# Revista Brasileira de Ensino de Física

Published by SciELO

Online ISSN: 1806-9126

Print ISSN: 1806-1117

Published by SciELO

Online ISSN: 1806-9126

Print ISSN: 1806-1117

Publications

Critical phenomena were discovered by Cagniard de la Tour in 1822, who died 150 years ago. In order to mark this anniversary, the context and the early history of his discovery is reviewed. We then follow with a brief sketch of the history of critical phenomena, indicating the main lines of development until the present date. Os fen\'omenos cr\'{\i}ticos foram descobertos pelo Cagniard de la Tour em Paris em 1822. Para comemorar os 150 anos da sua morte, o contexto e a hist\'oria initial da sua descoberta \'e contada. Conseguimos com uma descri\c{c}\~ao breve da hist\'oria dos fen\'emenos cr\'{\i}ticos, indicando as linhas principais do desenvolvimento at\'e o presente. Comment: Latex2e, 8 pp, 3 eps figures included

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Acceleration sensors built into smartphones, i-pads or tablets can
conveniently be used in the Physics laboratory. By virtue of the equivalence
principle, a sensor fixed in a non-inertial reference frame cannot discern
between a gravitational field and an accelerated system. Accordingly,
acceleration values read by these sensors must be corrected for the
gravitational component. A physical pendulum was studied by way of example, and
absolute acceleration and rotation angle values were derived from the
measurements made by the accelerometer and gyroscope. Results were corroborated
by comparison with those obtained by video analysis. The limitations of
different smartphone sensors are discussed.

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We proposed an analytical model for the calculus of illumination time of the
Earth for any time of year and any latitude, this model assumes the obliquity
of the ecliptic as constant, the light beams as parallels, the Earth as
spherical, the movement of translation of Earth as uniform circular, also this
model showed a context of the astronomy whereby the teachers can teach the
basic physics.It was built through a relationship between the movement of
translation and of rotation of the wave front light, then we found the of
illumination zone on the Earth and the illumination time is estimated in a
particular latitude with the uniform circular movement of Earth. Present model
was confronted with the numerical results of the Geoscience Australia Agency
and it is found a maxim perceptual error of 1,6%, this value was assigned
primarily to the difference between the circular trajectory, in this model, and
the elliptical trajectory that is the real. Without the use of spherical
trigonometry was obtained an analytical model that estimates very close the
solar illumination time at any time of year and any latitude on earth, the
model provides an authentic context for studying basic aspects of physics.

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The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed out.

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One dimensional quantum mechanics problems, namely the infinite potential
well, the harmonic oscillator, the free particle, the Dirac delta potential,
the finite well and the finite barrier are generalized for finite arbitrary
dimension in a radially symmetric, or angular invariant, manner. This
generalization enables the Schr\"{o}dinger equation solutions to be visualized
for Bessel functions and Whittaker functions, and it also enables connections
to multi-dimensional physics theories, like string theory.

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Physics has played a fundamental role in medicine sciences, specially in
imaging diagnostic. Currently, image reconstruction techniques are already
taught in Physics courses and there is a growing interest in new potential
applications. The aim of this paper is to introduce to students the electrical
impedance tomography, a promising technique in medical imaging. We consider a
numerical example which consists in finding the position and size of a
non-conductive region inside a conductive wire. We review the electric
impedance tomography inverse problem modeled by the minimization of an error
functional. To solve the boundary value problem that arises in the direct
problem, we use the boundary element method. The simulated annealing algorithm
is chosen as the optimization method. Numerical tests show the technique is
accurate to retrieve the non-conductive inclusion.

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Using the damped pendulum model we introduce the averaging method to study the periodic solutions of dynamical systems with small non--autonomous perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear perturbed damped pendulum. The averaging method provides a useful means to study dynamical systems, accessible to Master and PhD students.

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An analysis is performed of the role played by physical intuition in expressing the electromagnetic field in terms of its sources in the time-dependent case. The conclusion is that it is dangerous to dissociate physical intuition from the mathematical description of the phenomena.

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The blackbody radiation is analyzed in universes with $D$ spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density as well as the total energy density are sensible to the dimensionality of the universe. Wien's displacement law and the Stefan-Boltzmann law are properly generalized.

