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Question
(a) Verify that work input equals work output for a hydraulic system assuming no losses to friction. Do this by showing that the distance the output force moves is reduced by the same factor that the output force is increased. Assume the volume of the fluid is constant. (b) What effect would friction within the fluid and between components in the system have on the output force? How would this depend on whether or not the fluid is moving?
1. Please see the solution video.
2. Friction would make the work done in the slave cylinder ($W_2$) less than the work done on the master cylinder ($W_1$) since energy would be lost to friction. This is true only when the fluid is moving. Since $W_2 < W_1$, $F_2$ is reduced since $W_2 = F_2 d_2$. $d_2$ must stay the same, with or without friction, since the same volume of fluid would be displaced from one cylinder to the other, which means $F_2$ must reduce in order to make $W_2 < W_1$.
Solution Video