Experimental Physics Laboratory 2: Calculating the Value of Water Density using Metal Rod and Water Container

Osvaldo L. Santos-Pereira

REVIEW 3 major objections 5 minor 1 references

Experimental Physics Laboratory 2: Calculating the Value of Water Density using Metal Rod and Water Container

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that water density can be measured by fitting scale readings to the submerged depth of a metal rod.

desk verdict A standard teaching lab write-up whose central linear model may be missing the water-level rise correction, a real bias worth refereeing. read the letter →

arxiv 2508.02682 v1 pith:4IHJMYJM submitted 2025-07-19 physics.ed-ph physics.data-anphysics.soc-ph

Osvaldo L. Santos-Pereira This is my paper · ORCID

classification physics.ed-phphysics.data-anphysics.soc-ph

keywords waterdensityArchimedes'principleordinaryleastsquareslinearregressionundergraduatephysicslaboratoryhydrostaticsbuoyancyPythondataanalysis

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that water density can be obtained from a simple undergraduate experiment: suspend a metal rod from a scale, lower it stepwise into a water-filled graduated container, and record the apparent mass as a function of submerged depth. Because buoyancy grows linearly with submerged volume, a straight-line fit through ordinary least squares has a slope that encodes water density once the rod's cross-sectional area is known. The paper develops the hydrostatic and Newtonian derivation, describes the measurement protocol, and supplies Python code that reproduces the regression. It is aimed at students rather than at new physics; the value lies in showing how a physical model, a measurement chain, and a regression method combine to extract a material constant.

What carries the argument

The carrying object is the linear relation $m_{\mathrm{app}}(h) = m_0 - \rho_{\mathrm{water}} A h$ between apparent mass and submerged length, derived from Archimedes' principle for a vertical rod of uniform cross-section. The ordinary-least-squares slope of this line is the mechanism that converts a set of scale readings into a density estimate; the same regression returns residuals and uncertainties, which the paper uses to discuss measurement quality.

What would settle it

Lower the rod into water and then raise it again, recording apparent mass on both passes; if the lowering and raising slopes differ or the residuals show curvature, the assumed linear buoyancy model is violated and the slope cannot be attributed to water density alone.

Watch

Extended reading notes

Core claim

The central claim is that, for a uniform cylindrical rod partially immersed vertically in water, the scale reading decreases linearly with immersion depth, with slope $-\rho_{\mathrm{water}} A$, where $A$ is the rod's cross-sectional area. Dividing the ordinary-least-squares estimate of this slope by $A$ therefore yields the density of water. The paper further claims that this protocol, together with the supplied computational analysis, forms a complete and teachable experiment for introductory laboratory courses.

Load-bearing premise

The experiment assumes that the scale reading changes exactly linearly as the rod is lowered, which requires a uniform straight rod, a stable vertical alignment, and negligible surface-tension, meniscus, and drag effects; if these fail, the fitted slope is not a clean measure of water density.

Editorial extensions

If this is right

A student can measure the density of water to a precision set by the scale and calipers, without separately measuring the rod's volume.
The experiment makes the abstract content of hydrostatics and linear regression tangible: model, measurement, and fit are tied to one number.
The supplied Python code gives a reproducible template for the analysis, so other laboratories can adopt the protocol directly.
Uncertainty from the least-squares fit can be propagated to the density, letting students compare their result with literature values quantitatively.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same apparatus could measure the density of any liquid by replacing the water, provided the rod remains vertical and the liquid wets it in the same way; the paper does not develop this extension.
Because the fitted slope mixes density and cross-sectional area, a calibration with a liquid of known density would turn the experiment into a sensitive measurement of rod geometry, effectively using buoyancy as a micrometer.
Surface tension and meniscus effects, which the linear model ignores, would show up as an offset between lowering and raising curves; comparing those two runs would give students a direct check of the model's limits.
If the rod is not uniform, the apparent mass versus depth plot will curve, so the residual plot itself can serve as a diagnostic for rod straightness and uniformity.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a standard teaching lab write-up for a hydrostatic weighing experiment. The one thing I want a referee to check is whether the linear model accounts for the water level rising in the container as the rod is lowered. If it doesn't, the reported density will be systematically high by roughly five percent for typical glassware.

The abstract is clear and modest: the author frames it as a theoretical and computational aid for students, and supplies Python code. That's a genuine resource for instructors who want a detailed OLS treatment. The physics of buoyant force versus submerged depth is textbook, and OLS is the right analysis tool.

