Paper or Plastic?

Letter to the Editor

Formulas in Physics Have a “Standard” Form

The article discusses the importance of the ordering of symbols in physics formulas and identify conventions that rule the standard form for how formulas are written and interpreted. The elements of this form consisting of constants, parameters, and variables have been identified. Instructors are encouraged to make this convention explicit and encourage its use to assist students

Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on

Computational problems in introductory physics: Lessons from a bead on a wire

We have found that incorporating computer programming into introductory physics requires problems suited for numerical treatment while still maintaining ties with the analytical themes in a typical introductory-level university physics course. In this paper, we discuss a numerical adaptation of a system commonly encountered in the introductory physics curriculum: the dynamics of an object constrained to move along a curved path. A numerical analysis of this problem that includes a computer animation can provide many insights and pedagogical avenues not possible with the usual analytical treatment. We present two approaches for computing the instantaneous kinematic variables of an object constrained to move along a path described by a mathematical function. The first is a pedagogical approach, appropriate for introductory students in the calculus-based sequence. The second is a more generalized approach, suitable for simulations of more complex scenarios

The implications of a robust curriculum in introductory mechanics

We have developed a curriculum for introductory mechanics that emphasizes interactive engagement and conceptual understanding using the studio format. As previously reported, we have shown in three different quarters that the curriculum much improved the students’ conceptual understanding compared to the traditional course without significantly affecting the scores on a traditional final exam. Here we report the results for the entire three-year period during which the course was taught, 34 sections of the course were taught with 11 different instructors to over 1200 students. In each term, these sections had common exams, syllabus, and schedule. Student experiences were very similar in terms of activities. Student performance was measured using the force and motion conceptual evaluation or the force concept inventory; the average pre/post normalized gain was 0.59. There was no significant correlation with any instructor characteristics, including teaching experience, knowledge of interactive-engagement methods, and attitudes. Because the instructor characteristics are not important, it is the structure of the course that promotes the learning gains

Two-Dimensional Pendulum Experiments Using a Spark Generator

Student understanding of the superposition of perpendicular harmonic oscillators can be enhanced using a spark generator to record position-versus-time data for smallamplitude pendulum motion in two dimensions. Our students have used this arrangement to analyze the motion of a spherical pendulum and a “Y-suspended” (Blackburn) pendulum that has two effective lengths