F. HERRMANN, P. SCHMÄLZLE
Am. J. Phys. 49, 761 (1981)
Abstract:A well-known collision experiment can be carried out with an arrangement of several identical elastic balls each suspended by two threads and in contact with one another: a certain number of the balls is displaced from its equilibrium position and then released, so as to collide with the remaining balls at rest. After the collision, the same number of balls moves away to the other side as had initially been displaced It is shown that, contrary to common belief, the conservation laws of energy and momentum alone are not sufficient to explain this behavior. Indeed, a further condition must be satisfied by the system of balls; namely, it must be capable of dispersion-free energy propagation.
F. HERRMANN, M. SEITZ
Am. J. Phys. 50, 977 (1982)
Abstract: A well-known collision experiment can be carried out with an arrangement of several elastic balls suspended in a horizontal row. As we have shown in a previous article a necessary condition for the observed, simple behavior of this arrangement during collision is that the perturbation propagates throughout the system without dispersion. In the present paper, we show that the arrangement can be described by a series of spatially separated masspoints and springs of a special type: the exponent of the force law of the springs is 1.5 according to a theory of H. Hertz. It follows that the first collision sequence of such an experiment is not completely dispersion free. Indeed, slight dispersion during the first collision sequence creates the conditions for the total absence of dispersion in all the subsequent collisions.
F. HERRMANN, T. MÜHLBAYER
Am. J. Phys. 51, 344 (1983)
G. FALK, F. HERRMANN, G. BRUNO SCHMID
Am. J. Phys. 51, 1074 (1983)
Abstract: It is customary to say that energy exists in different forms which are transformed or converted into one another during physical processes. However, a careful analysis shows that thinking in and speaking of energy forms is inappropriate and conceptually even misleading. Since most textbooks use the term "energy form" without spelling out a clear procedure by which different "forms" of energy can be categorized, rigorous criteria for categorizing flowing and stored energy are discussed in this paper. These criteria show that the term "energy form" for the respective categories is unsatisfactory because it easily leads to the misinterpretation that there are different kinds of energy, rather than emphasizing the simpler and physically more correct picture of energy as an unalterable substance. Taking into account the well-known but little recognized natural law that energy always flows simultaneously with at least one other physical quantity, the concept of energy carrier is introduced. This concept provides a clear picture of how energy is transported, exchanged, and stored. This picture is scientifically accurate, yet simple and easy to present even at an elementary level.
F. HERRMANN, G. BRUNO SCHMID
Am. J. Phys. 52, 146 (1984)
Abstract: Newton's Second Law is equivalent to the continuity equation for momentum in integral form. This insight leads to an alternative picture of forces as momentum currents. The purpose of the present paper is to introduce a new approach to statics problems and their solutions in terms of momentum currents. In particular, the relation between the distribution of momentum currents and the elastic stresses within a medium will be considered and a simple way to pictorially represent those stresses with the help of momentum flow diagrams will be discussed. Handling statics problems in the momentum current picture immediately displays their relationship to analogous problems in electrical network theory. This uncovers a structural relationship between the role of electric charge in the theory of electricity and the role of momentum in mechanics. For example, it will be shown that the familiar method for the solution of statics problems in terms of free-body diagrams is equivalent to the use of a junction rule for momentum currents.
Response to "Comments on 'A simple explanation of a well-known collision experiment' "
HERRMANN, P. SCHMÄLZLE
Am. J. Phys. 2, 84 (1984)
G. B. SCHMID
Am. J. Phys. 52, 794 (1984)
Abstract: A unified approach to science teaching based upon a certain class of quantities which play fundamental roles in classical and modern physics is introduced. These quantities share the property of being substance-like, that is, each can be pictured to be contained in bodies and to flow from one body to another like a kind of "stuff." Such quantities include, for example, energy ( = mass), momentum, angular momentum, electric charge, particle number = amount of substance), and entropy. When emphasizing substance-like quantities, the breakup of physics into sub-branches is nothing more than a classification of natural processes according to the substance-like quantity playing the dominant role in each case. The method of presentation, however, remains the same from one sub-branch to another: different natural processes can be simply visualized and quantitatively described according to the same formal rules in terms of the increasing, decreasing, and flowing of the respective substance-like quantities in each case. Thus knowledge of a single branch of physics already provides an analogy for the ways and means by which processes are described in other branches (including chemistry and biology) as well. These claims are illustrated with the help of a few simple examples.
HERRMANN, G. BRUNO SCHMID
Am. J. Phys. 53, 415 (1985)
Abstract: Newton's second law is equivalent to the continuity equation for momentum in integral form. This insight provides an alternative picture of forces in terms of momentum currents. In such a picture, the forces exerted on an object via a field are completely described locally in terms of the momentum current density of the field. The momentum current picture leads to a representation of Maxwell's stress tensor which is easy to visualize and to sketch quantitatively. Computer sketches of the momentum current distributions for a few simple examples are presented. In particular, it is shown that two like charges are "pulled apart" by their common electric field and that two parallel wires carrying electric currents in the same direction are "pushed together" by their common magnetic field.
F. HERRMANN, G. BRUNO SCHMID
Am. J. Phys. 53, 735 (1985)
Abstract: A simple arrangement is discussed which demonstrates "spin-spin" and "spin-orbit" coupling between rotating systems both with and without dissipation.
