arXiv subjects

Kazumasa Kushida

Publications and source records attributed to Kazumasa Kushida.

2 recordsLinked to original sources

arXiv2026

Data-driven modeling in the introductory physics laboratory: Scaling analysis and data collapse in the specific heat of water experiment

In introductory physics laboratories, a central instructional goal is to help students construct and evaluate mathematical models from empirical data rather than applying given formulas. We present a data-driven redesign of the classic specific heat of water experiment that emphasizes scaling analysis and data collapse as tools for model construction. The activity combines structured experimental and analytical guidance with instructor-mediated questioning, while thermodynamic theory is deliberately postponed. Students collect temperature-time data under various experimental conditions, producing multiple data sets that initially appear unrelated. Through successive rescaling, students reduce the dimensionality of the variable space and achieve data collapse onto a single master curve, from which they formulate an empirical model relating energy input, mass, and temperature change. The analysis highlights a limitation of multiplicative scaling: the additive contribution of the calorimeter cannot be eliminated, leading to a structural non-identifiability of the subsystem contributions. To clarify the domain of validity of the model, a thermodynamic description is introduced a posteriori as a boundary-setting framework for interpreting the empirical model. In this sense, the central contribution of this work is to use data-driven modeling both to construct models and to reveal their intrinsic limitations. The experiment provides an accessible example of how scaling, data collapse, and theoretical reasoning can be integrated in an introductory laboratory.

physics.ed-ph↗

arXiv2026

From data to structure: Construction, breakdown, and reconstruction of an empirical representation in a black-box RC circuit

In introductory physics laboratories, a central instructional goal is to help students construct, evaluate, and revise mathematical representations from experimental data rather than apply given formulas. We present a guided data-driven activity in which an RC circuit is treated as a black box defined through observable input-output relations. Experimental and graphical procedures are provided, while standard RC circuit theory is initially withheld. Students first examine discharging data obtained under different nominal values of R and C. They rescale time using T=t/RC and compare the normalized voltage v=V/E across circuit conditions, bringing the discharging data closer to a common trajectory. Graphical linearization through a plot of lnv versus T provides a basis for proposing an empirical representation and allows RC to be interpreted as a time scale rather than being assigned that meaning a priori. When the representation proposed for discharging is tested with charging data, logarithmic linearity is lost despite the continued organization of the data by T. Replacing v with the distance from the steady state, 1-v, restores linearity, and the resulting linear relation provides a basis for proposing a revised representation for charging. The activity thus uses a familiar physical system to make representation construction, breakdown, and reconstruction experimentally explicit. It also emphasizes that an empirical representation must be accompanied by a specified domain of validity and that standard circuit theory can be introduced a posteriori to interpret the physical meanings that emerge from representational constraints.

physics.ed-ph↗