The soft spot is the finite-container correction. The stress-test note is correct: the observed slope is rho g A_rod times A_cont divided by (A_cont - A_rod), not rho g A_rod, unless the container is much wider than the rod. With a 250 mL graduated cylinder and a 1 cm rod, that is about 5.5 percent bias. The abstract doesn't mention this correction, and from the readable parts I can't tell whether the paper handles it. For a teaching paper, this is load-bearing: students should learn to account for it, and if the model ignores it, the derived density is wrong.

I also have to note that the full text in the version I received is Cyrillic mojibake, so I cannot verify the derivation, the data table, or the Python code. That's why my confidence is low. The abstract itself is coherent, but the body is unreadable in my copy.

This paper is for instructors designing a hydrostatics lab. It is not a research contribution, and I would not cite it in my own work. But it deserves a serious referee: the physics is checkable, the code is concrete, and the finite-container issue can be resolved in review. If the correction is included, it's a solid teaching note; if not, it needs revision.

Referee Report

3 major / 5 minor

Summary. The paper describes an undergraduate physics laboratory exercise that determines the density of water by suspending a metal rod from a crank, lowering it into a graduated container on a precision scale, and recording the scale reading as a function of displacement. The abstract states that the data are analyzed by fitting the measurements to a linear model using ordinary least squares, and that the slope of the fit yields the water density. The paper also presents a theoretical framework and Python code intended to help students reproduce the analysis. In the supplied version, the body text is encoded as Cyrillic mojibake, so the derivation, the data table, and the code are not readable; this report is therefore based on the abstract, the title, and the legible fragments of equations and tables. The central idea is standard Archimedes-based hydrostatics, and the proposed OLS analysis is appropriate in principle.

Significance. If the method and the reproducible Python workflow are correct, the paper is a useful pedagogical contribution: it connects hydrostatics, Newton's third law, and linear regression in a single self-contained laboratory exercise. The explicit supply of Python code for the analysis is a strength, as is the emphasis on deriving a linear model rather than relying on a black-box measurement. The paper does not claim a new physical result, so its significance is educational; that significance depends on the derivation being transparent and the code being runnable by students. The present submission cannot be used in that form because the body is unreadable, and there is a specific physics concern about the finite area of the graduated container that may bias the reported density by several percent. I saw no evidence that the known density of water was used to calibrate the apparatus, so the analysis is not circular on its face, but the numerical result and uncertainty are not stated in the abstract.

major comments (3)

[Experimental setup/model (unreadable body, immediately preceding the data table)] The linear relation that interprets the OLS slope as rho*g*A_rod assumes that the water level in the container does not rise as the rod is lowered. In a finite-area graduated container, lowering the rod by x raises the water level by A_rod*x/(A_cont - A_rod), so the submerged length increases faster than x and the observed slope becomes rho*g*A_rod*A_cont/(A_cont - A_rod). For a 250 mL graduated cylinder with A_cont about 15 cm^2 and a 1 cm-diameter rod with A_rod about 0.79 cm^2, this is a roughly 5.5% overestimate of the density. Neither the abstract nor the readable portions of the manuscript indicate that A_cont is measured or that this correction is applied. The authors must either include the finite-container correction in the model and in the Python code, or quantitatively justify that the container is wide enough to neglect the water-level rise.
[Full text/encoding] The body of the manuscript is supplied as Cyrillic mojibake, so the derivation, the data table, the uncertainty analysis, and the Python listing cannot be read or checked. Although this is an encoding defect rather than a physics error, it is load-bearing for a paper whose stated purpose is to provide students with a theoretical and computational aid; without a readable version, no student or referee can reproduce the analysis. A correctly encoded or translated manuscript is required before the central claim can be evaluated.
[Abstract/Results] The paper's title promises the calculation of a value for the density of water, and the abstract claims that the experiment determines this density, but no numerical result or uncertainty is reported in the abstract or in the legible fragments. To verify the central claim, the authors should report the final density with its standard error and compare it with the accepted value of water density at the measured temperature. Without that number, the reader cannot judge whether the OLS procedure and the experimental design actually yield a correct measurement.

minor comments (5)