F. HERRMANN, G. BRUNO SCHMID
Am. J. Phys. 54, 528 (1986)
Abstract: The Poynting vector field of a transformer with two separated coils and long, parallel arms has the same distribution as that of a pair of parallel electric conductors. The magnetic field between the arms of a transformer plays the same important role for the energy transport in a transformer as does the electric field for the transport of energy between the conductors of a conductor pair. In the latter case, the energy current ( = power) P is given by the familiar expression P = UI, where U is the electric tension between the conductors and I the electric charge current through them. In the former case, we find an analogous expression P = UmIm for the energy current in a transformer. Here Um is the magnetic tension Um = Integral dr H between the arms of the transformer (H = magnetic field vector) and Im = -Integral d A B is the Hertz magnetic current (B = the time derivative of the magnetic induction B) through them. An experiment will be described which shows that the energy loss in a transformer is related to a magnetic potential drop within each of the two arms of the transformer.
Am. J. Phys. 54, 658 (1986)
Am. J. Phys. 57, 707 (1989)
Abstract: By introducing the electromagnetic field in the customary way, ideas are promoted that do not correspond to those of contemporary physics: on the one hand, ideas that stem from pre-Maxwellian times when interactions were still conceived as actions at a distance and, on the other hand, ideas that can be understood only from the point of view that the electromagnetic field is carried by a medium. A part of a course in electromagnetism is sketched in which, from the beginning, the electromagnetic field is presented as a system in its own right and the local quantities energy density and stress are put into the foreground. In this way, justice is done to the views of modern physics and, moreover, the field becomes conceptually simpler.
F. HERRMANN, M. SCHUBART
Am. J. Phys. 57, 858 (1989)
Am. J. Phys. 59, 447 (1991)
Abstract: A widely recognized problem that physics teachers encounter is the difficulty that most students have when solving problems related to magnetic field line distributions in the presence of hard- and softmagnetic materials. Two causes of these difficulties are identified: (1) the fact that the hysteresis is introduced as the typical behavior of ferromagnetic materials; (2) the fact that the magnetic field strength H is almost absent in the electromagnetism course. In order to remedy the student's problems we propose: - to introduce four idealized magnetic materials, i.e. unmagnetic, hardmagnetic, softmagnetic and superconducting materials; - to use the magnetic field strength H, and not the magnetic induction B, when discussing problems of magnetostatics.
Am. J. Phys. 61, 119-121 (1993)
Abstract: Most physics students know little about energy flow distributions. The example shows the unexpected path of the energy in a familiar situation.
F. HERRMANN, D. SCHAETZLE
Am. J. Phys. 64, 1448 (1996)
(Answer by Roger Morehouse in Am. J. Phys. 66, 12 (1998))
F. HERRMANN, H. HAUPTMANN
Am. J. Phys. 65, 292 (1997)
Abstract: The stability of the nuclear fusion reaction in a star is due to the negative specific heat of the system. Examining the literature one gets the impression that this phenomenon results from a complicated interplay of the various pertinent field variables. We introduce a simple model system, which displays the same behaviour as a star and, which can be treated quantitatively without solving any differential equation.
Am. J. Phys. 65, 1135 (1997)
F. HERRMANN, H. HAUPTMANN, M. SULEDER
Am. J. Phys. 68, 171-174 (2000)
Abstract: We propose for the graphical representation of fields, not to limit to field lines but also to draw the orthogonal surfaces. Just as the ends of the electric or magnetic field lines tell us where the sources of the flux of a field are located, the borders of the orthogonal surfaces indicate us the sources of the field's circulation.
H. HAUPTMANN, F. HERRMANN, K. SCHMIDT
Am. J. Phys. 68, 421-423 (2000)
Abstract: As a star is evolving from the hydrogen to the helium burning stage, i. e. from the sun-like state to the state of a red-giant star, the temperature of its core increases whereas the volume decreases. At the same time the temperature of its shell decreases while the volume of the shell increases. This behaviour of the core and of the shell is explained qualitatively by a simple model. The star is considered to be composed of two homogeneous subsystems: the active core where the heat production takes place and the shell which plays the part of a thermal insulator. Each of these subsystems is stabilized by a feedback mechanism which is working thanks to the negative heat capacity of both systems.
T. WÜNSCHER, H. HAUPTMANN, F. HERRMANN
Am. J. Phys. 70, 599-606 (2002)
Abstract:Pictures of the energy density and the energy flow in distributions of incoherent light for various two-dimensional situations are shown and discussed. Rules are introduced that allow one to sketch and to interpret such pictures.
F. HERRMANN, P. WÜRFEL
Am. J. Phys. 73, 717-721 (2005)
Abstract: Thermodynamic states and processes involving light are discussed in which the chemical potential of light is nonzero. Light with nonzero chemical potential is produced in photo-chemical reactions, for example, in a light emitting diode. The chemical potential of black-body radiation becomes negative upon a Joule expansion. The isothermal diffusion of light, which is a common phenomenon, is driven by the gradient in the chemical potential. These and other examples support the idea that light can be interpreted as a gas of photons, with properties similar to a material gas.
F. HERRMANN, P. WÜRFEL
Am. J. Phys. 74, 591-594 (2006)
Abstract: An explanation of the principles of a pn junction is proposed without recourse to the band model, the space charge of the junction, and the charge carrier depletion at the interface. The explanation assumes that the processes in a pn junction can be considered as a chemical reaction between electrons, holes, and photons and that an n-type material is a conductor for electrons and an insulator for holes, and a p-type material is a conductor for holes and an insulator for electrons. We give a simple and concise explanation of rectification, light emission, and current generation by pn junctions.