bluuebunny/crossref_metadata_2025 huggingface dataset:
Breeder reactors: A renewable energy source
Authors: Cohen Bernard L.
Published: March 2005

Based on a cost analysis of uranium extracted from seawater, it is concluded that the world’s energy requirements for the next 5 billion years can be met by breeder reactors with no price increase due to fuel costs.(AIP)
Formulation of dynamical equations of motion
Authors: Kane Thomas R.
Published: March 2005

Advances in computer technology have brought into reach the solutions of many dynamics problems previously regarded as excessively complex. However, in order actually to carry out solutions, one must be able to generate computational algorithms in an effective way. In the present paper, this issue is confronted through the discussion of a law of motion that is, in essence, a generalization of Lagrange’s equations. Following the introduction of ‘‘generalized speeds,’’ ‘‘partial angular velocities,’’ and ‘‘partial velocities,’’ the equations of motion are formulated for a simple system in order to illustrate each of these concepts in concrete terms. To provide a basis for comparisons, the equations of motion of the system are then formulated also by employing Lagrange’s equations.
Generalized Fermat principle
Authors: Newcomb William A.
Published: March 2005

Fermat’s principle of least time in geometrical optics is shown to be applicable not only in the usual case of an isotropic medium but also for a general medium of arbitrary anisotropy.
Modification of the general theorem of equipartition: Application to the relativistic ideal gas
Authors: Buchdahl H. A.
Published: March 2005

According to the general theorem of equipartition 〈χ∂H/∂χ〉=kT, where χ is any appropriate coordinate or component of momentum. More generally, if f is any suitable function of the coordinates and momenta 〈 f∂H/∂χ〉=kT〈∂f/∂χ〉. This relation is used to obtain by elementary means relations describing the dependence of the energy of a relativistic ideal gas upon the parameter kT/mc2.
Study on diffusion and recombination of minority carriers by the method of photoconductive decay
Authors: Chow R. H.
Published: March 2005

This paper describes an experiment relating to the diffusion of charge carriers in homogeneous semiconductor material. Diffusion theory, as outlined in this paper, is applied to deduce from measurements a quantity called the bulk lifetime of excess minority carriers: a quantity which is independent of the size, shape, and surface condition of the semiconductor sample. Because of this independence, the bulk lifetime is used as one of the characterizing quantities of semiconductor material. In performing this experiment, the student will gain a working knowledge of diffusion theory as applied to semiconductor carriers, and at the same time become acquainted with an important technique for the characterization of semiconductor material. The actual duration of involvement will depend upon the amount of setting up of equipment, sample preparation, etc., that is expected of the student. An oscilloscope of fast rise time (200–MHz bandwidth), and a xenon flash tube with pulse duration of a few microseconds (General Radio 1542-B electronic stroboscope is a proven possibility), are the major items of equipment needed.
Unified formulation of quantum and statistical mechanics
Authors: Onyszkiewicz Z.
Published: March 2005

Using one and the same simple variational principle for average energy, a new equation is obtained equivalent to the set of two equations: the time-independent Schrödinger equation and that describing canonical Gibbs distribution.
Experimental picture of the band structure formation in a solid
Authors: Pireaux J. J. , Caudano R.
Published: March 2005

An experimental illustration of the formation of a band structure in a solid is presented. It is based on the structure analysis of the x-ray excited photoelectron valence band spectra recorded for a series of molecules with increasing length, the linear normal-alkanes (CnH2n+2 , where 1≤n≤∞). This experiment shows how a single atomic carbon 2s electronic level evolves to molecular orbitals, and then to a band, as the number n of carbon atoms increases in the molecule and simulates at the end a 1-D solid. It is thought that such a simple picture might help to understand and illustrate a solid state physics course about band structures.
Solitons in a wave tank
Authors: Olsen M. , Smith H. , Scott A. C.
Published: March 2005

A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations.
Forging, cooking, trimming, and riding on the bandwagon
Authors: Franklin Allan
Published: March 2005

Recent accusations of scientific fraud have raised serious questions both for science policy and science itself. If experimental results cannot be trusted then science becomes virtually impossible. Four cases from twentieth-century physics are examined to see if the normal procedures of science provide adequate safeguards against fraud. I conclude that repetition of experiments, particularly for those of theoretical importance, does provide a sufficient safeguard.
Experiment to verify the second law of thermodynamics using a thermoelectric device
Authors: Gupta V. K. , Shanker Gauri , Saraf B. , Sharma N. K.
Published: March 2005

An experiment to verify the second law of thermodynamics using a thermoelectric device is described. The response of the device when it is used as a Seeback-effect heat engine after filtering out the contributions of the associated irreversible parts is studied as a function of the temperatures of the hot and cold junctions. Likewise its response as a Peltier-effect heat pump is also investigated. The experimental results are in close agreement with the predictions of the second law of thermodynamics.
The polythermal ensemble: A rigorous interpretation of temperature fluctuations in statistical mechanics
Authors: Phillies George D. J.
Published: March 2005

