There has been a lot of interesting discussion about Blake Farrow's and Laszlo Mihaly (May 21) problems of the week. A lot of smart people were getting confused, and only now things are appearing to settle down as everyone begins to understand what they've got wrong. However, this story still has a few loose ends that are being hard to wrap my head arround, and I hope with this discussion things become clearer.
All the confusion in those problems seem to arise from the same place: the relation between internal forces of the fluid flow and the motion of the center of mass. So I'll highlight the two statements that are making me confused:
1.(This is a response by Michael Mendrin in a comment by Laszlo Mihaly in Michael's solution to the basic problem):
I got burned with that explanation, "...since the center of mass is steady, there is no change in weight". Well, turns out that it's not so simple in a gravitational field or accelerating frame. What we can say is that in a steady state system, with unchanging center of mass, there won't be any changes in weight. That doesn't mean it weighs the same as when things were not moving.
We can all have more argument about this claim, I'd love to hear them. I'd like a more careful explanation why is this necessarily so. Very fascinating subject, let's not give up on this.
Is this correct? Is it true that in an accelerating frame of reference, you can have a system with some center of some center of mass and some moving parts that weigh more than when the system is still, even if the center of mass stays in the same place? How is this not a system exerting a force on itself? Can someone give an example of such a system?
2.(This is a comment by Steven Chase in Blake Farrow's solution to the advanced problem)
Yeah, it's all about the acceleration of the COM. The scale is completely indifferent to the internal forces involved.
Okay, as far as I know, there are 2 ways of solving a problem like this, one is by considering the internal forces involved, like on Laszlo Mihaly's Solution on the basic problem, the other (astonishingly easyer) way is by considering the motion of the center of mass, like on Arjen Vreugdenhil's solution on the basic problem again. But the thing is that, as far as I know, those should always give the same results, in other words, weight increase due to center of mass acceleration can always be translated into a net force due to the internal forces. The acceleration of the center of mass does change the weight, but for that, something has to push down on the scale, and this something are the internal forces, right? If that is the case, how do we explain the phenomena in the advanced problem) using only the effects of internal forces? (wow, I said "internal forces" a lot)
Contributions are greatly apreciated.