Dimensional analysis and qualitative methods in problem solving

Abstract

The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y (the unknown) is a function f of other physical quantities A1, …, An (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition of the original problem into simple special cases. By simple special cases we mean special cases for which, by DA, the unknown function can be completely determined except for a dimensionless multiplicative constant. The concept of significant special representation of the unknown function is introduced.

Going Beyond Equations With Disciplinary Thinking In First-Year Physics

“…In applying PBT, important factors include: clarity of concepts and definitions, ability to make suitable assumptions (Fortus, 2009), understanding of the knowledge structure (Bagno, Eylon, & Ganiel, 2000;Ferguson-Hessler & de Jong, 1987;Snyder, 2000), facility in employing multiple representations (Kohl & Finkelstein, 2008) and dimensional analysis (Miller, 1952;Misic, Najdanovic-Lukic, & Nesic, 2010;Pescetti, 2008). In some situations, multiple graphing techniques are also useful, and can enhance appreciation of the different features of the data related to a problem .…”

Dimensional analysis in physics and the Buckingham theorem

“…the corresponding asymptotic behaviour of the function in the expression 0 = ( 1 ). According to [12], if we assume that 1 < 0, then the quantity 0 essentially depends on 1 if this is true…”

The Role of Dimensional Analysis in Teaching Physics

“…For example, this facet of dimensional analysis had been used to derive the gravitational power radiated by a celestial body that moves in a circular orbit, 7 the resistance force of a fluid that occurs when a body moves through it, 8 and the speed of the propagation of waves on water. 8 The number of works in the recent literature [9][10][11][12][13] attest to the enormous utility of this method in various disciplines of physics.…”