The usual treatment of temperature fluctuations in thermometry is based on an analysis of fluctuations in a mechanical variable in a system of constant temperature. This calculation is here inverted to discuss the uncertainty in the temperature for a system whose mechanical variables have been measured. The inversion is accomplished by introducing a new statistical-mechanical ensemble, the polythermal ensemble, which is obtained as an extension of the canonical ensemble. It is shown that temperature fluctuations in very small systems are larger than is sometimes believed. This is a sense in which β=(kBT)−1 is a more fundamental variable than is the temperature T.
The validity of the classical description of nuclear scattering
Authors: Hussein M. S. , Chen Y. T. , Almeida F. I. A.
Published: March 2005

A description of nuclear scattering using classical trajectory concepts is discussed. Analysis is made of the condition of validity of this description within the Bohr uncertainty arguments. Applications to the scattering systems p+28Si and 16O+28Si are made.
Electric fields and charges in elementary circuits
Authors: Heald Mark A.
Published: March 2005

In an effort to clarify the role of surface charges on the conductors of elementary electric circuits and the electric fields in the space around them, we present a quantitative analysis of (two-dimensional) circular current loops. It is also noted that, in general, lines of Poynting flux lie in the equipotential surfaces of quasistatic systems.
Gravitational waves on the back of an envelope
Authors: Schutz Bernard F.
Published: March 2005

Using only Newtonian gravity and a little special relativity we calculate most of the important effects of gravitational radiation, with results very close to the predictions of full general relativity theory. Used with care, this approach gives helpful back-of-the-envelope derivations of important equations and estimates, and it can help to teach gravitational wave phenomena to undergraduates and others not expert in general relativity. We use it to derive the following: the quadrupole approximation for the amplitude h of gravitational waves; a simple upper bound on h in terms of the Newtonian gravitational field of the source; the energy flux in the waves, the luminosity of the source (called the ‘‘quadrupole formula’’), and the radiation reaction in the source; order-of-magnitude estimates for radiation from supernovae and binary star systems; and the rate of change of the orbital period of the binary pulsar system. Where our simple results differ from those of general relativity we quote the relativistic ones as well. We finish with a derivation of the principles of detecting gravitational waves, and we discuss the principal types of detectors under construction and the major limitations on their sensitivity.
The spot of Arago: New relevance for an old phenomenon
Authors: Harvey James E. , Forgham James L.
Published: March 2005

The ‘‘spot of Arago’’ has been a controversial topic since its inception in 1818 when Poisson predicted its existence in an attempt to discredit Fresnel’s wave theory of light. Arago performed the experiment and found the surprising prediction was true, thus putting Fresnel’s theory on a firm technical foundation. In recent years, the spot of Arago, which exists as a bright spot at the center of the geometrical shadow of a circular obstruction, has caused substantial grief in various high-energy laser applications and has come to be considered more of a nuisance than a curiosity. This paper suggests that the size and shape of the spot of Arago is characteristic of the wave-front aberrations of the incident beam and can therefore be used to advantage as a beam sample for wave-front analysis of annular beams. The implementation of this wave-front sampling scheme would eliminate the requirement for a special beam-sampling optical component and thus reduce to a minimum the deleterious effects upon the beam frequently accompanying the use of such components. Both experimental and numerical results are presented along with a discussion of the capabilities and limitations of this particular beam sample for diagnostic purposes.
Stopping power of silver for 252Cf fission fragments
Authors: Desmarais D. , Duggan J. L. , Adair H. L.
Published: March 2005

The purpose of the present paper is to familiarize undergraduate students with the fission process. The stopping power of silver for 252Cf fission fragments of various energies will be measured. The experimental value for the stopping power is obtained from the measured energy loss of the fission fragments for five different thicknesses of silver absorber. The results are favorably compared to calculations making use of a semiempirical theoretical formula developed by Lindhard and revised by Müller. The theory is of such a form that an undergraduate student in physics can easily do the calculations
A comment on the relations between Einstein and Hilbert
Authors: Medicus Heinrich A.
Published: March 2005

A newly discovered letter written by Albert Einstein to a close friend, Heinrich Zangger, reveals Einstein’s reaction to David Hilbert’s work on the gravitational field equations in the theory of general relativity. Hilbert’s work was done at the same time as Einstein’s, and for a short while, Einstein felt that Hilbert had come close to plagiarizing.
WCA perturbation theory for one-dimensional Lennard–Jones fluids
Authors: Bishop Marvin
Published: March 2005

The Weeks–Chandler–Anderson perturbation theory is derived for one-dimensional Lennard–Jones systems. Its predictions are tested with molecular dynamics calculations on the full and repulsive Lennard–Jones potential. It is found that the prescription for the reference fluid is in excellent agreement with the computer calculations and that the high-temperature approximation for the full Lennard–Jones system is a good one at high temperatures.
De Broglie’s relativistic phase waves and wave groups
Authors: Brown Harvey R. , Martins Roberto de A.
Published: March 2005

