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Nov 2000

Volume 68, Issue 11, pp. 977-1065

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The physics tutorial: Some cautionary remarks

James J. Carr

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 977

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Abstract Unavailable
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01.50.-i Educational aids
42.25.-p Wave optics
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Dynamics of the baseball–bat collision

Alan M. Nathan

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 979 | Cited 23 times

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A model is developed for the collision between the baseball and bat, taking into account the transverse bending vibrations of the bat. By coupling the flexible bat to the ball via a parametrized force that each mutually exerts on the other, a complete description of the collision process is obtained, including the exit speed of the ball vf. It is shown that vibrations play an important role in determining vf. The model is in excellent agreement with experimental data at low impact velocities. At the higher velocities more appropriate to the game of baseball, vf is shown to coincide with the rigid-body value only over a very small region in the barrel of the bat and to drop off sharply for impacts removed from that region. Some interesting insights into the collision process are obtained, including the observation that for impacts in the barrel of the bat, the momentum transferred to the ball is essentially complete by the time the elastic wave first arrives at the handle and that any clamping action of the hands will affect the bat at the impact point only after the ball and bat have separated. This suggests that vf is independent of the size, shape, and method of support of the bat at distances far from the impact location. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
01.55.+b General physics
45.40.Gj Ballistics (projectiles; rockets)

Opposite momenta lead to opposite directions

Asher Peres

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 991 | Cited 2 times

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When a particle decays into two fragments, the wavefunctions of the latter are spherical shells with expanding radii. In spite of this spherical configuration, the two particles can be detected only in opposite directions. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

Laser trapping of microscopic particles for undergraduate experiments

Robert Pastel, Allan Struthers, Ryan Ringle, Jeremy Rogers, Charles Rohde, and Peter Geiser

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 993 | Cited 12 times

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We present detailed instructions for constructing and operating an optical trap using a hollow core fiber and two-laser beams. The trap is stable, confining 100-nm to 10-μm particles of a variety of materials for hours of leisurely observation. The trap operates at room temperature and atmospheric pressure, costs less than $1400, and requires no machining. The hollow fiber provides automatic relative beam alignment and shields trapped particles from the ambient convective flow. An experiment and analysis of the Mie scattering from the trapped particle is outlined. A list of other interesting experiments based on the trap is provided. © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
37.20.+j Atomic and molecular beam sources and techniques
42.62.-b Laser applications
41.20.Jb Electromagnetic wave propagation; radiowave propagation

Surface charges and fields of simple circuits

Norris W. Preyer

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1002 | Cited 10 times

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Interest in the surface charges on circuits, and their utility in the conceptual understanding of circuit behavior, has recently increased. Papers and textbooks have discussed surface charges either with qualitative diagrams or analytic results for very special geometries. Here, I present the results of numerical calculations showing the surface charges on several simple resistor-capacitor circuits. Surface charges are seen to guide the motion of charges and create the appropriate electric potential and Poynting vectors for the circuit, and hence are an important factor in the teaching of circuit theory. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
84.30.Bv Circuit theory
84.32.Ff Conductors, resistors (including thermistors, varistors, and photoresistors)
84.32.Tt Capacitors

Lorentz transformation of a system carrying “Hidden Momentum”

E. Comay

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1007 | Cited 3 times

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The relations between an energy–momentum tensor and its corresponding energy–momentum four-vector are discussed. A particular emphasis is put on conditions guaranteeing that spatial integrals of the energy–momentum densities pertain to a true four-vector. Cases where such integrals are not components of a true four-vector are analyzed and the usefulness of the notion of a false four-vector is pointed out. Results are used for explaining Lorentz transformation properties of “hidden momentum.” © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

Response to “Lorentz transformation of a system carrying ‘Hidden Momentum,’ ” by E. Comay [Am. J. Phys. 68, 1007 (2000)]

V. Hnizdo

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1014 | Cited 2 times

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We respond to Comay’s criticism of the use of covariant definitions of the electromagnetic and mechanical energy–momenta in an analysis of the role of hidden momentum in the total energy–momentum four vector of a macroscopic body. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

A circular twin paradox

Maria B. Cranor, Elizabeth M. Heider, and Richard H. Price

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1016 | Cited 6 times

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In the special relativistic twin paradox presented here, each twin lives on one ring of a counterrotating pair of infinitesimally separated rings, so that the twins travel on the same circular path but in opposite directions. The observers on the ring of one twin should see the clock of the other twin slowed by time dilation, but at each meeting of the twins symmetry demands that they agree on the amount of time that has passed since their previous meeting. The resolution of the paradox focuses attention on the relation of time dilation to clock synchronization. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

Can wave–particle duality be based on the uncertainty relation?

Stephan Dürr and Gerhard Rempe

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1021 | Cited 13 times

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Wave and particle properties of a quantum object cannot be observed simultaneously. In particular, the fringe visibility in an interferometer is limited by the amount of which-way information which can be obtained. This limit is set by the recently discovered duality relation. So far, all derivations of the duality relation are independent of Heisenberg’s uncertainty relation. Here we demonstrate that it is alternatively possible to derive the duality relation in the form of an uncertainty relation for some suitably chosen observables. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory
07.60.Ly Interferometers

The coefficient of restitution for collisions of happy balls, unhappy balls, and tennis balls

