Final answer:
The statement about dual master cylinders failing together is false; they are designed for redundancy. They provide safety by ensuring that if one circuit fails, the other remains operational. The hydraulic system principles dictate the pressure transmission and force multiplication according to the ratios of cylinder areas and diameters.
Step-by-step explanation:
The statement 'Dual Master Cylinders work together in such a way that if one fails, they both fail' is false. Dual master cylinders are engineered to have two separate circuits for redundancy. The function of dual master cylinders is that if one circuit fails, the other will still be operational, ensuring that some braking power remains, thereby enhancing safety. This is crucial in automotive braking systems.
These principles state that the pressure applied in a hydraulic fluid is distributed evenly throughout the system. According to Pascal's Law, the pressure applied at one point will be transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. When this principle is applied with different-sized cylinders, you can achieve multiplication of force.
For a system designed to exert a force 100 times as large as the input, the ratio of the areas of the slave and master cylinders would have to be 100:1. For the ratio of their diameters, you would square root the area ratio since the area is proportional to the square of the diameter. Lastly, the distance through which the output force moves will be reduced by a factor equal to the inverse of the force ratio, due to the conservation of energy, assuming no friction losses.