Louis de Broglie’s original theory of matter waves has until very recently received relatively little treatment in the literature on history and foundations of physics. This paper attempts to clarify a number of aspects of de Broglie’s theory, as formulated primarily in his famous thesis, which still give rise to confusion or debate. To this end, a re-examination is made of the scope and validity of the relativistic physics employed in de Broglie’s arguments concerning the existence of phase waves and their physical implications. Recent doubts concerning the soundness of de Broglie’s introduction of a wave group associated with the quantum are also analyzed in detail, and it is argued that the wave group indeed has a problematic, if minor, role in the overall theory.
Correspondence principle demonstrated
Authors: Chen Robert L. W. , Rhodes Michael Barry
Published: March 2005

A method of producing computer graphics for quantum mechanics has been adapted to portray processes with much shorter wavelengths in comparison to those in an earlier work by Chen. A set of pictures are produced which demonstrates the correspondence principle—that quantum mechanics reduces to classical mechanics in appropriate limits.
Motion of a harmonic oscillator with variable sliding friction
Authors: Lapidus I. Richard
Published: March 2005

The velocity of a harmonic oscillator with variable sliding friction is obtained as a function of the displacement. The ultimate stopping position is determined by an iteration procedure.
Internal space-time symmetries of massive and massless particles
Authors: Han D. , Kim Y. S. , Noz Marilyn E. , Son D.
Published: March 2005

A unified description is given for internal space-time symmetries for massive and massless particles. It is noted that the little groups governing the internal symmetries of massive and massless particles are locally isomorphic to the three-dimensional rotation group or O(3) and the two-dimensional rotation group or E(2), respectively. It is noted also that the E(2) group can be obtained from a large-radius/flat-surface approximation of O(3). This procedure is then shown to be directly applicable to that of obtaining the E(2)-like little group for massless particles from the O(3)-like little group for massive particles in the infinite-momentum/zero-mass limit.
Swinging Atwood’s Machine
Authors: Tufillaro Nicholas B. , Abbott Tyler A. , Griffiths David J.
Published: March 2005

We  examine the motion of an Atwood’s Machine in which one of the masses is allowed to swing in a plane. Computer studies reveal a rich variety of trajectories. The orbits are classified (bounded, periodic, singular, and terminating), and formulas for the critical mass ratios are developed. Perturbative techniques yield good approximations to the computer-generated trajectories. The model constitutes a simple example of a nonlinear dynamical system with two degrees of freedom.
O Botafumeiro: Parametric pumping in the Middle Ages
Authors: Sanmartín Juan R.
Published: March 2005

The pendular motion of a giant censer (O Botafumeiro) that hangs in the transept of the cathedral of Santiago de Compostela, and is cyclically pumped by men who pull at the supporting rope, is analyzed. Maximum angular amplitude attainable, and number of cycles and time needed to attain it, are calculated; the results agree with observed values (∼82°, ∼17 cycles, ∼80 seconds) to the few percent accuracy of both the analysis and the observations and parameter measurements. The energy gain in a pumping cycle is obtained for an arbitrary pumping procedure to two orders in the small fractional change of pendular length; the relevance of the ratio (characteristic radial acceleration during pumping)/g to the gain is discussed. Effects due to rope mass, air drag on both Censer and rope, and the fact that the Censer is not a point mass, are considered. If the pumping cycle is inverted once the maximum amplitude has been attained, the Censer could be swiftly brought to rest, avoiding the usual violent stop. Historically recorded accidents, rope shape, and the influence of relevant parameters on the motion are discussed.
The semiconducting vacuum
Authors: Prange Richard E. , Strance Peter
Published: March 2005

It is pointed out that the vacuum may be regarded as a semiconductor. In particular, the vacuum in the region close to the nucleus of a superheavy element is analogous to the inversion layer in a field effect transistor. This discovery was made in an noncalculus undergraduate course in modern physics, which is briefly discussed.
A simple model for the study of free Brownian motion
Authors: Modak R. S.
Published: March 2005

The relation representing the fluctuation–dissipation theorem for a free Brownian particle suspended in a fluid is derived from first principles using a simple model for the collisions of fluid molecules on a Brownian particle. This result is crucial in deriving the probability distribution for the velocity of a Brownian particle from the Langevin equation. The assumptions used in the model and its implications are also discussed.
Fraunhofer diffraction patterns of microparticles
Authors: Fischbach F. A. , Bond J. S.
Published: March 2005

An experiment for undergraduate optics laboratories is described based on the interaction of light with opaque particles of 10 to 100 μm size. The experiment demonstrates the phenomena of diffraction and interference in low-angle Fraunhofer patterns and shows how several structural parameters of microparticles can be determined from such patterns.
Idealized dynamics of balloon flight
Authors: Bachman R. A.
Published: March 2005

