The drawing shows a hydraulic system used with disc brakes. The force vector 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 = 9.39 10-3 m) in the master cylinder. The resulting pressure is transmitted by the brake fluid to the output plungers (radii = 2.11 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 vector F is 6.98 N. Assume that the input piston and the output plungers are at the same vertical level and find the force applied
To find the force applied by the output plungers, we can use the principle of Pascal's Law, which states that the pressure in an enclosed fluid is transmitted uniformly in all directions.
Here's how we can calculate the force applied by the output plungers:
1. First, we need to find the pressure exerted on the fluid by the force vector F. We can do this by dividing the magnitude of F by the area of the input piston.
Area of the input piston = π * (radius of input piston)^2
Area of the input piston = π * (9.39 x 10^-3 m)^2
Pressure = Force / Area of the input piston
Pressure = 6.98 N / (π * (9.39 x 10^-3 m)^2)
2. Next, we can use Pascal's Law to calculate the pressure exerted on the output plungers. Since the pressure is transmitted uniformly in all directions, the pressure exerted on the output plungers will be the same as the pressure exerted on the input piston.
Pressure on the output plungers = Pressure on the input piston
3. Finally, we can find the force applied by the output plungers by multiplying the pressure on the output plungers by the area of each plunger.
Force on the output plungers = Pressure on the output plungers * Area of each plunger
Force on the output plungers = Pressure on the output plungers * (2 * π * (radius of output plungers)^2)
Force on the output plungers = Pressure on the output plungers * (2 * π * (2.11 x 10^-2 m)^2)
By substituting the value of the pressure on the input piston calculated in step 1 into step 3, we can determine the force applied by the output plungers.