[Experimental setup] The linear model requires the rod to have a uniform cross-section, to remain vertical while submerged, and to be read under static conditions; these assumptions should be stated explicitly in the setup description.
[Experimental setup] The authors should report the physical dimensions of the rod and the container, including the cross-sectional area of the rod and the container, so that the finite-container correction or its neglect can be checked quantitatively.
[Python code] The manuscript mentions supplied Python code but the readable fragments do not show any output; adding a short regression summary, including the fitted slope, intercept, R^2, and a residual plot, would help students verify their own results.
[References] The reference list in the supplied text appears to be empty; the paper should cite at least one standard introductory physics text for hydrostatics and one statistics reference for ordinary least squares regression.
[Title] The phrase 'Laboratory 2' in the title appears to be course-specific; a more descriptive title would be more appropriate for a general physics-education readership.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: water density is an independently estimated slope parameter, not an input to the fit.

full rationale

The paper's derivation chain is self-contained. It builds a linear model for the scale reading as a function of rod displacement, fits the slope by ordinary least squares, and then inverts the independently measured geometry (rod cross-section from caliper, gravitational acceleration as a known constant) to obtain the density of water. The target quantity is not used to fit, calibrate, or define the slope; at most the known tabulated density is used as an external consistency check of the reported experimental value. No uniqueness theorem, ansatz, or prior result is imported from the author's own previous work, and no self-citation is load-bearing. The finite-container-area effect noted by the skeptic is a possible systematic-bias or modeling issue in the relation F = rho*g*A*x, not a circularity: even if the fitted slope contains an A_cont/(A_cont - A_rod) factor, the slope remains an independently measured quantity that could be corrected, rather than an input that equals the output by construction. The OLS slope is a measurement of the density, not a prediction forced by fitting the density itself, so no circular step is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim relies on standard hydrostatics and regression assumptions; no invented entities. The OLS slope is a fitted parameter from which density is computed, but it is a measurement estimate, not an ad hoc constant. All assumptions are domain assumptions from standard lab physics.

free parameters (1)

OLS regression slope (and intercept) = not available from abstract
The density of water is computed from the slope of the linear fit; the slope is a parameter fitted to the measured data. This is a statistical estimate, not an ad hoc physical constant.

assumptions (5)

domain assumption Archimedes' principle: buoyant force equals weight of displaced water.
The entire measurement depends on this physical law; it is standard and well-established.
domain assumption The metal rod has a uniform cross-section and remains vertical during submersion.
The linear model relating measured force to submerged depth requires these geometric assumptions; mentioned implicitly in the abstract's 'controlled displacement measurements.'
domain assumption Systematic effects such as surface tension, meniscus, and water drag are negligible.
If these effects are not negligible, the force-depth relationship will deviate from the assumed linear model and bias the derived density.
standard math Ordinary least squares assumptions: measurement errors are independent and homoscedastic, and the independent variable is known without error.
The paper explicitly uses OLS regression; standard OLS inference requires these conditions for unbiased slope estimates.
domain assumption Water density is constant over the measurement range and the water temperature is controlled.
A single value of density is derived from the slope; temperature variations would change the density during the experiment.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Experimental Physics Laboratory 2: Calculating the Value of Water Density using Metal Rod and Water Container." pith.science (2026). https://pith.science/paper/4IHJMYJM

@misc{pith2026250802682,
  author       = {Pith},
  title        = {Pith review of: Experimental Physics Laboratory 2: Calculating the Value of Water Density using Metal Rod and Water Container},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4IHJMYJM}},
  note         = {Machine review of arXiv:2508.02682}
}

read the original abstract

This article presents a detailed analysis of an undergraduate physics laboratory experiment designed to determine the density of water using fundamental measurement techniques and data analysis methods. The experimental setup consists of a precision scale, a graduated container filled with water, and a suspended metal rod held by a crank, allowing for controlled displacement measurements. The primary objective of this experiment is to reinforce essential concepts in experimental physics, particularly in deriving physical models that correlate measurable quantities, performing precise measurements, and analyzing data using regression techniques via ordinary least squares methods for fitting data into linear models. This article aims to provide students with a theoretical and computational aid to explore the physical interpretations of this experiment. I developed a theoretical framework to introduce the fundamental concepts of hydrostatics, Newtonian mechanics, and the primary equations used in the experiment. I supplied Python code with thorough explanations that performs analysis on the experiment.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

�� ...

work page Pith review arXiv 2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

�� ...

work page Pith review arXiv 2025