A theory of idealized balloon flight dynamics is developed for the case of a rigidly suspended payload. A system of dynamical equations is deduced from Newton’s second law for translation and rotation. Linear perturbation theory is used to study the small oscillations of the balloon system. It is proved that the horizontal and angular degrees of freedom are coupled, while the vertical degree is independent. A cubic secular equation is derived for the complex frequency of the motion. For the case of light damping and coupling, it is shown that the frequency is determined only by inertial and geometric factors. Physical arguments are used to elucidate the mechanism of linear coupling and damping. Finally, it is shown that the second-order vertical velocity perturbation is driven by the angular oscillation at a frequency twice as great.
Stirling’s cycle and the second law of thermodynamics
Authors: Simon Raul A.
Published: March 2005

In order to prove the general validity of the second law of thermodynamics, several instances of the Stirling cycle are studied, especially in relation to their efficiency.
On the Pauli–Schrödinger equation
Authors: Chapman Tim C. , Cerceau Octavio
Published: March 2005

Starting with the generally covariant Dirac equation we give equations showing that the spin of the Dirac particle couples directly with the background gravitational field. By restricting the metric to one describing a general 3-space metric (no gravitation) we reduce the spin-covariant Dirac equation to a two-component theory. Finally, the general form for the Pauli–Schrödinger equation is derived for any 3-space orthogonal curvilinear system of coordinates.
Distance dependence of fields as a function of source geometry using light sources
Authors: Sukow Wayne W.
Published: March 2005

Using a solar cell/photodiode in conjunction with a multimeter for measuring current/voltage, the output from the solar cell or photodiode was recorded as distance from a light source was varied. For a constant power source the distance dependence of the intensity depends only on the source geometry. Three source geometries for which students can derive the theoretical distance dependence are the point source, the line source, and ring source. For the line source the intensity decreases as r−1.01±0.01 compared with the theoretical behavior of r−1.00, exactly. For the point source it decreases as r−2.04±0.02 compared with the exact behavior of r−2.00. The ring source exhibits the expected maximum. Not only does the apparatus provide a quantitative method for students to evaluate how the distance dependence of fields varies with source geometry, it also enables students to study ‘‘end effects’’ which provide insights into that commonly used statement ... ‘‘ignoring the ends we have ... .’’
Derivation of the electric dipole–dipole interaction as an electric hyperfine interaction
Authors: Parker G. W.
Published: March 2005

The electric dipole–dipole interaction is derived by assuming that the electron and proton in hydrogen have intrinsic electric dipole moments that interact to give an electric hyperfine interaction. The electric field at the proton due to the electron’s presumed dipole moment then gives rise to a contact type term for l=0 and the normal dipole–dipole term for l≠0. When combined with our previous derivation of the magnetic hyperfine interaction [Am. J. Phys. 52, 36 (1984)], which used a similar approach, these derivations provide a unified treatment of the interaction of electric and magnetic dipoles. As an application of these results, the product of the electron’s and proton’s dipole moments is estimated to be less than 10−29 e2 cm2.
Electronic integrator for physics experiments
Authors: Albert Martin K. , Hayden Howard C.
Published: March 2005

For many applications involving ion or electron beams, it is necessary to know the total charge delivered to the target during an experiment. We have developed a reasonably inexpensive integrator for this purpose which could also serve equally well for other applications involving integration of voltage over time. The main components are a voltage-to-frequency converter and a digital counting circuit. All the parts needed to build the integrator are readily available. The circuit can easily be adapted for measuring capacitance, magnetic fields, and many other physical quantities.
Classical scattering patterns of a central potential
Authors: Arndt Richard A. , Roper L. David
Published: March 2005

Particle scattering patterns were examined for a Coulomb potential, a Yukawa potential, and a short-range attractive well. For the Yukawa potential and short-range well we found structures associated with classical particle resonances. A fortran Tektronix graphics simulation was used to obtain the results presented here.
Application of special relativity to a simple system in which a motional emf exists
Authors: Sirkis Murray D.
Published: March 2005

The currents that result from a motional emf in a simple circuit are considered. The speed of the moving parts of the circuit need not be small in comparison to the speed of light. Four simple examples are considered. In each example, the induced emf determined from Faraday’s law is used to calculate a current, which is identified with conduction current. For some observers, the conduction current does not have the same value in all parts of the simple circuit considered here. In parts of the circuit, the total current may include convection current as well as conduction current. The effects of self-inductance are neglected.
Undergraduate experiment in critical phenomena. II. The coexistence curve of a binary fluid mixture
Authors: Ngubane S. B. , Jacobs D. T.
Published: March 2005

An undergraduate experiment is described that uses meniscus heights to determine the coexistence curve of a binary fluid mixture. The data can be obtained with a minimum of equipment and yield results that are easily interpreted by the theory also presented. Data taken on the binary liquid mixture methanol–isooctane are presented and analyzed. The critical temperature and composition were found to be (42.5±0.5) °C and (67.3±0.2)% by volume isooctane, respectively.
Uniform solutions for scattering by a potential barrier and bound states of a potential well
Authors: Keller Joseph B.
Published: March 2005

