The force F is applied perpendicularly to the brake pedal. The pedal rotates abo

Question

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 = 8.61 x 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 2.43 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 8.17 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

P= F//A
Since the pressure in the hydraulic line must remain constant, the pressure on both piston heads will be the same.
F1/A1 = F2/A2
They are both circles, so pi will cancel.
F/R^2 = F/r^2
F/R^2 * r^2 = F

F =8.17 *2.4*2.43*10^-4/8.61*8.61*10^-6

F = 63.4 N

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