Rod Cross

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1025 | Cited 7 times

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A perfectly happy ball is one that bounces to its original height when dropped on a massive, rigid surface. A completely unhappy ball does not bounce at all. In the former case, the coefficient of restitution (COR) is unity. In the latter case, the COR is zero. It is shown that when an unhappy ball collides with a happy ball, the COR increases from zero to unity as the stiffness of the happy ball decreases from infinity to zero. The COR is independent of the mass of each ball. The implication of reducing the COR of a tennis ball, as a possible means of slowing the serve in tennis, is also considered. It is shown that (a) the COR for a collision with a racket varies with the impact point and is a maximum at the vibration node near the center of the strings, and (b) the serve speed is reduced by only about 20% if the COR for a bounce on the court is reduced to zero. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
01.55.+b General physics
45.40.-f Dynamics and kinematics of rigid bodies

Thermodynamics and occupation numbers of a Fermi gas in the canonical ensemble

K. Schönhammer

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1032 | Cited 3 times

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Exact results for the thermodynamic properties and mean occupation numbers of a system of noninteracting fermions with equidistant level spacing are presented for an arbitrary number of particles. It is discussed quantitatively how the results converge to the corresponding ones in the grand canonical ensemble when the thermodynamic limit is reached. From the simple calculations it also follows that the thermodynamics of an infinite two-dimensional electron gas is identical to that of a one-dimensional harmonic chain with linearized dispersion. The results generalize and simplify previous approaches to this model published in this journal. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
05.30.Fk Fermion systems and electron gas
05.30.Ch Quantum ensemble theory

Plumb line and the shape of the earth

Pirooz Mohazzabi and Mark C. James

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1038

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The equation for plumb line deviation currently presented in textbooks ignores the effect of earth’s flattening on the direction of true gravitational acceleration and is incorrect by nearly a factor of 2. The correct equation is consistent with the shape and dimensions of the earth with a very high degree of accuracy. The simple treatment of the problem uses Newton’s second law in an inertial reference system and is suitable for introductory physics courses. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
91.10.Nj Rotational variations; polar wobble
06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
91.10.Qm Harmonics of the gravity potential field; geopotential theory and determination

Tilted boxes on inclined planes

A. M. Nunes and J. P. Silva

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1042 | Cited 1 time

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We propose the study of a box placed on an inclined plane, with an initial tilt with respect to the plane. This is a paradigmatic example of the role played by friction as a link between translational and rotational motion. This example has two advantages over the usual example of a sphere (or cylinder) rolling down an inclined plane. First, it provides a good model for a much greater variety of “real-life” situations. Second, it exhibits a much richer structure in parameter space, even when the box starts from rest. © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
45.05.+x General theory of classical mechanics of discrete systems

Relativistic hydrogen atom revisited

R. P. Martínez-y-Romero

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1050 | Cited 9 times

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The hydrogen atom is solved using a simple method. We show that this system has an exact solution that can be written in terms of Laguerre polynomials of noninteger index, instead of the hypergeometric series. This point is important because Laguerre polynomials of integer index appear in the solution of the nonrelativistic hydrogen atom, giving students a more unified point of view for this system. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
02.10.De Algebraic structures and number theory

On the partial wave amplitude of Coulomb scattering in three dimensions

Qiong-gui Lin

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1056 | Cited 4 times

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The partial wave series for the Coulomb scattering amplitude in three dimensions is evaluated in a very simple way to give the closed result. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Nk Scattering theory
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Averages of static electric and magnetic fields over a spherical region: A derivation based on the mean-value theorem

Ben Yu-Kuang Hu

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1058 | Cited 1 time

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Abstract Unavailable
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01.50.-i Educational aids
41.20.-q Applied classical electromagnetism
03.50.De Classical electromagnetism, Maxwell equations

Erratum: “Incomplete descriptions and relevant entropies” [Am. J. Phys. 67 (12), 1078–1090 (1999)]

Roger Balian

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1060 | Cited 1 time

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Abstract Unavailable
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01.50.-i Educational aids
05.20.-y Classical statistical mechanics
05.70.Ce Thermodynamic functions and equations of state
02.50.Cw Probability theory
05.70.Ln Nonequilibrium and irreversible thermodynamics
99.10.Cd Errata
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Inexpensive wooden-ball models for close-packed crystal structures

Jon Eggert

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1061 | Cited 1 time

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The two common close-packed structures, face-centered cubic (fcc) and hexagonal close packed (hcp), play a leading role in discussions of crystal structure in solid-state physics courses. It is also common in crystal chemistry to describe many inorganic crystal structures based on either the fcc or the hcp structure, generally with one atom type occupying the close-packed lattice sites and other atoms occupying a fraction of the tetrahedral and octahedral interstitial sites. This note describes simple, inexpensive ball models for the fcc and hcp structures through which students can gain an intuitive, hands-on feel for the structures, their interstitial sites, and their primitive cells. © 2000 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
61.50.-f Structure of bulk crystals
61.72.J- Point defects and defect clusters
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Supersymmetry: Squarks, Photinos, and the Unveiling of the Ultimate Laws of Nature

Gordon Kane, Author and Hans Christian von Baeyer, Reviewer

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1064

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Abstract Unavailable
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01.30.Vv Book reviews
11.30.Pb Supersymmetry
14.80.Ly Supersymmetric partners of known particles

Physics from Fisher Information: A Unification

B. Roy Frieden, Author and Philippe M. Binder, Reviewer

American Journal of Physics -- November 2000 -- Volume 68, Issue 11, pp. 1064 | Cited 1 time

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Abstract Unavailable
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01.30.Vv Book reviews
01.50.-i Educational aids
02.30.Xx Calculus of variations
02.30.Yy Control theory
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