Final answer:
In a hydraulic system designed to increase force by 100 times, the area ratio of the wheel cylinder to the pedal cylinder should be 100:1, the diameter ratio should be 10:1, and the distance moved by the output force is reduced to 1/100th that of the input force.
Step-by-step explanation:
The question pertains to a hydraulic system that has a force multiplication factor of 100.
(a) Ratio of area of the wheel cylinder to the pedal cylinder
To determine the area ratio for the system designed to exert an output force that is 100 times greater than the input force, we use Pascal's Principle, which states that pressure is equally distributed throughout a fluid. Thus, if F1 is the input force applied to the pedal cylinder with area A1, and F2 is the output force from the wheel cylinder with area A2, the ratio F2/F1 = 100 must equal A2/A1. Therefore, the area ratio A2/A1 must be 100:1.
(b) Ratio of their diameters
The area of a circle is proportional to the square of its diameter. Therefore, if we have the area ratio, the diameter ratio is the square root of the area ratio. The diameter ratio d2/d1 would then be √100, which is 10:1.
(c) Factor by which distance moved by output force is reduced
Conservation of energy dictates that the work input must equal the work output (assuming no losses to friction). As work is the product of force and distance (W = F × d), for the output work to be equal to the input work with a force 100 times greater, the distance moved by the output force must be 1/100th the distance moved by the input force.