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I have a physics lab tomorrow and I would appreciate it if you could give me your opinion on whether my reasoning is correct for this situation or not:


The title of the lab is hydrostatic and is roughly described in the attached pic. We will take data using different weights to measure the deformation of the spring and the increase in the level of the water (yes, the fluid is water) and the thing that we have to find is the spring constant "k" but (and my professor was very clear about it) for the whole system.

Now I am having some doubts, but I think that he means that we have to find some function of F that uses d (deformation of the spring) and h (increase in water height) and then we'll use least squares (done this in previous labs) to find the constant k, what I'm currently thinking is

F = restitution force of the spring

m = mass of the submerged body
d = deformation of the spring h = increase in water level
W= weight of the submerged body
B = buoyant force
V= volume of the displaced liquid / small body

B=d(water density)*V*g


Taking upwards as positive


but now I have to find either a) the volume of the displaced fluid or the volume of the body, both of these are not data (or can't be found without the dimensions of the container or the small body as far as I know) at all, the Buoyant force has to be smaller than the weight since it's at equilibrium only after the spring force begins acting

Is my current train of thought correct?

1) since the difference in water level changes with different masses I think it's safe to assume that the body to be submerged is not completely inside from the beginning, since if it were that way after adding more masses the total displaced volume would not increase

II) Still having troubles with the F = W - B part, since I really can't figure how to calculate the Buoyant force without the volume of the object or the water displaced and I can't find the one of the water displaced since I do not know the dimensions of the container.

III) the most smart course of action seems to be to find F using only B and W and then use that F with d (spring deformation) to find ''k"

IV) I can't grasp what would happen if the mass were to get so big that the body would be completely submerged and "h" would stop growing but it's probably not going to happen in the laboratory

I have a feeling I'm missing something really obvious and even a small push in the right direction would be nice

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This is actually a really cool question because it is used as an example in renormalization theory. That is, see equation (1) through (2) in: arxiv.org/abs/hep-th/9912092 –  Carl Brannen Feb 26 '11 at 0:51

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