The one-dimensional Schrödinger equation is solved asymptotically for scattering of a particle by a potential barrier and for bound states of a potential well, when the potentials change little in a wavelength. Both solutions are represented uniformly in space, rather than nonuniformly as in the WKB method. This avoids matching expansions and using connection formulas. The scattering solution and the complex reflection and transmission coefficients are also uniform in the particle energy.
Sustained availability: A management program for nonrenewable resources
Authors: Bartlett Albert A.
Published: March 2005

The continued extraction from the earth of nonrenewable mineral and fuel resources is a cause for concern, particularly where the rates of extraction are growing. If the rate of extraction declines a fixed fraction per unit time, the rate of extraction will approach zero, but the integrated total of the extracted resource between t=0 and t=∞ will remain finite. If we choose a rate of decline of the rate of extraction of the resource such that the integrated total of all future extraction equals the present size of the remaining resource then we have a program which will allow the resource to be available in declining amounts for use forever. This program is called Sustained Availability (SA) and it is somewhat analogous to the program of ‘‘sustained yield’’ in the management of renewable resources such as agriculture. The mathematics of this program, the opportunities it presents, and its consequences are examined in detail.
Faraday’s law—Quantitative experiments
Authors: Nicklin R. C.
Published: March 2005

A cylindrical bar magnet is dropped through a coil which encircles a glass tube. A Commodore 64 computer equipped with an analog to digital converter digitizes and stores the resulting voltage pulse. The magnet velocity and the number of turns on the coil are varied and simple measurements on the voltage pulse give quantitative tests of Faraday’s law. Integration produces the total flux through the coil. Flux integral calculations which treat the magnet either as a dipole or as a uniformly magnetized cylinder lead to equations for the voltage pulses which give a good fit to the experimental data obtained with a set of variable area coils. Either model is good for radial distances >40% the magnet length. Other results include determination of dipole separation and pole strength and surface current density. A versatile program for data acquisition and inspection is described. Suggestions are made for demonstrations and laboratory work for students in introductory noncalculus and calculus based courses and for advanced experimental work for majors.
Derivation of the mirror equation
Authors: Burrows John W. W.
Published: March 2005

The mirror equation, giving the relationship between the object distance, the tangential image distance, the radius of curvature of a concave mirror, and the angle of incidence, is derived in a way which is different from that appearing in the literature. The derivation given here is for an ideally shaped mirror and involves no approximations. This new approach shows the equation to be more generally applicable than might otherwise be expected.
Production and use of a light beam with an intensity proportional to the distance from the source
Authors: Langlois P. , Boivin A. , Lessard R. A.
Published: March 2005

A laser beam arriving at normal incidence on a sharp edge produces a diffraction edge wave which appears on an observation screen as a bright line perpendicular to the edge. Provided some conditions are satisfied, it is shown that the intensity of this edge wave is proportional, within a finite range, to the distance from the diffracting edge to the screen. A brief history of the edge wave theory, which was first proposed by Thomas Young in 1802 to explain diffraction phenomena, is presented. Experimental results using this interesting proportionality between the diffraction edge wave intensity and distance are shown. These results concern the monitoring of a glider’s position on an air track under various conditions.
Periodic boundary conditions in special relativity applied to moving walls
Authors: Peters P. C.
Published: March 2005

A finite expanding space-time may be constructed from the space-time of special relativity by identifying points on walls which move uniformly away from each other. The two-dimensional space-time resulting from the suppression of two spatial dimensions has the peculiar feature that the space-time is Lorentz invariant (does not have a preferred frame) if the walls are moving, no matter how slowly, but is not Lorentz invariant (has a preferred frame) if the walls are at rest. Resolution of this paradox makes use of another property of this space-time, namely that there is a preferred location in any Lorentz frame if the walls are moving and no preferred location if the walls are at rest. Cosmological coordinates are defined for the space-time with moving walls to exhibit the similarities of the expanding space-time to some cosmological models which have been proposed in the past.
The classical polarizability of the hydrogen atom
Authors: Bowers Wayne A.
Published: March 2005

The electric polarizability of a ‘‘classical’’ hydrogen atom is calculated and found to have the value α=(21/4)a30 for an energy equal to the known quantum-mechanical ground state energy, as compared with the quantum-mechanical value of (18/4)a30.
Monte Carlo simulation of nonrelativistic electron scattering
Authors: Williamson W. , Duncan G. C.
Published: March 2005

A Monte Carlo calculation is described for the scattering and absorption of nonrelativistic electrons moving through a slab of uniformly distributed material of given atomic number, density, and thickness. We give an elementary discussion of the basic physics necessary for developing a computer simulation of the movement of electrons through the material. A basic program was written for microprocessors which determines backscattering, transmission, and absorption coefficients, and provides the user with a graphical output of the electron trajectories. We present the results of several simulations utilizing a moderate number of electrons. Such an approach might be used to teach intermediate to advanced students the physics of electron scattering. Several excercises are suggested for students who wish to pursue such problems in more depth.
Energy analysis of the conical-spring oscillator
Authors: Grant Frederick C.
Published: March 2005

