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

Question

The drawing shows a hydraulic system used with disc brakes. The force F rightarrow 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 = 8.47 times 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii =2.06 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 rightarrow is 9.43 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

If there is no leverage involved then

.
f2 = 9.43 *( (2.06*10^-2)/(8.47*10^-3) )^2 = 55.780 N

But most pedals have leverage as well. So the foot is applied to one end and the master cylinder is close to the fulcrum.

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