Question

A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the wheel cylinder to the area of the pedal cylinder? (b) What must be the ratio of their diameters? (c) By what factor is the distance through which the output force moves reduced relative to the distance through which the input force moves? Assume no losses to friction. What must be the ratio of the area of the wheel cylinder to the area of the pedal cylinder?

A. Ratio = 100
B. Ratio = 10
C. Ratio = 1/10
D. Ratio = 1/100

Answer 1

In a hydraulic system, the ratio of the area of the wheel cylinder to the area of the pedal cylinder must be 100 times larger to exert a force 100 times as large. The ratio of their diameters must also be 100. The distance through which the output force moves is reduced by a factor of 100 relative to the distance through which the input force moves.

Step-by-step explanation:

In a hydraulic system, the ratio of the area of the wheel cylinder to the area of the pedal cylinder must be 100 times larger to exert a force 100 times as large. This is because the force exerted by a hydraulic system is directly proportional to the area on which the force is applied. The ratio of their diameters will also be the same as the ratio of their areas. Therefore, the ratio of their diameters must also be 100.

The distance through which the output force moves is reduced relative to the distance through which the input force moves by the same factor as the ratio of the force. In this case, the output force is 100 times larger than the input force, so the factor by which the distance is reduced is also 100.