bluuebunny/crossref_metadata_2025 huggingface dataset:
Large amplitude simple pendulum: A Fourier analysis
Authors: Simon R. , Riesz R. P.
Published: March 2005

The nonisochronous behavior of a simple pendulum is well known. That this implies a large amount of anharmonicity is a conclusion which seems reasonable to many persons. This paper investigates this matter, and concludes that for all amplitudes the simple pendulum is highly harmonic.
What is a solitary wave?
Authors: Taylor Beverley A. P.
Published: March 2005

The exact solutions of classical nonlinear field equations which describe pulselike waves that are collisionally stable are known as solitary waves. The properties of these solutions are reviewed. Several of the classical equations which exhibit this type of solution are discussed. Examples of current uses in physics research are given for each field equation discussed.
Pressure-volume work exercises illustrating the first and second laws
Authors: Hoover William G. , Moran Bill
Published: March 2005

We present two exercises involving rapid compression and expansion of ideal gases. The exercises are useful teaching tools and illustrate the first and second laws of thermodynamics. The first problem involves the conversion of gravitational energy into heat through mechanical work. The second involves the mutual interaction of two gases through an adiabatic piston. Both local and global versions of the second law can be applied to this second exercise. Both problems are also treated by numerical fluid dynamics.
Canonical approach to the damped harmonic oscillator
Authors: Lemos Nivaldo Agostinho
Published: March 2005

We present a canonical treatment of the damped harmonic oscillator. The Hamiltonian is made simpler by means of a suitable canonical transformation. The ensuing equations of motion for the transformed canonical variables are then solved by the Hamilton-Jacobi method.
Undergraduate laboratories in physics: Two philosophies
Authors: Robinson M. C.
Published: March 2005

It is argued that experimental physics cannot be taught effectively in the traditional undergraduate laboratory which requires a student to follow a detailed set of instructions in order to ’’verify’’ a textbook theory or some other ’’known’’ result. In place of such methods, it is proposed that the student be presented, in ascending order of complexity, a series of problems or projects in experimental physics under conditions resembling as closely as is feasible those of a research laboratory.
The design of a radiotelescope: A multidisciplinary game
Authors: Celnikier L. M.
Published: March 2005

The ’’design’’ of a simple radio telescope is proposed as a multidisciplinary exercise, bringing together radioastronomy, electronics, and the theory of structures. The telescope can be built by relatively inexperienced students and used to observe Jupiter bursts as well as the quiet sun (under favorable conditions).
Representing arbitrary boosts for undergraduates
Authors: Frahm Charles P.
Published: March 2005

A derivation is given for the matrix representation of an arbitrary boost, i.e., a Lorentz transformation without rotation. The derivation utilizes standard vector and matrix techniques along with the well-known form for a special Lorentz transformation. However, it is done in such a way as to avoid a possible confusion over the meaning of parallel axes. Consequently it is believed to be suitable for students with modest backgrounds in mathematics and relativity.
Quantum theory of hyperfine structure transitions in diatomic molecules
Authors: Klempt E. , Kühl Th. , Ley R. , Schulze R.
Published: March 2005

An advanced laboratory experiment is described in which radio-frequency transitions between molecular hyperfine structure states may be observed. Aspects of quantum theory applied to the analysis of this physical system are discussed.
Pauli principle in Euclidean geometry
Authors: Hartung R. W.
Published: March 2005

A macroscopic toy of Dirac and Stong shows how to detect 2π rotations in our world. A theorem in geometry shows the toy is maximal; no device in three dimensions can measure bigger angles than this toy. Assuming then that the toy correctly models motion of fermions in our world, a ’’hand waving’’ derivation of the Pauli principle follows. Finally algebra is brought in to express the geometric truth. A famous sign ambiguity goes away.
Dynamic solutions for linear elastic collisions
Authors: Flansburg Leonard , Hudnut Karl
Published: March 2005

By numeric integration of the dynamic equations of motion for linear elastic collisions we show that the final velocities are different from those traditionally expected. Both air-track glider and compressible sphere collisions were modeled. Final velocities in all cases were independent of the force constants of the separating springs and the compressibility of the spheres. Experimental measurements of the final velocities for three body collisions of similar air-track gliders and of similar elastic spheres are presented which agree well with the calculations.
Approximate classical theory of scattering
Authors: Chen T. W.
Published: March 2005

An approximate method is developed for elastic scattering at large angle in the framework of classical mechanics. A simple formula for differential cross section is obtained. This formula which no longer involves any integrations provides a quick way of evaluating cross sections. Our method is illustrated through examples and is shown to work well.
A student’s experiment for the determination of the rest energy E0 of electrons
Authors: Ebel Maria F.
Published: March 2005

