In an ideal hydraulic lift system, an input piston applies force to an enclosed, incompres… — Armed Services Vocational Aptitude Battery (ASVAB)

In an ideal hydraulic lift system, an input piston applies force to an enclosed, incompressible fluid to lift a heavy load on an output piston. Match each modification made to the system on the left with its corresponding physical result on the right. Assume only the stated modification occurs and input force remains constant unless otherwise noted.

Doubling the cross-sectional area of the output pistonOutput force doubles; output piston travels half as far per unit of input stroke.
Halving the cross-sectional area of the input pistonSystem fluid pressure doubles; input piston must travel twice as far to maintain the original output distance.
Increasing the stroke distance of the input piston by a factor of twoOutput force remains unchanged; output piston travels twice its original distance.
Replacing the hydraulic fluid with one of a different densityTheoretical mechanical advantage and distance ratios remain unaffected.

Answer

The correct pairings link output area changes to inverse distance effects, input area reductions to increased system pressure, stroke length changes to proportional output distance changes, and fluid density changes to having no effect on theoretical mechanical advantage.

The correct pairings correctly apply the two governing rules of ideal hydraulics:

P = F/A

(which determines force multiplication) and

V = A \times d

(which determines piston travel distance). Every change to an area variable inversely affects the distance variable.

Step-by-Step Solution

Analyze the relationship for output force based on Pascal's Principle.

The formula is

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

This establishes how changes in either piston area affect the maximum lifting force.

Analyze the relationship for piston travel distances based on conservation of fluid volume.

The formula is

d_{out} = d_{in} \times \frac{A_{in}}{A_{out}}

This establishes the trade-off between force amplification and distance; mechanical advantage always comes at the cost of requiring greater input distance.

Evaluate each modification against both formulas simultaneously.

Doubling

A_{out}

doubles

F_{out}

but halves

d_{out}

. Halving

A_{in}

doubles pressure and

F_{out}

, but halves the volume displaced per inch of stroke, requiring twice the

d_{in}

Hydraulic systems must obey both the pressure equation and the conservation of volume simultaneously.

Key Concept

Pascal's Principle and Conservation of Volume in Hydraulics

Estimated Time:2m 0s

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