# Water column displacement physics?

1. Oct 6, 2012

### alibaba2

Hi,
in this setup we have a bucket of water 10 kgs of water inside. Attached is a weight meter measuring that in fig a. The weight is exactly 10kgs.

In fig b. A piston (red) is being pulled by a weight (z).
"z" has a pull force equivalent to the volume of the column of water above the piston, so it will push the piston up into the bucket.

In fig c. The piston has reached a certain point, has raised the level of the water corresponding to the volume of the piston inside the bucket.

My question is:
During the whole process from fig a to fig c while the weight is pulling the piston upwards, does the weight meter show a decrease in the weight of the bucket due to the movement of the piston inside the water?

Does the meter say "10 kg"in fig b and fig c?
Does the movement of the piston lead to a temporary loss of weight due to the column of water above the piston being moved?
what will change if the piston is cone shaped (sharp) instead of rectangular?
Thanks

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Last edited: Oct 6, 2012
2. Oct 7, 2012

### Staff: Mentor

Do you want to consider the movement itself, or the stationary case (with negligible movement)? In the first case, I would try to evaluate the acceleration of z. This, plus a nice force diagram, will give the apparent weight of the bucket. If the water flow is not negligible, this might disturb the setup a bit. In the second case, that acceleration is 0.

3. Oct 9, 2012

### haruspex

What do you think the answer is, and why, in fig b?
Since the weight matches the water's inital pressure on the piston, yet movement can occur, I take it the piston is weightless. But once the piston has risen a little (fig c) the force from the water will be less, so the piston will accelerate. If the piston is massless then the only thing to prevent infinite acceleration will be the flow of the water, making the whole thing very complex. But since you only need a qualitative answer, I think you can work it out from there. I suppose the piston's weight could be balanced some other way (from below), so it could be weightless yet have mass.