In a hydraulic system, what happens to the force if the area of the piston is doubled while keeping the pressure constant?

In a hydraulic system, what happens to the force if the area of the piston is doubled while keeping the pressure constant?

• A. The force is halved
• B. The force is doubled
• C. The force remains the same
• D. The area does not affect the force

Answer: (B)

In a hydraulic system, the relationship between pressure, force, and area is dictated by the formula: \[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \] If the pressure is held constant and the area of the piston is doubled, the force exerted by the piston must also increase in accordance with this relationship. Since pressure remains unchanged, we can express this as: \[ \text{Force} = \text{Pressure} \times \text{Area} \] If you double the area (let’s say the original area is \( A \) and becomes \( 2A \)), the new force will be: \[ \text{New Force} = \text{Pressure} \times (2A) = 2 \times (\text{Pressure} \times A) = 2 \times \text{Original Force} \] This clearly shows that when the area is doubled while keeping the pressure constant, the force is also doubled. Thus, it aligns perfectly with the correct answer, confirming the proportional relationship between area and force in a hydraulic system.

In a hydraulic system, the relationship between pressure, force, and area is dictated by the formula:

[

\text{Pressure} = \frac{\text{Force}}{\text{Area}}

]

If the pressure is held constant and the area of the piston is doubled, the force exerted by the piston must also increase in accordance with this relationship.

Since pressure remains unchanged, we can express this as:

[

\text{Force} = \text{Pressure} \times \text{Area}

]

If you double the area (let’s say the original area is ( A ) and becomes ( 2A )), the new force will be:

[

\text{New Force} = \text{Pressure} \times (2A) = 2 \times (\text{Pressure} \times A) = 2 \times \text{Original Force}

]

This clearly shows that when the area is doubled while keeping the pressure constant, the force is also doubled. Thus, it aligns perfectly with the correct answer, confirming the proportional relationship between area and force in a hydraulic system.