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 cylinder that is being controlled to the area of the master 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 due to friction.

(a) 1:100
(b) 1:10
(c) 10:1
(d) 100:1

Answer 1

The ratio of the area of the cylinders in a hydraulic system with a force ratio of 100:1 is 1:10. The ratio of their diameters is also 1:10. The distance through which the output force moves is reduced by a factor of 10:1 compared to the input force.

Step-by-step explanation:

The ratio of the area of the cylinder that is being controlled to the area of the master cylinder can be determined by the force ratio. Since the hydraulic system is designed to exert a force 100 times larger than the input force, the area ratio must be the square root of the force ratio. Therefore, the ratio of the areas is 1:10.

The ratio of the diameters of the cylinders can be found by taking the square root of the area ratio. Therefore, the ratio of their diameters is also 1:10.

Finally, the factor by which the distance through which the output force moves is reduced relative to the input force can be determined using the area ratio. Since the output force is 100 times larger than the input force, the distance ratio is the reciprocal of the square root of the area ratio. Therefore, the distance ratio is 10:1.