Electrons in the energy range of several kilo-electron-volts reach velocities of approximately one tenth the speed of light. Though for t these electrons the relativistic mass increase is less than 1%, it affects the results of x-ray photoelectron spectrometry (XPS) substantially. Thus a relativistic formalism allows the obtaining of the rest energy of electrons (E0) as an experimental result of a series of XPS measurements.
Experimental determination of the mass of air molecules from the law of atmospheres
Authors: Hayn Carl H. , Galvin Vincent
Published: March 2005

A sensitive gas pressure gauge has been constructed for use in a student experiment involving the law of atmospheres. From pressure data obtained at selected elevations the average mass of air molecules is determined and then compared with the average mass as calculated from the molecular weights and percentages by volume of the major gaseous constituents of the air.
An intuitive approach to group representation theory. II
Authors: Wolbarst A. B.
Published: March 2005

After the link ?R‖ψ (?r) 〉 = ‖ψ (r) 〉 between the real-space geometric operator ? and a uniquely associated new function-space operator ?R is established, the real-space development of Paper I is extended into function space. Several examples then illustrate the central theorem of group representation theory as used in quantum mechanics: for a given physical system, the energy eigenvectors {‖ψi(ν)(r) 〉} corresponding to the eigenvalue Eν constitute a subspace of Hilbert space invariant with respect to the system’s group of symmetry operators, and a set of basis vectors spanning that subspace can produce an irreducible representation of that group. Or, more simply, symmetry in real space determines symmetry in function space. And it is from and appreciation of the symmetry properties of states and operators in Hilbert space that the useful arguments of group representation theory flow.
Quark physics without quarks: A review of recent developments in S-matrix theory
Authors: Capra Fritjof
Published: March 2005

A review is given of the developments in S-matrix theory over the past five years which have made it possible to derive results characteristic of quark models without any need to postulate the existence of physical quarks. In the new approach, the quark patterns emerge as a consequence of combining the general S-matrix principles with the additional concept of order.
Physics for architects
Authors: Salamo Gregory J. , Brewer John A. , Berry James A.
Published: March 2005

We describe a program which was prompted by and designed to satisfy the modern needs of architects who will be confronted more and more with the constraints imposed by the principles of physics, particularly those relating to energy. The program is designed to make clear, through lectures and laboratory investigations, the relationship between concepts in physics and practice in architecture. It is designed to help the student of architecture recognize that the behavior of a structure is as much a part of his creativity as the structure itself. Experiments range from individual labortory experiments to group around-the-campus experiments.
Some psychoacoustical experiments with all-pass networks
Authors: Hartmann W. M.
Published: March 2005

It is shown how all-pass filter sytems can be used in labortory experiments in the physics and psychophysics of sound and music. Particular applications include studies of the following: (i) lateralization of sounds in headphone listening; (ii) the spectral modifications produced by phasers, compared with admixing a time-delayed signal; (iii) the pitch that can be obtained by dichotic processing of two spectrally flat noise signals, Huggins effect; and (iv) the perception of the dephasing of harmonics in complex tone. Some of the effects obtained from experiments on lateralization and on the Huggins effect appear to be new results.
Some remarks on the extended Galilean transformation
Authors: Greenberger Daniel M.
Published: March 2005

The Galilean transformation carries one inertial frame into another with a different velocity. The extended Galilean transformation carries an inertial frame into a rigid frame with uniform spatial, but arbitrary translational acceleration x′=x+ξ (t). Besides being useful in discussing the equivalence principle, this transformation provides a physical interpretation for the theorem in nonrelativistic quantum mechanics, that we cannot coherently combine states of different mass. This restriction comes about because we cannot distinguish between coordinate and proper time in nonrelativistic physics.
Comparison of classical and quantum mechanical uncertainties
Authors: Peslak John
Published: March 2005

A comparison of classical and quantum uncertainties is presented for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. It is found that the quantum results reduce to the classical in the limit of either very large quantum numbers or h→0. A classical uncertainty principle is derived and compared with its quantum analogue. A possible relationship between zero-point motion and the uncertainty principle is noted.
Cylindrical cardboard model for a rotating system in special relativity
Authors: Noerdlinger Peter D.
Published: March 2005

The illustration presented in this paper can be rolled on a common cardboard tube to yield a simple demonstration of the nature of simultaneity and the propagation of light in a rotating coordinate system. The increased circumference C′4πr of a rotating ring can be laid off on the diagram, as can the Hafele-Keating time offset. The device is useful at the undergraduate or graduate level.
Application of the parabolic approximation to predict acoustical propagation in the ocean
Authors: McDaniel Suzanne T.
Published: March 2005