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In this work we study the problem of one-dimensional elastic collisions of
billiard balls, considered as rigid bodies, in a framework very different from
the classical one presented in text books. Implementing the notion of impedance
matching as a way to understand eficiency of energy transmission in elastic
collisions, we find a solution which frames the problem in terms of this
conception. We show that the mass of the ball can be seen as a measure of its
impedance and verify that the problem of maximum energy transfer in elastic
collisions can be thought of as a problem of impedance matching between
different media. This approach extends the concept of impedance, usually
associated with oscillatory systems, to system of rigid bodies.

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We derive an exact closed-form representation for the Euclidean thermal Green
function of the two-dimensional (2D) free massless scalar field in coordinate
space. This can be interpreted as the real part of a complex analytic function
of a variable that conformally maps the infinite strip $-\infty<x<\infty$
($0<\tau<\beta$) of the $z=x+i\tau$ ($\tau$: imaginary time) plane into the
upper-half-plane. Use of the Cauchy-Riemann conditions, then allows us to
identify the dual thermal Green function as the imaginary part of that
function.

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The problem of bound states in a double delta potential is revisited by means
of Laplace transform method. Quite differently from direct methods, no
knowledge about the jump discontinuity of the first derivative of the
eigenfunction is required to determine the solution.

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A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the method. Comment: In Portuguese. To appear in RBEF

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In the present work we study the well-known Two Capacitor Problem from a new
perspective. Although this problem has been thoroughly investigated, as far as
we know there are no studies of the thermodynamic aspects of the discharge
process. We use the Free Electron Gas Model to describe the electrons' energy
levels in both capacitors in the low temperature regime. We assume that the
capacitors and the resistor can exchange energy freely with a heat reservoir.
We assume that the resistance is large enough to consider an isothermal heat
exchange between the resistor and the heat reservoir. Thereby we obtain a
positive entropy variation due to the discharge process, corroborating its
irreversibility.

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The electrostatic field energy due to two fixed pointlike charges shows some
peculiar features concerning the distribution in space of the field energy
density of the system. Here we discuss the evaluation of the field energy and
the mathematical details that lead to those peculiar and non-intuitive physical
features.

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Descreve-se neste trabalho uma proposta de curr\'iculo interdisciplinar para
a forma\c{c}\~ao de professores de ci\^encias da natureza. O curso permite a
obten\c{c}\~ao de quatro diplomas: professor de ci\^encias para o ensino
fundamental (nomenclatura brasileira), professor de biologia, f\'isica e
qu\'imica para o ensino m\'edio. O diploma de professor de ci\^encias \'e
obtido com a integraliza\c{c}\~ao de cr\'editos oferecidos ao longo dos tr\^es
primeiros anos do curso. Para cada ano subsequente \'e poss\'ivel obter os
diplomas de professor do ensino m\'edio. Os componentes curriculares
pertinentes \`as ci\^encias da natureza s\~ao inteiramente interdisciplinares
nos tr\^es primeiros anos. No quarto ano s\~ao oferecidas disciplinas
espec\'ificas de biologia, f\'isica e qu\'imica, para a respectiva
forma\c{c}\~ao de professor do ensino m\'edio.
An interdisciplinary curriculum for science teaching undergraduate course
will be described. The curriculum allows four degrees according the Brazilian
educational legislation: science teacher for the middle school, biology,
chemistry and physics teacher for the high school. The science teacher degree
is obtained by accomplishing the three initial years syllabus. For each
subsequent year it will be possible to obtain the other degrees. The components
of the curriculum for the three initial years are radically interdisciplinary,
with a pedagogical organization in such ways to prepare students for the
subsequent year dedicated to a specific discipline (biology, chemistry or
physics).

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When a circular loop composed by a RLC is put to oscillate, the oscillation
will eventually vanish in an exponentially decaying current, even considering
superconducting wires, due to the emission of electric and magnetic dipole
radiation. In this work we propose a modification on the Kirchhoff voltage law
by adding the radiative contributions to the energy loss as an effective
resistance, whose value is relatively small when compared to typical resistance
value, but fundamental to describe correctly real circuits. We have also
analysed the change in the pattern of the radiation spectra emitted by the
circuit as we vary both the effective and electrical resistance.

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Graphical representations of classical Friedmann's models are often
misleading when one considers the age of the universe. Most textbooks disregard
conceptual differences in the representations, as far as ages are concerned. We
discuss the details of the scale-factor versus time function for Friedmann's
solutions in the time range that includes the ages of model universes.

