The Introductory Physics Lab as a Consulting Firm

Many students in our calculus-based introductory physics courses plan to pursue careers in high technology industries. The laboratory curriculum entitled Mechanics, Inc. is designed to resemble the typical work environment of an R&D consulting firm. Upon entering, students begin a series of training activities focused on applications of physics topics to situations of interest to ersatz clients. These physics topics are chosen to complement the usual sequence encountered in the classroom. Inspiration for the instructional design of the curriculum comes from Modeling Instruction, a well-known approach disseminated to science teachers in workshops across the country, and from Cognitive Apprenticeship, which is less well known in physics pedagogy but widely used in language instruction and other areas. Students are coached and guided in the development of laboratory skills, application of physics concepts, and in the communication of laboratory work in a formal report. During the training activities, components of that formal laboratory report are added sequentially; the initial emphasis is on readable figures and captions. After several activities that each focus on another section of a conventional report, the final training activity brings all sections together in a full, formal laboratory report. With a few weeks remaining in the course, the students apply what they have learned in training activities to tasks needed by another ersatz client. These present somewhat ambiguous problems that students must first clarify. Their responses to the client’s challenges are presented in a formal laboratory report

Acoustic Testing and Modeling: An Advanced Undergraduate Laboratory

This paper describes an advanced laboratory course in acoustics, specifically targeted for students with an interest in engineering applications at a school with a strongly integrated industrial co-op program. The laboratory course is developed around a three-pronged approach to problem solving that combines and integrates theoretical models, computational models, and experimental data. The course is structured around modules that begin with fundamental concepts and build laboratory skills and expand the knowledge base toward a final project. Students keep a detailed laboratory notebook, write research papers in teams, and must pass laboratory certification exams. This paper describes the course layout and philosophy, and shares personal experience from both faculty and student perspectives

Choose Wisely: Static or Kinetic Friction—The Power of Dimensionless Plots

Consider a problem of sliding blocks, one stacked atop the other, resting on a friction-less table. If the bottom block is pulled horizontally, nature makes a choice: if the applied force is small, static friction between the blocks accelerates the blocks together, but with a large force the blocks slide apart. In that case, kinetic friction still forces the upper block forward but with less acceleration than the lower block. The choice, then, lies in the relative terms—what is meant by small and large? After a confusing experience during a recent exam, we’ve found a demonstration and graphical presentation that can help clarify the distinction between static and kinetic friction

A Simple Electric Field Probe in a Gauss\u27s Law Laboratory

Early in our calculus-based introductory course, students are introduced to electric fields and sometimes struggle with the abstraction of a vector field. They have less familiarity with the phenomena associated with electric fields, and the connection between phenomena and mathematical formalism is weaker. Our very next topic is Gauss\u27s law

Vector Acoustic Intensity Around a Tuning Fork

The acoustic intensity vector field around a tuning fork is investigated. Theory for a longitudinal quadrupole source predicts a well-defined transition between near-field and far-field, with significant circulation of sound energy in the near-field. Vector components of the time-averaged intensity were measured using a two-microphone intensity probe and found to agree well with predictions from theory. The vector intensity map is interpreted, and shown to provide useful information about the near-field of an acoustic source

Better Understanding of Resonance through Modeling and Visualization

Students encounter cavity resonance and waveguide phenomena in acoustics courses and texts, where the study is usually limited to cases with simple geometries: parallelepipeds, cylinders, and spheres. Long-wavelength approximations help with situations of more complexity, as in the classic Helmholtz resonator. At Kettering University, we are beginning to employ finite element modeling in our acoustics classes to help undergraduates better understand the acoustic modes of actual structures. This approach to the time-independent wave equation (the Helmholtz equation) was first used in a research and measurements class to investigate two classic resonance problems. The first problem was a study of resonance in bottles of various shapes. The second problem, a standard application of the Helmholtz resonator, aimed to control noise in a duct at a single “problem frequency.” Students employed swept-sine tests with their structures to determine acoustic mode frequencies. For some of the bottles, pressure mode shapes were also measured by moving a small microphone. The measurements were then compared to results from a time-harmonic finite element model, and when possible, to predictions based on simplified models (the Helmholtz resonator and cylinders). The dependence of the mode shape on varying cross-section enriched the understanding that the textbooks could deliver. In the noise control problem with a duct and resonator, the interaction of the resonator with standing waves of the duct was made clear through visualization. In particular, the model could simulate an infinite duct—not available in our lab!—to clarify the effect of the Helmholtz resonator. Measurements and models from student work will accompany discussion, and ideas for future implementation in courses will be mentioned