In a hydraulic car lift system, a mechanic applies a downward force of 150\text{ N} on a s… — Armed Services Vocational Aptitude Battery (ASVAB)

In a hydraulic car lift system, a mechanic applies a downward force of $150\text{ N}$ on a small input piston with a cross-sectional area of $5\text{ cm}^2$ . This force is transmitted through hydraulic fluid to a larger output piston that has a cross-sectional area of $100\text{ cm}^2$ . Assuming ideal conditions, what is the maximum upward force exerted by the larger piston?

A
7.5 N
B
750 N
3,000 NAnswer
D
15,000 N

Answer

3,000 N

The correct answer is

3,000\text{ N}

. According to Pascal's Principle, the fluid pressure in the system remains constant (

P = F_1/A_1 = 150/5 = 30\text{ N/cm}^2

). Multiplying this pressure by the area of the larger piston (

30 \times 100

) yields an upward force of

3,000\text{ N}

. Alternatively, the mechanical advantage is the ratio of the two areas (

100/5 = 20

). Multiplying the input force by this mechanical advantage (

150 \times 20

) directly gives

3,000\text{ N}

Step-by-Step Solution

Calculate the pressure exerted by the input piston on the hydraulic fluid.

P = \frac{F_1}{A_1} = \frac{150\text{ N}}{5\text{ cm}^2} = 30\text{ N/cm}^2

Pascal's Principle states that pressure applied to a confined fluid is transmitted undiminished in all directions.

Calculate the resulting upward force on the larger output piston.

F_2 = P \times A_2 = 30\text{ N/cm}^2 \times 100\text{ cm}^2 = 3,000\text{ N}

The uniform pressure of

30\text{ N/cm}^2

acts over the entire

100\text{ cm}^2

area of the larger piston, multiplying the original force.

Key Concept

Pascal's Principle and Hydraulic Mechanical Advantage

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic