A hydraulic theater stage lift is used to raise a heavy set piece. The output piston suppo… — Armed Services Vocational Aptitude Battery (ASVAB)

A hydraulic theater stage lift is used to raise a heavy set piece. The output piston supporting the stage has a cross-sectional area of $120 \text{ in}^2$ , while the input piston connected to the control system has an area of $8 \text{ in}^2$ . If the set piece and stage exert a combined downward force of $2,400 \text{ lbs}$ on the output piston, how much input force, in pounds, must be applied to the input piston to hold the stage steady?

Answer: 160 lbs

Answer

160

Based on Pascal's Principle, an enclosed fluid transmits pressure equally. The stage creates a pressure of

20 \text{ psi}

(

2,400 \text{ lbs} / 120 \text{ in}^2

). Because this

20 \text{ psi}

is transmitted to the input piston, which has an area of

8 \text{ in}^2

, the required force is

20 \text{ psi} \times 8 \text{ in}^2 = 160 \text{ lbs}

Step-by-Step Solution

State Pascal's Principle for the system.

P_{in} = P_{out}

, meaning

\frac{F_{in}}{A_{in}} = \frac{F_{out}}{A_{out}}

Pascal's Principle dictates that pressure applied to an enclosed fluid is transmitted equally in all directions.

Calculate the pressure at the output piston.

P = \frac{2,400 \text{ lbs}}{120 \text{ in}^2} = 20 \text{ psi}

This establishes the uniform pressure throughout the entire hydraulic system.

Calculate the required input force.

F_{in} = P \times A_{in} = 20 \text{ psi} \times 8 \text{ in}^2 = 160 \text{ lbs}

Applying the system pressure to the smaller area of the input piston yields the necessary input force.

Key Concept

Pascal's Principle and Mechanical Advantage

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