The output area A1 of the piston in the hydraulic press in...

The output area $A_{1}$ of the piston in the hydraulic press in Fig. $13-3$ is $400 \mathrm{~cm}^{2}$, and it supports a load of $600 \mathrm{~kg}$. What must be the input area $A_{2}$ if an input force of $100 \mathrm{~N}$ is to keep the load in equilibrium?

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Key Concepts

Mechanical Advantage in Hydraulics

Hydraulic systems provide mechanical advantage by allowing a small input force to generate a much larger output force when applied to pistons of different areas. By designing the system with a smaller piston for the input and a larger piston for the output, the force is multiplied, making it easier to lift heavy loads.

Pascal's Principle

This principle states that any change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid. In the context of hydraulic systems, it means that the pressure generated by the input force on one piston is evenly distributed to the other piston, regardless of the difference in their areas.

Pressure and Force Relationship

Pressure is defined as force per unit area. In hydraulic systems, knowing the pressure allows us to calculate the force on any piston by multiplying the pressure by the piston’s area. This relationship is crucial for setting up equilibrium between pistons of varying sizes.

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