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why do you make the modle equations dimensionless

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 51P: Consider the physical quantities s,v,a, and t with dimensions [s]=L,[v]=LT1,[a]=LT2 and [t]=L ....

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why do you make the modle equations dimensionless

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Consider the physical quantities s,v,a, and t with dimensions [s]=L,[v]=LT1,[a]=LT2 and [t]=L . Determine whether each of the following equations is dimensionally consistent. (a)v2=2as;(b)s=vt2+0.5at2;(c)v=s/t;(d)a=v/t
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The purpose of this problem is to show the entire concept of dimensional consistency can be summarized but the old saying "You can't add apples and oranges." It you have studied power series expansions in a calculus course, you know the standard mathematical funstions such as trigonometric functions, logarithms, and exponential function can be expressed as infinite sums of the form where the an are dimensionless constants for all n = 0, 1, 2, ... and x is the argument of the function. (If you have not studied power series in calculus yet, just trust us.) Use this fact to explain why the requirement that all terms in an equation have the same dimensions is sufficient as a definition of dimensional consistency. That is, it actually implies the arguments of standard mathematical funstions must be dimensional consistency. That is, it actually implies the arguments of standard mathematical functions must be dimensionless, so it is not really necessary to make this latter condition a…