A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. A technique for solving the parabolic equation is presented, and transmission loss predicted by this method is compared with experimental results for sound propagation in a coastal environment.
Monte Carlo calculation as an aid in teaching solid-state diffusion
Authors: Murch G. E.
Published: March 2005

A simple Monte Carlo method is used to simulate an atomistic model of solid-state diffusion. This approach illustrates some of the principles of diffusion and in particular verifies a solution to Fick’s second law. The role and calculation of the diffusion correlation factor is also discussed.
Brachistochrones, tautochrones, evolutes, and tesselations
Authors: McKinley John M.
Published: March 2005

The force fields of uniform gravity and of gravity inside a spherical body of uniform density were previously known to possess the property that the brachistochrone and the tautochrone are identical (cycloid and hypocycloid, respectively,). It is shown that centrifugal force in a rotating reference frame possesses the same property. In a plane normal to the axis of rotation the brachistochrone tautochrone is the epicycloid. The evolutes of hypocycloid and epicycloid are found. The figures of cycloid, hypocycloid, and epicycloid each with its evolute are shown to produce tesselations of the plane. In a plane including the axis of rotation the rotating reference frame has other brachistochrones and tautochrones which are not identical.
Semiclassical quantization of the electron-dipole system
Authors: Turner J. E.
Published: March 2005

A recent note by Fox called attention to a semiclassical treatment by Fermi in 1925 of the motion of an electron in the field of two stationary positive charges. The similarity of this problem to that of an electron moving in a dipole field prompted the author to investigate the latter system under semiclassical quantization. It is shown that Bohr quantization leads to the value Dmin = (3√3/4) ea0=1.30ea0 for the minimum dipole moment required to bind an electron. The implied separation of unit dipole charges is identical with a special value for unit positive-charge separation given by Fermi. Furthermore, this semiclassical value of Dmin is more than twice the quantum-mechanical value Dmin=0.639ea0.
Continuity conditions on Schrödinger wave functions at discontinuities of the potential
Authors: Branson David
Published: March 2005

Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discusssed. Three arguments which it is hoped are more satisfactory are then presented.
Measurement oriented basic physics laboratory
Authors: Yeatts F. Richard
Published: March 2005

Physical Measurements 1 is a measurement oriented basic physics laboratory course required of all sophomore students at the Colorado School of Mines. The course is intended to introduce students to the principles of measurement theory at a higher level than is common in an elementary physics lab. The subjects of error analysis, graphing, least-squares analysis, experimental design, measuring instruments, and report writing are covered in a 1-h/week lecture session. Experiments from mechanics and electricity and magnetism, that illustrate equally the principles of measurement theory and the principles of physics, are performed in 2-h/week laboratory sessions. A workbook entitled Concepts of Physical Measurement serves both as a textbook in measurement theory and a laboratory notebook.
Simplified relativistic force transformation equation
Authors: Stewart Benjamin U.
Published: March 2005

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic force on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and show that the constant of proportionality in Coulomb’s law is equal to the speed of light squared times the constant of proportionality in the Biot-Savart law. All is done with simple vector algebra without using four vectors, tensors, or Maxwell’s equations. The simplification results from the fact that when one takes the usual force transformation law: F′=A (U)F, and rewrites it using the inverse transformation matrix, as F=A−1(U)F′, the resulting expression is more simple because A−1(U) is linear in the velocity, U but A (U) is not.
Grundfagligt Speciale: An advanced laboratory-research course for nonphysicists taught by physicists
Authors: Gordon R. A. , Lebech J. , Mygind J. , Pedersen N. F. , Lynggaard-Jensen A. , Petersen H. G.
Published: March 2005

The pedagogical and research advantages of an advanced laboratory-research course for nonphysicists taught by physicists are discussed. The practical considerations which determine the structure and content of such a course are emphasized with particular attention given to those features which would be most helpful to others contemplating a similar course. A successful example of such a course developed by the authors is discussed in detail.
Topological solitons in physics
Authors: Parsa Zohreh
Published: March 2005

We present an introduction to topological solitons. A broad definition of solitons and a discussion of their role in physics is given. To illustrate this concept, we describe in some detail vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions.
Molecular beams and effusive flows
Authors: Leiby C. C. , Besse A. L.
Published: March 2005

Molecular flux emanating from an aperture in a beam oven and incident on a point on the beam axis is discussed. The vector flux density is characterized by its vector-velocity (rather than speed) probability distribution. As a consequence, the integrals of the velocity components orthogonal to the beam axis yield the observed dependences of beam intensity upon aperture area and distance from the aperture. Both rectangular and circular apertures are considered. The velocity integrals for the circular aperture are exact and demonstrate how the velocity distribution of the flux density gradually changes from that of the Maxwell flux at the aperture to that of a beam flux at large distances from the aperture. (This cannot be shown with the speed distribution.) An expression then is obtained for the flux from a circular aperture incident on an off-axis point by making use of the concept of a virtual aperture which simplifies the problem considerably. This expression then is used to calculate both the normal flux density distribution and the total flux incident on a finite plane collector. These treatments may be applied to systems with apertures and collectors of almost any shape and/or size.
The Zitterbewegung of a free localized Dirac particle
Authors: Lock J. A.
Published: March 2005

