Volume 46, Issue 1, January 1978
 Papers


UMR, Incorporated: A scenario for roleplaying in an advanced undergraduate physics laboratory
View Description Hide DescriptionThis paper describes a scenario for an upper‐level undergraduate laboratory in which the students take roles as staff members in a contract research company, UMR, Inc. Each student is assigned to a role as Senior Scientist, Researcher, or Technician based on their letter of application, resume, and personal interview. Students are assigned to research groups and participate in a project feasibility study and in writing the resulting proposal. The assembly of apparatus, data taking, and data analysis proceed as in the usual project laboratory. At the end of the semester each student writes a section of the final report and presents a 10‐min technical talk. The instructor and the assisting graduate student assume the roles of President/Chief Consultant and Vice President/Associate Consultant/Stockroom Man, respectively.

The nature of things—a one‐semester survey for nonscientists
View Description Hide DescriptionAn attempt to survey all of the topics traditionally covered in undergraduate physics courses in one semester, with strong emphasis on everyday phenomena of nature, is described. In order to compress a survey course in physics into one semester, a number of unusual techniques were used and are described. A point was also made, during the course, to debunk certain brands of pseudoscience popular among college students, with mixed success. The course was aimed at the mass audience of nonscience majors having only a one‐semester general sciences degree requirement, used no details of mathematics, and relied heavily on lecture demonstrations, slides, film‐loops, and overhead projector artwork.

Newtonian mechanics and the human body: Some estimates of performance
View Description Hide DescriptionNon‐trivial but elementary numerical examples of basic mechanics are lacking in most introductory textbooks. This paper gives several very simple examples which relate to numbers for which many students already have some intuition. In particular, we estimate the speeds of running, cycling, and walking, the length of a good broad‐jump, the heights of a polēvault and a vertical high jump from rest, and the time for running up a flight of stairs. These estimates and the observed numbers are found to match rather well.

EER, COP, and the second law efficiency for air conditioners
View Description Hide DescriptionIt is pointed out that there is a close relationship between the energy efficiency ratio (EER) of an air conditioner unit and the coefficient of performance (COP) of its refrigeration cycle. This connection helps to bridge the gap between pure thermodynamics and practical energy‐related problems. In this spirit, two other efficiency parameters, the total COP and total EER, measured relative to the energy extracted by a primary energy source (e.g., a fossil fuel), are defined. A comparison of the actual total COP (or total EER) relative to its maximum allowed value, consistent with the second law of thermodynamics, leads to an estimate for air conditioners of the recently proposed s e c o n d l a w e f f i c i e n c y.

Why does the sun shine?
View Description Hide DescriptionIn order to understand the fundamental properties of a star in radiative equilibrium, a simplified model is introduced which yields relations for physical quantities by elementary methods. In particular, the dependence of these quantities on the parameters of the star and on the fundamental constants of nature is exhibited. Numerical evaluation of these relations is in good agreement with observation and with more elaborate calculations.

A new course: The physical principles of biological instrumentation
View Description Hide DescriptionWe present the outline of a new course designed to teach the physical principles underlying biological measurements. This course, intended for undergraduate and first‐year graduate students who have taken noncalculus introductory physics, is primarily aimed at biological science and biophysics majors interested in research careers in those fields. The course consists of lectures and demonstrations on a series of topics including NMR, ultracentrifugation, electronics, and optical and electron microscopy. Our intent is to teach the student the principles underlying the measurements they perform in their laboratories and the uses and limitations of the various techniques.

Quantization of radiant energy in waveguides
View Description Hide DescriptionThe electromagnetic field within a waveguide is described in terms of an infinite discrete set of variables which permits the application of the formalism of quantum mechanics. The quantized field exhibits potential energy which depends on the structure of the guide and the mode of the field but not on the frequency. The radiant energy experiences a compression during the transition from one guide into another one of smaller cross section.

Anharmonic vibrations of an ’’ideal’’ Hooke’s law oscillator
View Description Hide DescriptionThe vibrations of a mass connected to fixed supports by two ’’ideal’’ Hooke’s law springs are considered. Although the longitudinal vibrations of this system are always harmonic, the transverse vibrations are, in general, anharmonic even though both springs obey Hooke’s law. In fact, it is found that as the supports are brought together, allowing the springs to become slack, the purely transverse motion becomes strongly anharmonic even for small displacements of the mass from its equilibrium position. This independent oscillator model seems to possess many of the properties of an ion in a crystal undergoing a soft mode activated transition. We suggest that the model may serve as a useful conceptual starting point in the study of these transitions. Some particular solutions of the dynamical equations for the model system are investigated in detail.

Holographic interferometry for pure rotation
View Description Hide DescriptionAn experimental arrangement which can be used for double exposure holographic interferometry is described. We have used this setup to measure a series of rotations which range from 4×10^{−5} to 5×10^{−4} rad. The result is in excellent agreement with theory.