Traditionally, the spring-hanging mass oscillator has been modeled as a textbook harmonic oscillator with an augmented hanging mass to account for the finite mass of the spring. This traditional model distorts the partition of energy between the spring and the hanging mass while the present analysis reveals the true partition of energy. Changes in effective spring mass and spring constant are tracked across the range of hanging mass in terms of kinetic and potential energy distributions on the coil spring. Results for the case farthest from the textbook, that of the spring along, reveal how, as hanging mass is removed, the spring effectively shortens, stiffens, and uses it own free-end as a hanging mass.
The naming of the deuteron
Authors: Stuewer Roger H.
Published: March 2005

The naming of the deuteron involved a protracted debate between 1933 and 1935. The principal protagonists were Harold C. Urey, Gilbert N. Lewis, Ernest O. Lawrence, and Ernest Rutherford, but others on both sides of the Atlantic entered the fray as well. This paper examines the arguments and issues that emerged in the debate, and the process by which agreement was finally achieved on the name for this new particle.
The pendulum—Rich physics from a simple system
Authors: Nelson Robert A. , Olsson M. G.
Published: March 2005

We provide a comprehensive discussion of the corrections needed to accurately measure the acceleration of gravity using a plane pendulum. A simple laboratory experiment is described in which  g was determined to four significant figures of accuracy.
The influence of physics laboratories on student performance in a lecture course
Authors: Long Dale D. , McLaughlin Gerald W. , Bloom Allan M.
Published: March 2005

We have studied the lecture course performance of approximately 2500 students enrolled in general physics over a five-year period to determine the influence of laboratory enrollment on lecture course performance. A statistical analysis showed the major determinants of lecture performance to be the SAT math score, overall grade average, and lab enrollment, with a significant interaction between overall grade average and lab enrollment. The results show that grades of good and poor students were influenced very little, while those of intermediate students were helped significantly by concurrent lab enrollment.
Bohr–Sommerfeld, WKB, and modified semiclassical quantization rules
Authors: Geldart D. J. W. , Kiang D.
Published: March 2005

The WKB approximation for energy eigenvalues can be advantageously introduced to students when the Bohr–Sommerfeld quantization rule is discussed. A simple heuristic derivation of these quantization rules is given. Exceptional cases occur when conditions necessary for the validity of semiclassical approximations are violated, but appropriate modifications can still provide useful semiclassical approximations even in such cases. Various situations are illustrated by examples.
The Runge–Lenz vector as an ‘‘extra’’ constant of the motion
Authors: Kaplan Harvey
Published: March 2005

Using a straightforward analytic procedure that requires no physical intuition other than the realization that it is useful to look for isolating constants of the motion in Newtonian mechanics, we show that the Runge–Lenz vector is a constant of the motion for a point mass moving in the field of a fixed gravitational center and simultaneously find all other constants of the motion for this problem. Various points concerning the derivation are amplified and related to recent work on the integrability of mechanical systems having two degrees of freedom. A formula enabling one to look for similar constants of the motion, including ‘‘extra’’ ones in systems having three degrees of freedom, is presented.
p
V cycle area equals work done: An undergraduate experiment
Authors: Dempsey Daniel F. , Hartman J. Keith
Published: March 2005

A simulated heat engine is described which can raise weights to a higher level. The engine’s pressure and volume data, when plotted on a pV diagram, give a closed cycle whose area is in good agreement with mgh, the work accomplished during the cycle.
The Schrödinger equation in classical physics
Authors: Flatté Stanley M.
Published: March 2005

The use of the Schrödinger equation in classical physics was begun in 1950; in the classical context it is known as the parabolic wave equation. The derivation of the parabolic wave equation from the full classical wave equation is analogous to deriving the Schrödinger equation from the Klein–Gordon equation. An introduction to the Schrödinger equation by this route could be of help in introductory quantum-mechanics classes.
Using the virial theorem
Authors: Sivardiere Jean
Published: March 2005

Elementary applications of the virial theorem are presented. The driven harmonic oscillator and the anharmonic oscillator are considered, along with the Kepler motion.
Microscopic observations on a kinetic Ising model
Authors: Marro J. , Toral R.
Published: March 2005

We comment on the practical realization and physical relevance of a kinetic Ising model which has played an important role during the last decade as a guide for real experiments and for the development of theory. We stress the possibility of performing microscopic observations during the computer evolution of the model system. This is illustrated by discussing the observed behavior of some general concepts of physics such as energy, specific heat, and metastable states.
Quantizing the damped harmonic oscillator
Authors: Yurke Bernard
Published: March 2005

A damped harmonic oscillator can be modeled as a manifestly conservative system by replacing the dissipative element with a string or transmission line of infinite extent. This conservative system can be quantized in a straightforward manner using the standard techniques of canonical quantization. The system may be used to illustrate various aspects of the quantum mechanics of a particle interacting with a field.
Casino physics in the classroom
Authors: Whitney Charles A.
Published: March 2005

