The hydraulic lift in an auto repair shop has a cylinder...

The hydraulic lift in an auto repair shop has a cylinder diameter of $0.2 \mathrm{~m}$. To what pressure should the hydraulic fluid be pumped to lift $40 \mathrm{~kg}$ of piston/ arms and $700 \mathrm{~kg}$ of a car?

Key Concepts

Area Calculation of a Circle

The cross-sectional area of a circular piston is found using the formula A = ?*(radius)². Calculating this area is essential for determining how much force a given pressure will produce, since the force is the product of the pressure and the area over which it is applied.

Force Calculation from Mass

In physics, the force due to gravity on an object (its weight) is calculated by multiplying its mass by the acceleration due to gravity (F = mg). This concept is important in hydraulic systems, as it allows us to calculate the total force that must be counteracted by the hydraulic pressure to lift a load.

Pascal's Principle

This principle states that in an enclosed fluid, an applied pressure change is transmitted undiminished to every portion of the fluid and to the walls of its container. It is the fundamental reason why hydraulic systems can multiply forces and is critical to understanding how a small input pressure can generate a large lifting force in a hydraulic lift.

Pressure and Force Relationship

Pressure is defined as the force applied per unit area (P = F/A). This relationship is central to hydraulic mechanics because it shows that for a given pressure, the total force exerted on a surface depends on the area of that surface. Applying pressure to a small area can be transmitted to a larger area to create a greater force.

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