Two hydraulic piston/cylinders are connected with a line....

Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of $5 \mathrm{cm}^{2}$, creating a pressure of $1000 \mathrm{kPa}$. The slave cylinder has an area of $3 \mathrm{cm}^{2}$. If $25 \mathrm{J}$ is the work input to the master cylinder, what is the force and displacement of each piston and the work output of the slave cylinder piston?

Key Concepts

Mechanical Advantage

Hydraulic systems utilize the difference in piston areas to create a mechanical advantage. A small input force over a larger displacement can be converted into a larger output force over a smaller displacement, allowing for amplification of force in the system.

Conservation of Energy

This concept ensures that in an ideal hydraulic system, the total energy (work input) is equal to the total energy (work output), even though the force and displacement may be different at different points in the system. It underpins the calculations relating work at the master and slave pistons.

Pascal's Principle

This principle states that when pressure is applied to an enclosed fluid, it is transmitted equally in all directions throughout the fluid. This forms the basis for hydraulic systems, where force applied at one piston is transferred with the same pressure through the fluid to another piston.

Pressure

Pressure is the amount of force exerted per unit area. In hydraulic systems, knowing the pressure and the area of a piston allows you to calculate the force exerted on that piston by using the relationship Pressure = Force/Area.

Work and Energy

Work is defined as the product of force and the displacement in the direction of the force. In hydraulic systems, the work input into one piston is transferred through the fluid and becomes the work output of the other piston, assuming there are minimal energy losses.

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