{ lbs}.
These variables are required to apply Pascal's Principle.
2
Calculate the mechanical advantage (area ratio) of the hydraulic system.
A2A1=648=8\frac{A_2}{A_1} = \frac{64}{8} = 8.
The ratio of the output area to the input area determines how much the input force will be multiplied.
3
Calculate the generated output force.
F2=F1×Area Ratio=35 lbs×8=280 lbsF_2 = F_1 \times \text{Area Ratio} = 35 \text{ lbs} \times 8 = 280 \text{ lbs}.
Pascal's Principle states that pressure is transmitted equally throughout an enclosed fluid, meaning force increases proportionally with area.

Key Concept

According to Pascal's Principle, pressure applied to an enclosed fluid is transmitted equally in all directions. In a hydraulic system, this means the ratio of output force to input force is equal to the ratio of output area to input area (F1/A1=F2/A2F_1/A_1 = F_2/A_2).
Estimated Time:45s
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Topics

Pascal's Principle and Hydraulics

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