Much of the lore of the Zitterbewegung of a free Dirac particle is found to need revision for the situation when the particle is initially localized. We find that in this case the rapid violent oscillations of angular frequency ∠2mc2/h/ in the average position of the particle are a transient rather than sustained phenomenon. Instead, the Zitterbewegung is manifested by a growth in the size of the particle but this growth is many orders of magnitude smaller than h//mc, the magnitude usually quoted. This behavior is contrasted with that of the Foldy-Wouthuysen position for which the Zitterbewegung is absent. Finally, the applicability of these ideas to the situation of a localized Dirac particle in an external field is commented on.
Application of the Dirac delta function to electric current and magnetic multipole distributions
Authors: Namias Victor
Published: March 2005

We discuss the equivalent current density for different types of magnetic distributions, discrete as well as continuous, generated by electric currents. The equivalent current density for the point magnetic dipole and quadrupole is constructed from the basic current element. It is shown that the third-order tensor representing the quadrupole moment satisfies certain cyclic relationships which are a consequence of current conservation. Surface and volume distributions of dipoles are briefly discussed and results analogous to the electrostatic case are given. Finally, starting from Poisson’s equation for magnetism, we directly obtain a multipole expansion of an arbitrary current distribution yielding the equivalent current density for each multipole.
Eigenvalues of J2
Authors: Brownstein K. R.
Published: March 2005

Most derivations of the possible eigenvalues of J2 [i.e., h/2j (j + 1), j = 0, 1/2, 1, 3/2,...] rely upon the eigenvalues, h/m, of a component of J, say Jz. A derivation of the J2 eigenvalues is presented in which the concept of Jz eigenvalues does not appear. The derivation is based upon addition of angular momenta and the algebraic properties of the Pauli spin matrices.
Momentum operators for curvilinear coordinate systems
Authors: Leaf Boris
Published: March 2005

Expressions for the covariant and contravariant components of the quantum momentum operator (h//i) ∇ are formulated for curvilinear coordinates in three-dimensional space. The classical formalism is modified to take account of the noncommutivity of coordinates and momenta in the quantum case. These components are shown to be simply related to canonical momentum operators conjugate to the curvilinear coordinates. Expressions for components of angular momenta are also obtained. These results are specialized for orthogonal curvilinear coordinates and illustrated for spherical polar coordinates.
Dirichlet’s integral formula and the evaluation of the phase volume
Authors: Fernandez-Pineda C. , Mengual J. I. , Diez de los Rios A.
Published: March 2005

The phase volume in the microcanonical ensemble is not easily obtained even in the cases where the Hamiltonian function is separable. Dirichlet’s integral formula constitutes a consistent method to evaluate the phase volume for simple situations. Several examples where Dirichlet’s integral formula is used to obtain the phase volume are presented in this paper.
Science and society test IV: The 94th Congress
Authors: Hafemeister David
Published: March 2005

Back-of-the-envelope calculations are carried out on some science related issues that surfaced in the 94th Congress (1975–1976) such as: oil pricing, automobile efficiency standards, inter-racial busing, leverage on uranium exports, enrichment capacities, Project Pacer, and tax incentives for conservation. This approach attempts to find a middle ground in the science and public policy debates between the vague qualitative essays (which often lack substance) and the highly sophisticated quantitative efforts (which only a few understand and/or believe).
Correlation in the Langevin theory of Brownian motion
Authors: Manoliu A. , Kittel C.
Published: March 2005

In Brownian motion the ensemble average of the product of the displacement and the random force is zero. This result was assumed by Langevin to be true, although it appears to contradict the intuitive feeling that the net displacement should be in the direction of the net impulse. The literature contains a statement that the Langevin assumption is incorrect, and this led us to an examination of the question. We show that the relevant correlation function in one dimension is 〈x (t) A (t−τ) 〉=2(kBT/M)[1−exp(−βτ)] which is zero at equal times and approaches 2(kBT/M) as τ→∞.
Holographic animation apparatus
Authors: Johnston Sean F.
Published: March 2005

Simple apparatus for producing strip holograms is described. Moving the object slightly between exposures permits motion to be simulated, analogously to an animated motion picture. The resulting hologram is viewed by scanning the eyes vertically across the slits. The hologram maintains full horizontal parallax, but the slit aperture reduces the vertical viewing angle of the animated object.
Coulomb phase shift
Authors: Clark Charles W.
Published: March 2005

