The piston of a hydraulic automobile lift is 0.30 m in diameter. What gauge pressure, in pascals

step 1 In this problem, we want to know what pressure is needed inside a hydraulic lift in order to lif

The piston of a hydraulic automobile lift is 0.30 m in...

The piston of a hydraulic automobile lift is 0.30 $\mathrm{m}$ in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 $\mathrm{kg}$ ? Now express this pressure in atmospheres.

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Key Concepts

Unit Conversion

Unit conversion is important when expressing pressure in different units. For instance, converting pressure from pascals to atmospheres involves recognizing that one atmosphere is approximately 101,325 pascals, which facilitates comparisons and practical applications in various contexts.

Force and Weight

The weight of an object is the gravitational force acting on its mass. Calculating this force (mass times gravitational acceleration) is essential when determining the pressure needed to lift the object using a hydraulic system.

Area Calculation

For circular pistons, the area is determined using the formula for the area of a circle (A = ?r²). This calculation is critical for converting the force required to lift an object into the pressure that must be applied over the piston’s surface.

Pressure

Pressure is defined as the force applied per unit area. In the context of hydraulic lifts, this concept is used to determine the necessary pressure to generate a force sufficient to support or lift a load.

Pascal's Principle

Pascal's principle states that a pressure change occurring anywhere in a confined fluid is transmitted undiminished throughout the fluid. This principle allows hydraulic systems to multiply force and is fundamental to the operation of hydraulic lifts.

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