Approximations in Physics: A Pedagogic Perspective
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Approximations in Physics: A Pedagogic Perspective∗ K K Mashood, Arvind Kumar and Anwesh Mazumdar
This article reviews and illustrates some simple aspects of approximations in physics, which should be useful to students at the undergraduate level.
1. Introduction K K Mashood is a faculty
Approximations are encountered all too frequently in physics. Why are they so necessary? The simple reason is that real systems in nature are far too complex for physics to analyze them exactly in every detail. A macroscopic system (i.e. a system of ordinary length, mass and time scales), in general, will need a large number of variables to describe it fully, even if we ignore for the moment its microscopic constitution. For example, a rocket that is moving against gravity by jet action due to the exhaust of gases produced by some combustible substances inside has mixed mechanical, chemical and thermodynamic description, and it would be difficult if not impossible to analyze the system in its full detail. Instead, we handle the problem by ignoring some features and focusing on others, depending on our interest. For example, if our main interest is the motion of the rocket as a whole, we need to know only some mechanical variables (the original mass, the rate of mass depletion, the exhaust velocity relative to the rocket and gravitational acceleration.). The problem is then reduced to the standard variable mass problem in mechanics. Further approximations may be made to simplify the treatment such as taking exhaust velocity and gravitational acceleration to be constants; and so on. On the other hand, if our interest is in, say, the explicit calculation of the mass depletion rate and exhaust velocity, we will focus on the thermodynamics and chemical ki-
∗
member at the Homi Bhabha Centre for Science Education (TIFR). His interests are in physics education research and cognitive science.
Arvind Kumar was a faculty member at the Homi Bhabha Centre for Science Education (TIFR) till his retirement in 2008. His main interests are theoretical physics and physics education.
Anwesh Mazumdar is a faculty member at the Homi Bhabha Centre for Science Education (TIFR). His research interests include stellar astrophysics and physics education.
Vol.25, No.7, DOI: https://doi.org/10.1007/s12045-020-1009-8
RESONANCE | July 2020
915
GENERAL ARTICLE
Keywords Approximation, derivations, mod-
netics of the fuel and ignore for the moment the overall motion of the system.
elling, pedagogy.
This strategy of truncation of reality and approximate description of systems in nature is generally known as ‘modelling’, and it has worked wonderfully in physics. A model is not the real system; it aims to mirror approximately features or aspects of the system that interest us.
This strategy of truncation of reality and approximate description of systems in nature is generally known as ‘modeling’, and it has worked wonderfully in physics. A model is not the real system; it aims to mirror approximately features or aspects of the system that interest us
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