5th December 2007 - 04:26 AM
Since the big tube has 4 times the area of the small tube, the 200N force will be amplified by 4 times for a total of 800N.
But note that when the small syringe is pushed in "one unit"'s distance, the large syringe will move only "1/4 unit"'s distance. Thus, energy is conserved since the work done on input (Force times distance) will be the same for input and output: 1x200 = 1/4x800. You can see also that an equal amount of fluid is transfered from one tube to the other (well, it has to since it's got no where else to go) so just by computing the result of moving a given volume of fluid from one sized tube to another sized tube the distances work out.
This setup is the so-called "hydraulic princple" that makes all those big earth-moving machines practical. It's essentially a lever-arm for liquids.
Edit: I just found a small article discussing this at: Hydraulics