The small piston of a hydraulic lift (Fig. P15.6) has a...

The small piston of a hydraulic lift (Fig. P15.6) has a cross-sectional area of $3.00 \mathrm{cm}^{2},$ and its large piston has a crosssectional area of $200 \mathrm{cm}^{2}$ What downward force of magnitude $F_{1}$ must be applied to the small piston for the lift to raise a load whose weight is $F_{g}=15.0 \mathrm{kN} ?$

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Key Concepts

Pascal's Principle

Pascal's principle states that any change in pressure applied to an enclosed fluid is transmitted uniformly in all directions throughout the fluid. This foundational idea allows hydraulic systems to multiply forces, as a small force applied on a small-area piston creates an equal pressure throughout the fluid, which then acts on a larger-area piston to exert a larger force.

Hydraulic Systems

Hydraulic systems use an incompressible fluid to transfer force from one piston to another. They exploit the area difference between pistons to amplify input forces. This means that a relatively small force acting on a smaller piston can lift a much larger load on a bigger piston due to the proportional relationship between force and area.

Pressure

In mechanics, pressure is defined as the force exerted per unit area. In hydraulic systems, the pressure created by a force acting on one piston is transmitted equally throughout the fluid to act on another piston. The relationship between force, pressure, and area (Pressure = Force/Area) is crucial in determining how much force is required on one side of the system to achieve a desired force on the other side.

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