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

Question

The drawing shows a hydraulic system used with disc brakes. The force Frightarrow 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 = 8.45 times 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 1.48 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 Frightarrow is 6.40 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 pressure applied on a fluid is transmitted without loss across it.

the pressure at the input piston = F/A where A is the area of the piston

= 6.4/pi*r^2 = 6.4/pi*(8.45*10^-3)^2 = 28530.95 pascal

this pressure is transmitted along to the out put piston.

force at the poutput piston = P*A

= 28530.95 * pi*(1.48*10^-2)^2 = 19.62N at EACH of the output brakes.

so a total force of 39.2 N on the wheel

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