To find the force acting on the master cylinder, we can use the principle of moments. The moment about a point is the product of the force and the perpendicular distance from the point to the line of action of the force.
1. Force acting on the master cylinder:
The formula for the moment is: Moment = Force x Distance
We know that the load distance is 70mm and the effort distance is 280mm. Let's call the force acting on the master cylinder F_master.
Using the principle of moments, we can set up the equation: F_master x 280mm = 450N x 70mm
Simplifying the equation, we find: F_master = (450N x 70mm) / 280mm
2. Brake line pressure:
The brake line pressure can be calculated using the formula: Pressure = Force / Area
The area of the master cylinder can be found using the formula: Area = π x (radius)^2
The radius of the master cylinder is half of the diameter, which is 28.6mm / 2 = 14.3mm
Converting the radius to meters: 14.3mm / 1000 = 0.0143m
Now, we can calculate the area: Area = π x (0.0143m)^2
The pressure can be found using the formula: Pressure = F_master / Area
3. Operating force of front and rear cylinders:
To find the operating force of the front and rear cylinders, we need to use the principle of hydraulic pressure. In a hydraulic system, pressure is transmitted equally throughout.
The pressure acting on the front and rear cylinders will be the same as the brake line pressure.
Using the formula: Force = Pressure x Area
For the front cylinder: Force_front = Pressure x Area_front
For the rear cylinder: Force_rear = Pressure x Area_rear
By following these steps, you should be able to calculate the force acting on the master cylinder, the brake line pressure, and the operating force of the front and rear cylinders. Remember to substitute the appropriate values into the formulas and use the correct units for your calculations.