This article describes a seminar on the elements of probability and random processes that is computer centered and focuses on Monte Carlo simulations of processes such as coin flips, random walks on a lattice, and the behavior of photons and atoms in a gas. Representative computer programs are also described.
Volume exclusion correction to the ideal gas with a lattice gas model
Authors: Pimbley J. M.
Published: March 2005

The thermodynamic properties of the classical ideal gas are well known and documented. The departure of real gases from ideal behavior requires modification of the ideal equation of state. We derive an exact solution for an ‘‘excluded volume’’ system in which the constituent particles have nonzero volume and only one particle may occupy a specific region in space. To incorporate this volume exclusion, we propose a lattice gas model and find a simple combinatorial solution to this model. We construct the partition function, equation of state, and several other thermodynamic quantities.
A surrealistic tale of electricity
Authors: Fuchs Hans U.
Published: March 2005

Using thermodynamics as an analogy, an ‘‘electricity machine’’ is constructed and analyzed. This machine runs through a ‘‘Carnot’’ cycle. The analysis leads to the construction of a ‘‘new’’ quantity called ‘‘reduced electricity’’ (charge). The example shows what life in electrodynamics would be without the substancelike quantity which we call electrical charge. (This state of affairs is accepted in thermodynamics.) Imagine the development of the theory of electricity had fallen into the hands of the thermodynamicists. As fairy and other tales go, they have an air of surrealism surrounding them.
Comment on ‘‘Three perspectives on Schrödinger’s cat’’ [Am. J. Phys. 5
2, 1089 (1984)]
Authors: Ballentine L. E.
Published: March 2005

Since the purpose of the paper1 in question was to examine the responses to Schrödinger’s cat paradox that are engendered by three particular approaches to quantum mechanics, it is appropriate to comment only on the extent to which the given responses do indeed represent the views of proponents of the various interpretations. For the cases of quantum logic and the many worlds interpretation, I believe that the author has indeed captured the essence of a response that a supporter of that interpretation would give. But I should hope that a supporter of the Copenhagen interpretation would not give the response attributed to him, for it completely misses the point.
Angular size in an expanding universe
Authors: Janis Allen I.
Published: March 2005

The redshift zm at which angular size (for objects of equal linear size) is a minimum is examined for expanding, dust-filled, Robertson–Walker universes obeying the Einstein field equations with vanishing cosmological constant. It is shown that zm and the deceleration parameter q are monotonically decreasing functions of one another, and that closed-form expressions can be obtained for both zm(q) and q(zm). The explicit form of the latter function is presented.
Surface and kinetic energy densities: A fluid dynamics laboratory exercise
Authors: Hageseth Gaylord T.
Published: March 2005

The flow of water from a vertical column through a horizontal capillary tube is observed. As the height of the water column decreases the horizontal range of the water escaping from the capillary tube also decreases. The horizontal velocity of the water leaving the capillary tube is determined from the trajectory and compared to the velocity of the water inside the capillary tube as calculated from the equation of continuity. The difference between the kinetic energy density of the water inside the capillary and outside the capillary is 190 J/m3 and is independent of the pressure applied to the tube. This energy density difference is equal to the increase in surface energy density that results when small drops are formed as the water leaves the capillary. The viscosity of the water is determined by applying Poiseuille’s law. When the height of the water column becomes less than 40 cm the water no longer falls in a trajectory but rather runs outside the capillary tube and adheres to the outside surface where it slowly drips and falls in the vertical direction.
Angular velocity and time derivative of angular displacement
Authors: Schuster J. , Good R. H.
Published: March 2005

It is shown that, given the angular displacement vector Φ(t)for a rigid object, the angular velocity can be found by rotating dΦ/dt about Φ through angle 1/2  Φ and decreasing the component perpendicular to Φ by (1/ 1/2  Φ)sin  1/2  Φ. The result is illustrated by considering a regular precession at a fixed angle with the vertical.
Using a classroom variable star in introductory astronomy courses
Authors: DuPuy David L.
Published: March 2005

A digitally synthesized classroom variable star has been constructed for lecture demonstrations to illustrate three types of variable stars, with real-life light curves for RR Lyrae, eclipsing binary, and multiperiodic stars. The artificial star has been used both as a classroom demonstration as well as in the laboratory, and students gain some experience in data acquisition. A simple classroom photometer is also described, with a large digital readout for classroom use. The data for the light curves is stored in an EPROM memory chip and may be changed to suit the instructor’s preferences.
Computation of Fresnel diffraction
Authors: Heald Mark A.
Published: March 2005

A review and commentary is given of practical methods for computing the Fresnel diffraction patterns of circular and linear apertures. The general problem of approximating transcendental functions is also considered.
Are fundamental constants really constant?
Authors: Norman Eric B.
Published: March 2005

