The drawing shows a hydraulic system used with disc brakes. The force F is appli

Question

The drawing shows a hydraulic system used with disc brakes. The force F is applied perpendicularly to the brake pedal. The pedal rotates about the axis shown in the drawing and causes a force to be applied perpendicularly to the input piston (radius = 8.06 x 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 2.75 x 10-2 m), which are covered with the brake linings. The linings are pressed against both sides of a disc attached to the rotating wheel. Suppose that the magnitude of F is 6.44 N. Assume that the input piston and the output plungers are at the same vertical level, and find the force applied to each side of the rotating disc.

Explanation / Answer

According to Pascal's law, pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions.
P1 = P2
Pressure = Force/Area
F/A1 = F2/A2
F2 = (A2/A1) x F
F2 is the force appplied to the disc
F is the input force
A1 = pi x (8.06 x 10-3)2 = pi x 64.9636 x 10-6 m2.
A2 = pi x (2.75 x 10-2)2 = pi x 7.5625 x 10-4 m2.
A2/A1 = 11.64
F2 = 6.44 x 11.64 = 74.9616 N

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