Random walks and diffusion
View Description Hide DescriptionThe usual solution of the diffusion equation gives inaccurate results for short diffusion times for displacements which are relatively large compared to the maximum range of the diffusion. A method is proposed for solving the diffusion equation by a random‐walk approximation technique which utilizes the appropriate generatingfunctions and the complex integration method of steepest descent. The power of the method is illustrated for a one‐dimensional random walk (SRW) and for physical situations in which the elementary diffusion process is governed by a normal or a rectangular probability distribution. Formulas for higher approximations applicable to any probability distribution are also derived. The method, which can also be applied to two and three dimensions, is capable of yielding high accuracy for the diffusionsolution over the entire diffusion domain.

Electric energy density in a dissipative medium by circuit analog
View Description Hide DescriptionIn a dispersive and dissipative medium, the electric energy density is no longer given by (1/2)E⋅D. When the dielectric function is given, the electric energy density of a monochromatic wave can be calculated by considering the energy stored in an equivalent linear circuit.

An individualized laboratory system
View Description Hide DescriptionThis paper describes an individualized laboratory system used in an introductory physics course for science and engineering students. The system makes extensive use of video tapes, primarily for prelab instructions. The design and operation of the system are described, and the observations of both the instructor and the students are presented.

An interactive computer experiment for the introductory laboratory
View Description Hide DescriptionThe use of an interactive computer terminal in an introductory laboratory experiment is described. In addition to taking data with the equipment available in the laboratory, students are encouraged to use a computer terminal that has been programmed to act as their lab assistant in an experiment that leads to the student’s discovery of Stokes Law. This experiment is designed to be the students’ first introduction to the use of an interactive computer terminal.

Net force of an ideal conductor on an element of a line of charge moving with extreme relativistic speed
View Description Hide DescriptionA line of charge moving horizontally at an extreme relativistic speed through an evacuated space above an infinite plane ideal conductor experiences a net downward force, towards the conducting surface, which can be determined by the method of images. The image moves through the half‐space occupied by the conductor, keeping pace with the charge pulse and positioned symmetrically with respect to the surface. Corresponding to the Green function approach, there is a viewpoint commonly employed in the analysis of relativistic problems which can lead to erroneous conclusions if one is not careful. We discuss the present problem from this point of view, first giving the incorrect arguments with the erroneous corresponding conclusions, and then the corrected picture.

Orbits of two‐body problem from the Lenz vector
View Description Hide DescriptionThe orbits with reference to the center of mass of two bodies under mutual inverse square law interaction are obtained by use of the eccentricity vector which is equivalent to the Lenz vector within a numerical factor. The parameters and orientation of the orbits are given.

On the complementary Lagrange formalism of classical mechanics
View Description Hide DescriptionCorben and Stehle pointed out the possibility of a Lagrange formalism in classical momentum space. In the present paper a more detailed discussion of this formalism is given, stressing two facts: (1) Contrary to Corben and Stehle’s opinion this formalism might be of real practical importance. (2) This formalism makes it evident that dissipation is still a problem in classical mechanics.

The classical Kepler problem in momentum space
View Description Hide DescriptionContrary to a current opinion, it is shown that the integration of a problem of classical mechanics can be as easy in momentum space as in configuration space. This is demonstrated with the Kepler problem, thus rendering a new very simple integration of it. The results strongly suggest that we consider b o t h Laplace vectors, if dynamical invariance symmetries of the Kepler problem are to be studied.
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 Papers


Generalized heat conduction equation
View Description Hide DescriptionThe linear constitutive relation between heat flux and temperature gradient known as Fourier’s law is modified to be nonlocal in time; i.e., the heat flux depends on the past history of the temperature gradient. It is shown that this leads to a generalized heat conductionequation which can be hyperbolic and thus possess a wavelike solution with finite velocity of propagation of a heat pulse. In two extreme limits of very short and very long memory the equation reduces, respectively, to the usual parabolic heat conductionequation and to a hyperbolic wave equation. For in between memory the equation has the properties of a telegraph equation characterized by a relaxation time. Such equations have arisen in treatments of second sound, exciton transport, and quasiparticle transport in ^{3}He.

Classes of units in the SI
View Description Hide DescriptionThe mathematical nature of the categories of b a s e, s u p p l e m e n t a r y, and d e r i v e d units in the SI is explained, and the usual definition of ’’supplementary’’ modified to be more precise. An argument is presented for adding ’’neper’’ to the SI as a supplementary unit.

Demonstration of phase transition and properties of metallic glasses for undergraduates
View Description Hide DescriptionSimple and inexpensive (?$10) demonstrations of some properties of metallic glasses are presented. Metallic glasses are new materials of intense current scientific and engineering interest. The viscoelastic behavior is observed during the phase transition from amorphous to crystalline states. Comparisons are made of some mechanical, electrical, and magnetic properties between the two states. It is hoped that this note can generate interest in the undergraduate community toward working in current research areas.