The relationship between the energy derivative of the Coulomb phase shift and the classical expression for the time delay is discussed.
Modular electronic system for the introductory laboratory
Authors: Dart S. Leonard , Tubbs Eldred F.
Published: March 2005

A system of small inexpensive electronic modules has been developed for instruction in the introductory physics laboratory. These modules may be used to teach digital electronics, construct digital systems for the instrumentation of standard experiments, or, with the addition of standard test equipment, used to teach analog electronics. The modules are described and some of the design considerations given. Typical experiments are described.
Multipacting mechanism as the origin of breakdown in high-frequency electrical discharges in gases
Authors: Harmon G. S.
Published: March 2005

The mechanism by which gas at low pressure breaks down when subjected to a high-frequency electrical field is considerably different from that of other types of electrical discharge. Provided the pressure is sufficiently low, the breakdown electric field strength is independent of the kind of gas, depending instead on the type, condition and separation of electrode surfaces, and the frequency of alternation of the electric field. The multipacting mechanism as developed by several authors is summarized and brought together in a single framework.
Coordinate-free rotation operator
Authors: Leubner C.
Published: March 2005

The use of a coordinate-free rotation operator is suggested for the teaching of rotations in Euclidean three space because of its twofold didactic advantage. On the one hand, the only ingredients of the simply structured rotation operator are axis and angle of rotation, in terms of which the student conceives an actual physical rotation. Thus, he is able to write down immediately the correct rotation operator or sequence of rotation operators. Scalar multiplication by the members of a particular set of basis vectors subsequently produces a particular representation in an unambiguous way. On the other hand, the use of the rotation operator as distinct from its various representations stresses the existence of vectors and operators as physical entities independent of an observer’s frame and thus prepares the student at an elementary level for a similar language in modern quantum theory. The potentialities of the coordinate-free rotation operator approach are illustrated by a number of examples.
Propagation of a step in the amplitude or envelope of a pulse or wave packet
Authors: Bradford Henry M.
Published: March 2005

The propagation of a steplike change in the amplitude of a dc pulse and a step in the envelope of a plane sinusoidal wave are investigated. It is shown that a step (e.g., the beginning or end of a pulse or wave) propagates like a pulse in the medium; i.e., its velocity is a weighted average of the group velocity, and its rate of spread is determined by the distribution of group velocities within the spectrum of the step. The results apply to a real pulse (e.g., sound) in an infinite, homogeneous, dispersive, lossless medium, and to the quantum-mechanical wave function of a free particle.
Small group approach to introductory physics
Authors: Emkey William L.
Published: March 2005

This paper describes a system which is used to teach introductory physics to students majoring in science and engineering. The class is divided into groups of three and/or four. During class the groups work on their assignments while interacting with both their peers as well as with their instructor. The system was implemented as an alternative to lecture/recitation approach in an attempt to improve the learning environment.
Equivalence of the Maxwell and wave equations
Authors: Patsakos George
Published: March 2005

The conditions under which the inhomogeneous wave equation for the electromagnetic field tensor becomes equivalent to the Maxwell equations are derived for the case of prescribed sources.
Classical orbits of a charged particle in a magnetic monopole field
Authors: Zia R. K. P.
Published: March 2005

The orbits of a charged particle in the magnetic field due to a magnetic monopole are reexamined and interpreted intuitively: they are straight lines (geodesics) on a cone. The general case in which an arbitrary central force is superimposed is analyzed. It is shown that bound orbits in the central force which do not ordinarily close may be closed by the addition of a monopole of suitable strength.
Black liquid solar collector demonstrator
Authors: Weichman F. L. , Austen D. J.
Published: March 2005

A solar collector, suitable for an undergraduate laboratory project or lecture demonstration has been built and the details of the construction and the way in which it can be used by students in elementary or advanced courses is described. A simple and efficient system results from using a black liquid to absorb the energy and from using the thermosyphon effect to drive the liquid through the collector. A floodlamp is used as a surrogate sun. The collector is of considerable current interest in the field of solar energy.
Do springboard divers violate angular momentum conservation?
Authors: Frohlich Cliff
Published: March 2005

No. However, divers and trampolinists can perform somersaults and twists even though they have zero angular momentum at all times during the stunt. Also, if a diver is somersaulting in space and possesses angular momentum only about his somersaulting axis, he can make a single discrete change in the position of his arms which initiates continuous twisting motion even in the absence of any applied torque. These apparent paradoxes have confused both physicists and coaches for some time. The present paper attempts to reduce this confusion. It discusses several different methods that performers use to initiate somersaults and twists and presents concrete examples of each method. Wherever possible quantitative calculations are presented and evaluated using information about the moments of inertia, mass, etc., of ’’typical’’ performers.
Simple C
p/C
v resonance apparatus suitable for the physics teaching laboratory
Authors: Smith D. G.
Published: March 2005

