# Work by a variable force

"A cylindrical tank of height h is half full of water, all of which is to be pumped up over the side of the tank. If the total mass of the water is m, how much work must be done by the pump?"

At first I tried this the easy way by simply assuming that I need to pump a mass m up to a height h, so the work would be just mgh, but somehow the result should be (3/4)mgh, I guess I have to account for the fact that not all the water comes from the same height, I however have no idea how to express this mathematically.

## Answers and Replies

Well, the average distance along which the force FG acts is 3/4h (h is the height of the tank) - you can think of all the mass being situated in this height.

I dont understand, it says that the tank is half full.

Doc Al
Mentor
The top layer of water needs to be raised a distance h/2 while the bottom layer needs to be raised the full distance h. Thus the average height that each element of water needs to be raised is 3h/4.