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 slave cylinder 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 to friction.
Step-by-step solution Step 1 o f 10 In the hydraulic lift, the pressure is same on the master and the slave cylinder but force changes with the change in cross section area. Pascal’s principle for hydraulic system is, Step 2 o f 10 (a) The relation between force and cross section area is, …… (1) Here is force applied to master cylinder, is cross sectional area of master cylinder, is force created at each of the slave cylinder, is cross sectional area of slave cylinder. Step 3 o f 10 Force applied at system is so the force exerted on system is 100 times the applied force. Therefore, From equation (1) Step 4 o f 10 Substitute in the above equation, Step 5 o f 10 Hence, the ratio of the area of the slave cylinder to the area of master cylinder is .