A barber uses a hydraulic system to lift a customer in a chair. The output piston beneath … — Armed Services Vocational Aptitude Battery (ASVAB)

A barber uses a hydraulic system to lift a customer in a chair. The output piston beneath the chair has a cross-sectional area that is exactly 10 times larger than the input piston connected to the foot pedal. If the barber applies a downward force of $25 \text{ lbs}$ on the input piston, how much upward force does the output piston generate?

A
$2.5 \text{ lbs}$
B
$25 \text{ lbs}$
$250 \text{ lbs}$ Answer
D
$2,500 \text{ lbs}$

Answer

The output piston generates

250 \text{ lbs}

of upward force.

Based on Pascal's Principle, hydraulic systems multiply force proportionally to the increase in the cross-sectional area of the pistons. Because the output piston's area is 10 times larger than the input piston's area, the output force is 10 times the input force. Multiplying the

25 \text{ lbs}

of input force by 10 gives

250 \text{ lbs}

of output force.

Step-by-Step Solution

Identify the mechanical advantage (MA) based on the area ratio.

The area ratio is given as 10 to 1, meaning the MA is 10.

Pascal's Principle states that pressure is transmitted equally, so force is multiplied by the same factor as the area increases.

Calculate the output force by multiplying the input force by the mechanical advantage.

25 \text{ lbs} \times 10 = 250 \text{ lbs}

The output force is directly proportional to the increase in area.

Key Concept

Pascal's Principle and Hydraulic Force Multiplication

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