The drawing shows a hydraulic system used with disc brakes. The force F is appli
ID: 2204083 • Letter: T
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 = 9.42 x 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 2.32 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 7.00 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 drawing shows a hydraulic system used with disc brakes. The force 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 = 8.10 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 1.31 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 is 11.27 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 dis The hydraulic amplification is proportional to the area ratio between the master cylinder and the plungers. The area ratio is proportional to the square of the radii k = (1.31e-2/8.1e-3)**2 = 2.6156... So if the input force is 11.27 N the output is Fout = k*11.27 = 29.5 N This seems light, so in the diagram that I can't see, there is probably a moment arm between where the force is applied and the master cyclinder. You would multiply by the lever ratio as well to get the final answer. =)
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