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We present a matrix formalism, inspired by the Minkowski four-vectors of
special relativity, useful to solve classical physics problems related to both
mechanics and thermodynamics. The formalism turns out to be convenient to deal
with exercises involving non-conservative forces and production or destruction
of mechanical energy. On the other hand, it provides a framework to treat
straightforwardly changes of inertial reference frames, since it embodies the
Principle of Relativity. We apply the formalism to a few cases to better show
how it works.

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Em 1952, Kac e Ward desenvolveram uma formulação combinatorial do modelo de Ising em duas dimensões que é um outro método para se obter a famosa fórmula de Onsager para a energia livre por sítio no limite termodinâmico do modelo. Feynman fez importante contribuição a esta formulação conjecturando uma relação matemática crucial que completou as idéias de Kac e Ward. Neste trabalho, o método de Kac, Ward e Feynman para o modelo de Ising em duas dimensões sem campo é revisada e a fórmula de Onsager é calculada.

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Neste texto fazemos um apanhado inicial e geral das principais id¥eias relacionadas a teoria dos sistemas complexos.

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Hadron spectra and other properties of quark systems are studied in the framework of a non-relativistic spin-independent phenomenological model. The chosen confining potential is harmonic, which allowed us to obtain analytical solutions for both meson and baryon (of equal constituent quarks) spectra. The introduced parameters are fixed from the low-lying levels of heavy quark mesons. The requirement of flavor independence is imposed, and it restricts the possible choices of inter-quark potentials. The hyper-spherical coordinates are considered for the solution of the three-body problem.

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Is it allowed, in the context of the Lagrange multiplier formalism, to assume that nonholonomic constraints are already in effect while setting up Lagrange's function? This procedure is successfully applied in a recent book [L. N. Hand and J. D Finch, {\it Analytical Mechanics}] to the problem of the rolling penny, but it does not work in general, as we show by means of a counterexample. It turns out that in many cases the use of nonholonomic constraints in the process of construction of the Lagrangian is allowed, but the correct equations of motion are the little known Voronec's equations.

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Cosmology is a field of physics in which the use of General Relativity theory
is indispensable. However, a cosmology based on Newtonian gravity theory for
gravity is possible in certain circumstances. The applicability of Newtonian
theory can be substantially extended if it is modified in such way that
pressure has a more active role as source of the gravitational field. This was
done in the neo-Newtonian cosmology. The limitation on the construction of a
Newtonian cosmology, and the need for a relativistic theory in cosmology are
reviewed. The neo-Newtonian proposal is presented, and its consequences for
cosmology are discussed.

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I briefly present the foundations of relativistic cosmology, which are,
General Relativity Theory and the Cosmological Principle. I discuss some
relativistic models, namely, "Einstein static universe" and "Friedmann
universes". The classical bibliographic references for the relevant tensorial
demonstrations are indicated whenever necessary, although the calculations
themselves are not shown.

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In this paper, using the Lagrangian formalism of classical mechanics and some
assumptions, we obtain cosmological differential equations analogous to both
Friedmann and Einstein equations, obtained from the general theory of
relativity. This method can be used to a universe constituted of incoherent
matter, that is, the cosmologic substratum is comprised of dust.

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The problem of bound states in delta potentials is revisited by means of
Fourier transform approach. The problem in a simple delta potential sums up to
solve an algebraic equation of degree one for the Fourier transform of the
eigenfunction and the problem for more than one delta function also reveals
itself to be a simple matter. Quite differently from direct methods, no
knowledge about the jump discontinuity of the first derivative of the
eigenfunction is required to determine the solution of the problem.

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The calculation of the minimum of the effective potential using the zeta function method is extremely advantagous, because the zeta function is regular at $s=0$ and we gain immediately a finite result for the effective potential without the necessity of subtratction of any pole or the addition of infinite counter-terms. The purpose of this paper is to explicitly point out how the cancellation of the divergences occurs and that the zeta function method implicitly uses the same procedure used by Bollini-Giambiagi and Salam-Strathdee in order to gain finite part of functions with a simple pole.

