A hydraulic jack whose piston has a cross-sectional area of 115 cm^2 supports a pickup truck we

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A hydraulic jack whose piston has a cross-sectional area of...

A hydraulic jack whose piston has a cross-sectional area of $115 \mathrm{~cm}^{2}$ supports a pickup truck weighing $1.20 \times 10^{4} \mathrm{~N}$. Compressed air is used to apply a force on the second piston with cross-sectional area $25.0 \mathrm{~cm}^{2} .$ How large must this force be to support the truck?

Key Concepts

Pascal's Principle

Pascal's Principle states that when pressure is applied to a confined incompressible fluid, the pressure change is transmitted equally in all directions. This principle is fundamental in understanding how hydraulic systems work, as it allows a small force applied at one part of the system to be transformed into a larger force at another part, depending purely on the areas over which the forces are applied.

Pressure and Force Relationship

The relationship between force, pressure, and area is expressed by the formula P = F/A, where P is pressure, F is force, and A is the area over which the force is distributed. This relationship is crucial in hydraulic systems because it shows how a given force can create a certain pressure in the fluid, which, when applied across a different area, produces a new force. It underpins how varying piston areas can amplify or diminish forces.

Mechanical Advantage in Hydraulic Systems

Mechanical advantage in hydraulic systems describes how a smaller input force can generate a larger output force due to differences in piston areas. This is achieved by applying a force to a piston with a small area, which creates a pressure that, when transferred to a piston with a larger area, results in a proportionally larger force. This concept is critical in designing devices like hydraulic jacks, where significant loads are lifted with relatively small input forces.

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