A resonance apparatus for the measurement of Cp/Cv for different gases is described. In the apparatus a magnetically supported piston in a vertical cylindrical glass tube containing the gas is forced into oscillation by means of a standard audio signal generator. The apparatus is simple and inexpensive, and may be used for general work on forced oscillations and resonance.
How monochromatic is laser light?
Authors: Jacobs Stephen F.
Published: March 2005

Two derivations of the fundamental laser linewidth are presented that have been used successfully in introductory courses. The cause of the finite linewidth is identified with phase fluctuations in the electric field due to spontaneous emission. A factor of 2 discrepancy between the energy and field analyses is explained. A number of ’’back-of-the-envelope’’ relationships are derived that have proven useful in teaching this subject.
Relativistic transformations of light power
Authors: McKinley John M.
Published: March 2005

Using a photon-counting technique, we find the angular distribution of emitted and detected power and the total radiated power of an arbitrary moving source. We compare these expressions to the incorrect or incomplete expressions previously reported. We use the technique to verify the predicted effect of the earth’s motion through the cosmic blackbody radiation.
New mathematical proof of the uncertainty relation
Authors: Williams David N.
Published: March 2005

We present a new proof of the uncertainty relation for wave functions that are absolutely integrable and have absolutely integrable Fourier transforms.
Cardiovascular simulator for the undergraduate physics laboratory
Authors: Bruner L. J.
Published: March 2005

An apparatus for simulation of blood flow through the heart and systemic circulation has been constructed. Catheter coupling to an externally mounted strain gauge transducer permits dynamic measurement of arterial and venous pressures. With the simulator, students can observe the effects of stroke volume and rate upon maximum, minimum, and mean arterial pressure. Additional demonstrations are discussed.
Analog computer laboratory with biological examples
Authors: Strebel Donald E.
Published: March 2005

The use of biological examples in teaching applications of the analog computer is discussed. In an introductory general physics laboratory class which included biology majors, the addition of some biologically relevant analog computer problems was well received. The response indicates that such problems can be particularly useful in physics classes which include life-science students or which explore biophysics topics. Several suitable examples from mathematical ecology, enzyme kinetics, and tracer dynamics are described.
Simple astronomical theory of climate
Authors: Benumof Reuben
Published: March 2005

By applying perturbation theory to a highly simplified solar system, we find that the semimajor axis of the Earth’s orbit is secularly invariant, the square of the eccentricity varies approximately sinusoidally with a secular period of 93 000 years, and the perihelion precesses toward the northern summer solstice with a period of approximately 21 000 years relative to the moving vernal equinox. The Earth’s axis also nutates with a period of 41 000 years. These periods correlate very well with the periods found in the climatic record. The secular periods of the Earth’s orbital parameters determine the variation with time of the average intensity of solar radiation and thus may trigger the onset of ice ages.
Lagrangians and systems they describe—how not to treat dissipation in quantum mechanics
Authors: Ray John R.
Published: March 2005

A Lagrangian that yields equations of motion for a damped simple harmonic oscillator is shown not to describe this system, but a completely different physical system. Thus, we have a simple counterexample to the statement: ’’If a Lagrangian gives the correct equations of motion for a given system then the Lagrangian describes the system.’’ We also construct a physical system that the Lagrangian describes and derive some of its properties. The quantum theory based on the above Lagrangian has been used to attempt to discuss the quantum theory of dissipation. This is, however, incorrect since the system the Lagrangian describes has no dissipation.
Pseudopotentials for excited states of hydrogen: A vivid illustration of limitations to the use of pseudopotential results
Authors: Goodfriend P. L.
Published: March 2005

It is shown that exact pseudopotentials for excited states of hydrogen atoms can be derived. Use is made of this novel application of pseudopotential theory to display limitations to the use of pseudopotential results.
An inexpensive torsional pendulum apparatus for rigidity modulus measurement
Authors: Tyagi S. , Lord A. E.
Published: March 2005

We describe an easy to assemble torsional pendulum which can be put together for about $5 from parts available at any hardware store. The accuracy obtained in the measurement of the modulus of rigidity, G, is comparable the accuaracy obtained with the more expensive commercially available student models.
Nonrelativistic contribution to Mercury’s perihelion precession
Authors: Price Michael P. , Rush William F.
Published: March 2005