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We present a derivation of the Lindblad equation - an important tool for the
treatment of non-unitary evolutions - that is accessible to undergraduate
students in physics or mathematics with a basic background on quantum
mechanics. We consider a specific case, corresponding to a very simple
situation, where a primary system interacts with a bath of harmonic oscillators
at zero temperature, with an interaction Hamiltonian that resembles the
Jaynes-Cummings format. We start with the Born-Markov equation and, tracing out
the bath degrees of freedom, we obtain an equation in the Lindblad form. The
specific situation is very instructive, for it makes it easy to realize that
the Lindblads represent the effect on the main system caused by the interaction
with the bath, and that the Markov approximation is a fundamental condition for
the emergence of the Lindbladian operator. The formal derivation of the
Lindblad equation for a more general case requires the use of quantum dynamical
semi-groups and broader considerations regarding the environment and
temperature than we have considered in the particular case treated here.

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The expressions of momentum and energy of a particle in special relativity
are often derived in a quite unconvincing manner in elementary text, by
resorting either to electrodynamic or quantum considerations, or via the
introduction of the less-than-elementary concept of a four-vector. It is
instead possible, by exploiting considerations introduced by P. Epstein and A.
Einstein and exploited later by Feynman, to obtain a fully elementary
derivation of these expressions and of the $E=mc^2$ formula exploiting only
Lorentz transformations and the postulate of the conservation of quantities
defined for point-like particles which reduce to the Newtonian expressions of
momentum and energy in the classical limit.

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In 1848 Pasteur conjectured that the rotation of the polarization plane of the light in a dilute dielectric medium is generated by the molecular symmetries of the medium where the light propagates. Our objective is to show that Pasteur hypothesis was correct using basic knowledge of electromagnetism and quantum mechanics. In Sections 2-5 we present a brief review of the fundamental concepts of the electromagnetism necessary to study the optical activity. In Sections 6-8 using the quantum mechanical perturbation theory and taking into account the molecular symmetries we calculate the optical activity of the medium. It will be shown that the theoretical predictions that are in good agreement with the experimental results give support to the Pasteur hypothesis.

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A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys. \textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schr\"odinger equation is presented. Equations are further simplified and generalized for computing wave functions of any given one-dimensional potential, providing accurate solutions not only for bound states but also for scattering and resonant states, as demonstrated here for a few examples.

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Scientific education and divulgation not only amplify people's vocabulary and repertory of scientific concepts but, at the same time, promote the diffusion of certain conceptual and cognitive metaphors. Here we make some hypothesis about this process, proposing a classification in terms of visible, invisible, basic and derived metaphors. We focus our attention in contemporary and classical physics metaphors applied to psychological and socio-economical phenomena, and we study two exemplar cases through an exhaustive exam of the online content of large Brazilian journalistic portals. Finally, we present implications and suggestions from the cognitive metaphor theory for the scientific education and divulgation process. Comment: In portuguese, 20 pages, 2 figures, new version submitted to RBEF

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O modelo estático de Einstein foi o primeiro modelo cosmológico relativista. O modelo é estático, finito e de simetria espacial esférica. Utilizo a solução das equações de campo de Einstein, em um universo homogêneo e isotrópico -a equação de Friedmann -, para calcular o raio de curvatura deste modelo, denominado universo de Einstein. Mostro, também, utilizando uma analogia newtoniana, a sua mais conhecida característica, qual seja, a instabilidade sob pequenas perturbações do estado de equilíbrio.

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The human sense of hearing perceives a combination of sounds 'in tune' if the
corresponding harmonic spectra are correlated, meaning that the neuronal
excitation pattern in the inner ear exhibits some kind of order. Based on this
observation it is suggested that musical instruments such as pianos can be
tuned by minimizing the Shannon entropy of suitably preprocessed Fourier
spectra. This method reproduces not only the correct stretch curve but also
similar pitch fluctuations as in the case of high-quality aural tuning.

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In this paper we give a rigorous proof of the equivalence of some different
forms of Faraday's law of induction clarifying some misconceptions on the
subject and emphasizing that many derivations of this law appearing in
textbooks and papers are only valid under very special circumstances and not
satisfactory under a mathematical point of view.

