Figure P14.68 shows the essential parts of a hydraulic brake...

Figure P14.68 shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is $1.8 \mathrm{cm}^{2}$ and that of the piston in the brake cylinder is $6.4 \mathrm{cm}^{2} .$ The coefficient of friction between shoe and wheel drum is $0.50 .$ If the wheel has a radius of $34 \mathrm{cm}$ determine the frictional torque about the axle when a force of $44 \mathrm{N}$ is exerted on the brake pedal. (FIGURE CANT COPY)

Key Concepts

Pascal's Principle

Pascal's Principle is a fundamental concept in fluid mechanics stating that when pressure is applied to a confined fluid, the pressure change is transmitted uniformly in all directions. This principle is central to the operation of hydraulic systems where a force applied on a small piston results in an equivalent pressure being exerted on a larger piston, amplifying the force.

Force Multiplication by Area Ratio

In hydraulic systems, force multiplication occurs due to the difference in the areas of the master and slave cylinders. The ratio of these areas amplifies the input force, allowing a relatively small force exerted on the master cylinder to generate a larger output force on the slave cylinder.

Coefficient of Friction and Frictional Force

The coefficient of friction quantifies the resistance between two contacting surfaces. In braking systems, the frictional force generated is the product of the normal force and the coefficient of friction, which plays a critical role in transferring the hydraulic force into a resistive force that slows the system.

Torque Calculation

Torque is the measure of the turning force on an object and is calculated as the product of the force applied (in this case, the frictional force) and the radius at which the force is applied. This concept helps determine the frictional torque about the axle in braking systems.

Mechanical Advantage

Mechanical advantage refers to the amplification of an input force to achieve a greater output force. In brake systems, both the hydraulic subsystem (through the area ratio) and the lever arm provided by the wheel's radius contribute to the overall mechanical advantage, enhancing the system's efficiency.

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