Adding Physical Quantities in Introductory Physics

In [3] we proposed a unified approach to addition of resistors and capacitors such that the formulæ are always simply additive. This approach has the advantage of being consistent with the intuition of students. To demonstrate the effectiveness of our approach, we proposed some problems. In this companion to the original paper, we give the solutions of the problems and we add new problems from different areas of physics. We hope that it can serve as a resource paper for problems on the subject. 1 Summary of the Approach In [3], motivated by the fact that we have found no books in which end-of-chapter problems using continuous versions of the equations 1 R = 1 R1 + 1 R2 + . . . , (1) 1 C = 1 C1 + 1 C2 + . . . , (2) are given, we presented a new point of view in which only additive physical quantities are used in the solution of problems. This approach, we believe, is straightforward and logical for students and eliminates part of a student’s frustration arising from inappropriate handling of the physical quantities. Students often forget the physical reasoning behind a problem and they tend to add (integrate) quantities only in one way. However, physics contains much more than mathematics and, when integrating quantities in physics, physical arguments are indispensable as they dictate ‘the way we integrate’. Our intention in this paper is three-fold. First of all, we would like to present the solutions of the suggested problems given in the original paper [3]. Secondly, we would like to collect all the basic formulæ in one place. Finally, we would like to present some additional results and add some problems which can serve as examples of the effectiveness of our approach. [email protected] [email protected]