We present here a calculation of the precession of the perihelion of Mercury due to the perturbations from the outer planets. The time-average effect of each planet is calculated by replacing that planet with a ring of linear mass density equal to the mass of the planet divided by the circumference of its orbit. The calculation is easier than examples found in many undergraduate theoretical mechanics books and yields results which are in excellent agreement with more advanced treatments. The perihelion precession is seen to result from the fact that the outer planets slightly change the radial period of oscillation from the simple harmonic period usually calculated for small displacements from equilibrium. This new radial period therefore no longer matches the orbital period and the orbit consequently does not exactly retrace itself. The general question of whether a given perturbation will cause the perihelion to advance or regress is shown to have the following answer: if a perturbing force is central and repulsive and also becomes stronger as the distance from the force center increases, the perihelion will advance. If the central perturbing force is attractive and also becomes stronger as the distance from the force center increases, the perihelion will regress.
A rapid, convenient, and precise method for the absolute determination of the acceleration of gravity
Authors: Manche Emanuel P.
Published: March 2005

A compact and portable apparatus for the measurement of the value for the gravitational acceleration g is described and the results of an experiment is given. It consists of a falling mercury drop and an electronic timing circuit which conveniently and automatically generates a large number of data in a short period of time, yielding results with a high degree of precision. In an experiment on 47 consecutive trials, a value of 982.44 cm sec−2 was obtained with a standard error of the mean of ±0.02 cm sec−2, and an accuracy of 0.22%.
Simplified derivation of the Fokker-Planck equation
Authors: Siegman A. E.
Published: March 2005

An alternative derivation of the Fokker-Planck equation for the probability density of a random noise process is presented, starting from the Langevin equation. The derivation makes use of the first two derivatives of the Dirac delta function. The derivation of the Fokker-Planck equation then becomes simpler and more transparent, at least for those willing to accept these singularity functions.
Physics of the tennis racket
Authors: Brody H.
Published: March 2005

Several parameters concerning the performance of tennis rackets are examined both theoretically and experimentally. Information is obtained about the location of the center of percussion, the time a ball spends in contact with the strings, the period of oscillation of a tennis racket, and the coefficient of restitution of a tennis ball. From these data it may be possible to design a racket with improved playing characteristics.
Analogy between thermodynamics and mechanics
Authors: Peterson Mark A.
Published: March 2005

We note that equations of state—by which we mean identical relations among the thermodynamic variables characterizing a system—are actually first-order partial differential equations for a function which defines the thermodynamics of the system. Like the Hamilton-Jacobi equation, such equations can be solved along trajectories given by Hamilton’s equations, the trajectories being quasistatic processes which obey the given equation of state. This gives rise to the notion of thermodynamic functions as infinitesimal generators of quasistatic processes, with a natural Poisson bracket formulation. This formulation of thermodynamic transformations is invariant under canonical coordinate transformations, just as classical mechanics is, which is to say that thermodynamics and classical mechanics have the same formal structure, namely a symplectic structure.
Thermodynamic derivation of the equilibrium distribution functions of statistical mechanics
Authors: Stoeckly Beth
Published: March 2005

A simplified derivation of the equilibrium distribution functions is presented. The derivation proceeds from the change in the Helmholtz free energy when a particle is added to a system of fixed temperature, volume, and chemical potential. Besides its simplicity, this form of the derivation offers a clear view of the relationship between statistical mechanics and macroscopic thermodynamics.
Simple laser scattering experiment for biology-oriented physics labs
Authors: Orwig L. , Schrank G.
Published: March 2005

A low intensity laser light scattering laboratory exercise has been designed and introduced into the lower division physics course for biology students at the University of California, Santa Barbara. Students determine the diameter of micron-sized latex spheres (simulated microbes) in water suspension. By using their own eyes as part of the measuring apparatus the students become personally involved in the experiment, which is relevant to their field of interest. Accuracies of 1%–2% are normal, and student response has been unusually positive.
A novel light trapping phenomenon in fluid media
Authors: Devlin J. C. , Tolles W. M.
Published: March 2005

Injection of a thin layer of solution at the boundary of a moving solvent is utilized to create a thin fluid sheet having an index of refraction greater than that of the surrounding medium. Conditions are such that light trapping is easily observed in the thin fluid sheet. Diffusion effects give rise to a concentration profile which is quadratic at the boundary. As a consequence of this quadratic dependence, an interesting hopping and refocusing of a trapped beam is observed as it traverses the fluid sheet. The observed phenomenon is readily modeled by use of the Navier Stokes equation and the diffusion equation.
Electrostatic problems? Relax!
Authors: DiStasio M. , McHarris W. C.
Published: March 2005

We describe the numerical methods of relaxation and over-relaxation for solving Laplace’s equation for a system of conductors. These methods are quite tractable nowadays using only modest sized computers. Several simple (analytically solvable) though moderately complicated (arising from experimental situations) examples of their use are given.
Multichannel analyzer built from a microcomputer
Authors: Spencer C. D. , Mueller P.
Published: March 2005

