Hydraulic Lift II.The piston of a hydraulic automobile lift is 0.30 m in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 kg? Also express this pressure in atmospheres.

Verified step by step guidance

1. Calculate the force needed to lift the car using the formula F = m imes g, where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Determine the area of the piston using the formula A = \pi \times r^2, where r is the radius of the piston. Convert the diameter to radius by dividing it by 2.
3. Calculate the required gauge pressure using the formula P = \frac{F}{A}, where F is the force calculated in step 1 and A is the area of the piston calculated in step 2.
4. Convert the gauge pressure from pascals to atmospheres using the conversion factor 1 atm = 101325 Pa.
5. Summarize the results by stating the gauge pressure in both pascals and atmospheres.

Key Concepts

Hydraulic Systems

Hydraulic systems utilize incompressible fluids to transmit force. According to Pascal's principle, a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid. This principle is fundamental in hydraulic lifts, where a small force applied on a small piston generates a larger force on a larger piston, allowing heavy objects to be lifted with relative ease.

Pressure Calculation

Pressure is defined as force per unit area, typically measured in pascals (Pa) in the SI system. To calculate the pressure required to lift an object, one must first determine the weight of the object (mass times gravitational acceleration) and then divide this force by the area of the piston. This relationship is crucial for determining the gauge pressure needed in hydraulic systems.

Conversion of Units

In physics, it is often necessary to convert between different units of measurement. For pressure, the conversion from pascals to atmospheres involves knowing that 1 atmosphere is equivalent to 101,325 pascals. Understanding how to perform these conversions is essential for accurately interpreting and communicating results in various contexts, such as engineering and physics problems.