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 = 8.62 x 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 2.37 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 8.72 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

The input piston radius rin = 8.62*10^-3m

 The radius of the output flunger rout = 2.37*10^-2m

The input force F = 8.72N

 From pascal law

since when the input and output levels are at same heigth the pressure is same

so    Fin/Ain = Fout /Aout

 Then  Fout = (Aout/Ain) Fin

              = ( rout^2 / rin^2) Fin

             =(2.37*10^-2m)^2 /(8.62*10^-3m)^2 ( 8.72 N ) = 65.92 N

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