The diameter of the large piston of a hydraulic press is 20...

The diameter of the large piston of a hydraulic press is $20 \mathrm{~cm}$, and the area of the small piston is $0.50 \mathrm{~cm}^{2}$. If a force of $400 \mathrm{~N}$ is applied to the small piston, $(a)$ what is the resulting force exerted on the large piston? (b) What is the increase in pressure underneath the small piston? ( $c$ ) Underneath the large piston?

Key Concepts

Pressure Calculation

Pressure is defined as the force applied per unit area and is calculated using the formula P = F/A, where P is the pressure, F is the force, and A is the area. This concept is crucial in understanding how forces are transmitted in hydraulic systems and how changes in area affect the pressure distribution.

Force Multiplication in Hydraulic Systems

In hydraulic systems, the force exerted by or on a piston is related to its cross-sectional area. The larger piston can exert a greater force than the smaller piston if the pressure is constant throughout the fluid. This force multiplication is achieved by taking the ratio of the areas of the two pistons, enabling small input forces to generate large output forces.

Pascal's Principle

This principle states that any change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid in all directions. It is the foundational concept behind hydraulic systems, where a force applied on a small-area piston results in a proportionally larger force on a larger-area piston, due to the uniform pressure transmission.

Area Calculation for Circular Pistons

Since pistons are typically circular, calculating the area of a piston involves using the formula A = ?r², where r is the radius of the circle. This geometric calculation is essential to determine the areas of the pistons, which in turn is necessary for computing the pressure and the resulting forces in hydraulic systems.

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