Reasons for suspecting that fundamental constants might change with time are reviewed. Possible consequences of such variations are examined. The present status of experimental tests of these ideas is discussed.
Electrostatic levitation of a dipole
Authors: Griffiths David J.
Published: March 2005

It is shown that the electric field lines of a electric dipole  droop  and thus the dipole receives an upward force balancing that of gravity. (AIP)
The sweet spot of a baseball bat
Authors: Brody H.
Published: March 2005

The physics of the three sweet spots of a baseball bat is discussed and the location of the ball impact point on the bat that leads to maximum ‘‘power’’ (greatest batted ball speed) is determined.
Putting together a research-grade laser refractometer in a teaching laboratory
Authors: Zaidi A. A. , Makdisi Y. , Waldenstro/m S. , Naqvi K. Razi
Published: March 2005

The fixed angle of incidence method was developed in Trondheim as an alternative to the classical minimum deviation method [Am. J. Phys. 46, 1009 (1978)]. Modifications to the original apparatus, which has since been duplicated elsewhere, are made, and greater accuracy is achieved by (i) replacing the conventional light source with a laser and (ii) measuring two lengths instead of the deviation angle. Using a tunable dye laser, we have been able to reproduce the dispersion curve of water in the range 366–644 nm with a modicum of effort and equipment.
Nuclear structure and beta decay (1932–1933)
Authors: Brown Laurie M. , Rechenberg Helmut
Published: March 2005

Before the discoveries of the neutron and the positron in 1932, the only known fundamental material particles were the electron and the proton (referred to sometimes as ‘‘negative and positive electricity’’), which were also thought to be the only constituents of all matter, including the atomic nucleus. Well-known nuclear phenomena, especially β decay, seemed to require that nuclei contain electrons, even though their presence violated accepted principles of microscopic physics. During 1932 and 1933, however, the picture changed considerably and the foundation was laid for a future theory of nuclear structure and β decay, with the nucleus composed of only neutrons and protons as fundamental building blocks.
Oscillations of a suspended chain
Authors: Bylsma Rick , Ai Nguyen , Van Baak D. A.
Published: March 2005

The venerable problem is considered of finding the natural frequencies of small oscillations about the equilibrium configuration of a suspended chain, under the assumptions of a continuous, perfectly flexible, inextensible, and lossless chain, supported at two fixed endpoints in a uniform gravitational field. A variety of analytical, variational, and numerical methods gives results that are valid over the full range of chain span-to-length ratios, including the limiting cases of very slack and very taut chains. Some surprising predictions of the theory are confirmed by experimental data.
General aspects of the bound-state solutions of the one-dimensional Dirac equation
Authors: Coutinho F. A. B. , Nogami Y. , Toyama F. M.
Published: March 2005

Two theorems regarding the bound-state solutions of the one-dimensional Dirac equation are verified: A—There is no degeneracy of energy; B—When the potential is a Lorentz scalar and the potential is continuously varied, the energy does not cross zero. Some features of the Dirac equation related to these theorems are discussed.
Algebraic computing and the geodesics of the Kerr metric
Authors: Esteban E. , Ramos E.
Published: March 2005

Using algebraic computing, a given algorithm is solved to reproduce easily the well-known results concerning the equatorial test particle’s motion in the background of the Kerr metric. As another application, the radii of the equatorial circular null geodesics in the Kerr–Newman and Kerr metrics are calculated. Furthermore, this approach can be easily extended to study the equatorial timelike and null geodesics in any axisymmetric and stationary metric.
Physics of a ballistic missile defense: The chemical laser boost-phase defense
Authors: Grabbe Crockett L.
Published: March 2005

The basic physics involved in proposals to use a chemical laser based on satellites for a boost-phase defense are investigated. After a brief consideration of simple physical conditions for the defense, a calculation of an equation for the number of satellites needed for the defense is made along with some typical values of this for possible future conditions for the defense. Basic energy and power requirements for the defense are determined. A summary is made of probable minimum conditions that must be achieved for laser power, targeting accuracy, numbers of satellites, and total sources of power needed.
An aging harmonic oscillator
Authors: Lo C. F.
Published: March 2005

The adiabatic theorem has been investigated by studying an analytic example of an aging harmonic oscillator. Closed-form solutions to the corresponding time-dependent Schrödinger equation are available and the validity of the theorem can be explicitly tested. The results are consistent with the conventional proof by means of the series expansion method in the perturbation theory.
The Gibbs–Appell equations of motion
Authors: Desloge Edward A.
Published: March 2005

A particularly simple and direct derivation of the Gibbs–Appell equations of motion is given. In addition to the conventional results, a relatively unknown but elegant and useful form of the equations of motion is also obtained. The role of virtual displacements in generating generalized equations of motion is discussed. The relationship between the Gibbs–Appell equations of motion and Lagrange’s equations of motion is discussed. Auxiliary results that facilitate the application of the Gibbs–Appell equations of motion to rigid bodies are presented. The theory is demonstrated by generating equations of motion for a disk rolling on a horizontal plane.