Constants of Proportionality: " The Heart of The Equation "
Kisak, Paul F.
Synopsis "Constants of Proportionality: " The Heart of The Equation ""
Constants of proportionality are wonderful "equalizers" that are used by science to make the leap from observables to equations. These constants define our universe and the perspective, scale and interaction of the physics within the universe. It is the opinion, of this author, that a solid discussion on the method and philosophy of the constants of proportionality are sadly lacking at the undergraduate collegiate level. A simple example follows: From the fundamental viewpoint, as Newton and many other's have seen, we can observe that when we apply a force to a body it accelerates in a linear manner. The first order conclusion that can be made is that Force (F) is directly proportional to acceleration (a), where F and a are vectors (bold type). Using basic algebra we know that the equation for a line is of the form y = sx + b, where F = y and a = x, s is the slope of the line and b is the y intercept when x = 0. In our case b = 0 because when F = 0, a = 0; as observed.If the observer then applies various forces to the object and measures the resulting acceleration, an X-Y plot of the resulting data will show a line of the form y = sx + b or in this case F = sa. Knowing that we have F for each a, we can calculate 's' by dividing F by a; s = F/a. In this case the calculation of the slope of the line is relatively straightforward and yields the result s = m; where m is equal to the mass of the object. The mass (m) is the constant of proportionality between any specific F and a.This book discusses how constants of proportionality are used to generate the equations that define our universe and is designed to be a reference and provide an overview of the topic and give the reader a structured knowledge to familiarize yourself with the topic at the most affordable price possible.The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most current knowledge on the topic, based on the date of publication.
