Bubble in water tank affects overall weight?

[Cri85]

I would like to think with forces and the distance only. The work is the force by the distance, if the bubble accelerates and moves up when the container move down from A to B with a constant velocity: the force F works from A to B. Then if the weight is lower or higher (it was logical it is higher if the bubble accelerates to up, the water accelerates to the bottom), the work from the weight is lower/higher too, Fd. The center of mass can move, but forces are applied to the bottom of the container, not in the center of mass. So, if I want to calculate the work from F I must draw another force ?

http://imageshack.com/a/img905/5034/IebquJ.png

 

[jbriggs444]

Force F times distance d is the work done by the container on the generator/restraining mechanism. Yes. That force is reduced because the water is accelerating downward with respect to the container.

Energy is conserved -- the work done by the generator/restraining mechanism on the container is the negation of this quantity of work.

Then you can consider the work done by the container on the water and the work done by the water on the container. That part is more difficult. Water is not rigid. It can absorb mechanical energy. The work done across the interface between water and container (computed by multiplying the force supporting the water by the motion of the container) is not equal to the pseudo-work (computed by multiplying the force supporting the water by the motion of the water's center of mass). Energy is still conserved. The difference manifests as turbulent energy in the water.