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A simple harmonic oscillator model is proposed to describe the mechanical power involved in human locomotion. In this framework, by taking into account the anthropometric parameters of a standard individual, we are able to calculate the speed-power curves in human walking. The proposed model accounts for the well known Margaria's law in which the cost ofthe human running (independent from the speed) is fixed to 1 Kcal/(Kg Km). The model includes the effects of a gentle slope (either positive or negative) and the effect due to the mechanical response of the walking surface. The model results obtained in the presence of a slope are in qualitative agreement with the experimental data obtained by A. Leonardi et al. Comment: 13 pages, 5 figures, submitted to EPJ B

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We study a process of heat transfer between a body of heat capacity C(T) and
a sequence of N heat reservoirs, with temperatures equally spaced between an
initial temperature T_0 and a final temperature T_N. The body and the heat
reservoirs are isolated from the rest of the universe, and the body is brought
in thermal contact successively with reservoirs of increasing temperature. We
determine the change of entropy of the composite thermodynamic system in the
total process in which the temperature of the body changes from T_0 to T_N. We
find that for large values of N the total change of entropy of the composite
process is proportional to (T_N-T_0)/N, but eventually a non-monotonic behavior
is found at small values of N.

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This paper presents the validation of a computational tool that serves to
obtain continuous measurements of moving objects. The software uses techniques
of computer vision, pattern recognition and optical flow, to enable tracking of
objects in videos, generating data trajectory, velocity, acceleration and
angular movement. The program was applied to track a ball around a simple
pendulum. The methodology used to validate it, taking as a basis to compare the
values measured by the program, as well as the theoretical values expected
according to the model of a simple pendulum. The experiment is appropriate to
the method because it was built within the limits of the linear harmonic
oscillator and energy losses due to friction had been minimized, making it the
most ideal possible. The results indicate that the tool is sensitive and
accurate. Deviations of less than a millimeter to the extent of the trajectory,
ensures the applicability of the software on physics, whether in research or in
teaching topics.

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The theory of relativity, which was proposed in the beginning of the 20th
century, applies to particles and frames of reference whose velocity is less
than the velocity of light. In this paper we shall show how this theory can be
extended to particles and frames of reference which move faster than light.

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The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis of the scattering of particles in a step potential with an arbitrary mixing of vector and scalar couplings reveals that the scalar coupling contributes for increasing the threshold energy for the particle-antiparticle pair production. Furthermore, it is shown that the pair production is only feasible whether the vector coupling exceeds the scalar one. An apparent paradox concerning the localization of a particle in an arbitrarily small region of space, due to the presence of the scalar coupling, is solved by introducing the concept of effective Compton wavelength.

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The motion of a projectile with horizontal initial velocity V0, moving under
the action of the gravitational field and a drag force is studied analytically.
As it is well known, the projectile reaches a terminal velocity Vterm. There is
a curious result concerning the minimum speed Vmin; it turns out that the
minimum velocity is lower than the terminal one if V0 > Vterm and is lower than
the initial one if V0 < Vterm. These results show that the velocity is not a
monotonous function. If the initial speed is not horizontal, there is an angle
range where the velocity shows the same behavior mentioned previously. Out of
that range, the volocity is a monotonous function. These results come out from
numerical simulations.

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It is presented a simple model for the calculation of the transition rate for impurities in semiconductors in which electron-phonon interaction is taken into account in a second order time dependent perturbation theory. This result shows the explicit dependence of the transition rate on the phonon density of states and that the absorption curve of a semiconductor is modulated by the phonon structure.

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Discutimos detalhadamente a solução de um problema originalmente proposto para um examevestibular, envolvendo a oscilação de um sistema massa-mola num referencial acelerado e a determinação da amplitude de oscilação a partir do instante em que cessa a aceleração do referencial.Mostramos que o valor dessa amplitude depende essencialmente da relação entre o tempo duranteo qual permanece a aceleração do referencial e o período de oscilação. Na situação limite em queo período de oscilação é muito maior do que o tempo de aceleração, o sistema aproxima-se de umsistema conservativo e a amplitude de oscilação pode ser determinada por conservação da energiamecânica. O problema apresentado constitui um interessante exercício para a discussão (em nívelmédio ou universitário) de temas como forças fictícias, mudanças de coordenadas e não-conservaçãode energia mecânica em referenciais não-inerciais.