A 1024 channel multichannel analyzer has been built using eight-bit S-100 bus microcomputer hardware. The analyzer has pulse height analysis and multiscaling data acquisition modes. A Mössbauer control signal is provided. The output modes are an oscilloscope display, print data, and send data to another computer. The system’s hardware and software are described. Costs and advantages relative to commercial multichannels are discussed.
Contemporary American physics fiction
Authors: Friedman Alan J.
Published: March 2005

The great post-Newtonian revolution in physical science culminated with Einstein’s general theory of relativity in the second decade of our century, and with the establishment of the quantum theory in the third decade. The responses of literature over the past half century to these changes in world view have served as stimulating examples of cultural interchange. The novels of Thomas Pynchon, William Gaddis, Robert Coover, Joseph McElroy, Don DeLillo, and Robert Pirsig make use of the new physics as metaphor for three traditional activities of novelists: examining order and disorder, questioning cause and effect, and seeking unity in the human and physical universes.
Bode’s law and the ’’missing moons’’ of Saturn
Authors: Tomley Leslie J.
Published: March 2005

A theory concerning the orbital spacing patterns in the solar system, more intriguing than many of the traditional topics to our general studies astronomy students and useful pedagogically since it is accessible to such students in quantitative as well as qualitative terms, is presented. The orbital distributions of the planets and major satellite systems are fitted with a Bode-type form. The Saturnian system requires vacant orbitals if the best fit is to have an accuracy comparable to that obtained for the other systems. One pattern of vacant orbitals is shown to be consistent with what would be expected if Titan produced resonant perturbations on the forming satellite system.
Spin and uncertainty in the interpretation of quantum mechanics
Authors: Hestenes David
Published: March 2005

A rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron. Since the dispersion in electron momentum is determined by the zero-point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.
A windmill’s theoretical maximum extraction of power from the wind
Authors: Inglis David Rittenhouse
Published: March 2005

The fraction of the kinetic energy of the wind impinging on its area, that a wind turbine can convert to useful power, has been shown by Betz in an idealized laminar-flow model to have an upper limit of 16/27 or 59%. The limit is here simply rederived and it is shown how deviations from the idealized model, involving rotational kinetic energy of the downwind stream and turbulent mixing from outside the boundaries of the idealized stream, can either increase or decrease the power available. The limit is thus not a strict upper limit in practice.
Intrinsic angular momentum of light
Authors: Santarelli Vincent
Published: March 2005

A familiar theorem involving a balance between net torque and rate of change of angular momentum in the electromagnetic field is rederived. This version of the theorem includes the intrinsic torques exerted by the fields on the polarized medium. It is seen that these terms lead naturally to the expression for the intrinsic angular momentum carried by a localized pulse of electromagnetic radiation. In the present treatment the expressions for the external and intrinsic angular momenta arise naturally as separate entities, in contrast to standard treatments, in which both arise out of what is evidently only the external angular momentum.
Equivalence of Einstein’s 1925 unified field theory and his relativistic theory of the nonsymmetric field
Authors: Johnson Coates R.
Published: March 2005

It is shown that Einstein’s final unified field theory, the relativistic theory of the nonsymmetric field, is identical to a theory Einstein proposed in 1925.
Inexpensive time-of-flight velocity measurements
Authors: Everett Glen E. , Wild R. L.
Published: March 2005

An inexpensive circuit useful in time-of-flight velocity measurements is described. Its use for bullet velocity determination in connection with the ballistic pendulum demonstration of momentum conservation is described. Mechanical construction considerations are outlined.
Rigidly connected accelerated clocks
Authors: Giannoni Carlo , Gro/n O/yvind
Published: March 2005

Standard clocks at rest in (i) a rigidly hyperbolically accelerated reference frame, (ii) on a rotating disk, and (iii) on the surface of the earth are considered. Special relativity is sufficient to predict the behavior of the clocks in cases (i) and (ii). In case (iii), however, gravitational effects are important, which is taken account of by use of the principle of equivalence. It is concluded that in cases (i) and (ii) clocks connected along a line in the direction of the acceleration do not maintain Einstein synchronization. As to the rate of standard clocks on the surface of the earth, the drifts caused by the rotating motion of the earth and the deviation of the earth’s surface from a sphere cancel each other. On the geoid this cancellation is exact. This means that the synchronization of clocks at every position at the mean sea level, no matter how far apart on the earth they are located, is not destroyed by these effects. Owing to tidal effects clocks on the earth at different positions in the solar gravitational field do not maintain their synchronization. This effect is several orders of magnitude less than the above ones.