Find the absolute pressure in a hydraulic jack with a small...

Find the absolute pressure in a hydraulic jack with a small piston of area $23.0 \mathrm{~cm}^{2}$ when a force of $125 \mathrm{~N}$ is applied. The area of the large piston is $46.0 \mathrm{~cm}^{2}$.

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Key Concepts

Pressure

Pressure is defined as the force exerted per unit area and is a measure of how concentrated a force is on a surface. It is calculated using the formula P = F/A and is typically measured in Pascals (Pa) in the SI system.

Force and Area Relationship

The relationship between force and area is central to understanding pressure; as the same amount of force distributed over a smaller area results in a higher pressure, and conversely, over a larger area produces a lower pressure. This relationship is key in analyzing scenarios involving mechanical devices such as jacks and presses.

Unit Conversion in Pressure Calculations

Accurate pressure calculations often require converting measurements to consistent units. For instance, when areas are provided in units like square centimeters (cm²), converting them to square meters (m²) is essential to match the SI unit system and to correctly apply the formula P = F/A.

Pascal's Law

Pascal's Law states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. This principle is fundamental in hydraulic systems, enabling devices like hydraulic jacks to multiply force while maintaining a uniform pressure throughout the system.

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