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 = 9.69 times 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 1.72 times 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 10.37 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

Use pressure. P= F//A
Since the pressure in the hydraulic line must remain constant, the pressure on both piston heads will be the same.
F/A = F/A.
They are both circles, so pi will cancel.
F/R^2 = F/r^2
F/R^2 * r^2 = F
9/(9.50 x 10^-3)^2 * (1.90 x 10^-2)^2 = F = 36N

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