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Neste artigo tratamos de um estudo realizado com o objetivo de utilizar diagramas conceituais no ensino da física, incorporados às aulas expositivas e demonstrativas, visando promover a aprendizagem significativa de conteúdos de ondulatória, acústica e óptica em nível de ensino médio. Foram elaborados "Diagramas de Referência", embasados na estratégia dos mapas conceituais propostos por Joseph Novak. Participaram do estudo duas turmas com vinte e cinco alunos cada, uma submetida às atividades com mapas conceituais, outra submetida às atividades tradicionais tais como: resenhas, resolução de problemas e exercícios formais em física. A análise qualitativa dos diagramas elaborados pelos alunos possibilitou identificar deficiências conceituais e também verificar que os diagramas conceituais elaborados pelos alunos no final do semestre foram superiores em relação aos primeiros diagramas no sentido de que evidenciaram maior facilidade dos alunos em expor organizadamente suas idéias, elaborar proposições e conclusões. Um questionário de opinião mostrou que os alunos aprovaram a utilização desse recurso didático.

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La inserción de un Resonador Helmholtz (RH) en las paredes laterales de un tubo, con ondas estacionarias en su interior, logra suprimir uno o más de sus modos resonantes si se elige adecuadamente la frecuencia del resonador. El RH puede actuar también como filtro de ondas propagantes.' En este caso, el RH atenua las ondas en un rango de frecuencia muy selectivo. En la mayoría de los textos de acústica, solamente se desarrolla la teoría que explica el filtrado de ondas propagantes. Sin embargo, en los laboratorios de física basica, donde se dispone solamente de tubos de Kundt de pequeña longitud, no es simple realizar un arreglo experimental que asegure la presencia de ondas propagantes puras en su interior. La falta de una teoría para ondas estacionarias y las dificultades experimentales que señalamos han producido algunas confusiones en trabajos que tratan sobre el tema. En este artículo se presenta un modelo teórico que describe satisfactoriamente el comportamiento del RH cuando funciona como filtro de ondas estacionarias y se marcan las diferencias con la situación en que opera como filtro de ondas propagantes.

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Diversos setores organizados da sociedade têm chamado a atenção para as alterações provocadas pelo homem na natureza e, dentre estas, destacamos aquelas diretamente relacionadas à produção de energia elétrica em larga escala. O debate em torno desta questão limita-se, na maioria das vezes, aos meios técnicos e acadêmicos. Porém um grande número de pessoas vivencia os principais problemas decorrentes da utilização das diversas tecnologias de produção de eletricidade em larga escala. Dentre as propostas que procuram qualificar um grande número de pessoas para participar deste debate, destacamos o processo educativo. Neste sentido, considerando as sugestões presentes em atuais propostas curriculares, procuramos neste trabalho identificar e sistematizar os principais elementos das discussões ocorridas nos meios técnicos e acadêmicos, que versam sobre produção de energia elétrica em larga escala e a temática ambiental e que poderiam ser convertidos em conteúdo escolar.

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Este artigo descreve experimentos em que foram utilizadas simulações como ferramentas para alterar as concepções espontâneas apresentadas por estudantes, de modo a explorar as possibilidades apontadas pela estratégia de conflito cognitivo (Posner et al., 1982). Os experimentos foram concebidos para tentar modificar as concepções espontâneas apresentadas em Mecânica por estudantes de nível universitário básico no desenvolvimento do conteúdo 'Leis de Newton'. Nossa abordagem ao problema baseou-se no uso de um programa de simulação chamado Prometeus, especialmente desenvolvido para esse objetivo. Realizamos três experimentos para verificar a eficácia do programa e propor a melhor estratégia de ensino a ser adotada ao utilizá-lo. Inicialmente, o programa foi testado independentemente da seqüência formal de ensino desenvolvida pelo professor. Embora a abordagem utilizada tenha se revelado útil para levar os estudantes a questionar suas crenças pessoais, a estratégia usada no primeiro experimento, baseada no uso do programa de forma isolada, não foi suficiente para promover mudanças significativas nas idéias prévias dos estudantes. No segundo experimento, o programa foi inserido no plano de ensino da disciplina como um recurso instrucional, sendo introduzido após a formalização do conteúdo 'Leis de Newton'. Como os resultados obtidos não foram satisfatórios, realizamos um terceiro experimento, com algumas modificações em relação ao anterior. Os resultados deste sugerem que a nova estratégia, somada à motivação do grupo experimental, influenciou de forma significativa a modificação das concepções dos estudantes desse grupo.

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Top-cited authors

- Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)