Revista Brasileira de Ensino de Física

Published by SciELO
Online ISSN: 1806-9126
Print ISSN: 1806-1117
Publications
Portrait of Cagniard de la Tour, courtesy of the Universidade do Minho, Portugal. 
The improved siren, invented and named by Charles Cagniard de la Tour. Photograph courtesy of the Ecole  ́ Polytechnique Paris, France. 
The first page of Cagniard de la Tour’s article, in which the discovery of critical phenomena is reported. 
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
 
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.
 
Corte de la Tierra a latitud φ vista desde PNT.
Posición angular del plano M en tiempo t.
Zonas iluminadas al principio y al final de una fracción de revolución terrestre.
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.
 
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.
 
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.
 
Layout of the electrical impedance tomography. An electrodes belt is attached on the body surface. A voltage source applies a stimulus on the electrodes and the corre- sponding response is measured and supplied to a computer. A specific software reconstructs the interior body image. 
Scheme of the numerical example: cylindrical conductive wire with length 10.0 and diameter 1.0 with a nonconductive region of radius 0.3 located 7.0 units far from extremity a.
Error functional surface in logarithm scale. It presents almost flat regions and a channel that contains a prominent global minimum.
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.
 
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.
 
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.
 
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.
 
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.
 
Integration contour in the complex plane used in (a) Eq. (4) and (b) Eq. (5).
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.
 
Esboço da condição de quantização e −2ξ = |1 − 2ξ/a| para a > 0. Curva contínua para e −2ξ. Curvas tracejadas (a > 1) e pontilhadas (a < 1) para |1 − 2ξ/a|. Curva espessa para φ par, e curva delgada para φ ´ ımpar.
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.
 
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
 
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.
 
-Geometry for the evaluation of the interaction energy of two point charges.  
-The distribution of the electrostatic energy density for two similar positive point charges.  
-Geometry for the evaluation of the negative energy density contribution.  
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.
 
nterconexões temáticas e conceituais no quarto semestre. 
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).
 
A circular loop with radius a composed by a RLC circuit showing the capacitor radiating as electric dipole. The loop and the inductor also radiate (not shown) as magnetic dipole.
The power spectrum showing its line width as function of the total resistance that include magnetic and electric radiation.  
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.
 
Open (Ω•=0.5), flat and closed (Ω•=2) Friedmann's models. This is an example of their most common graphical representation. Time, in the abscissas, is in units of 2/(3H•), the age of the flat model. The fine features at R < 2 are absent in most textbooks and popular reviews of cosmology.
The ages of open, flat and closed Friedmann's models as functions of the density parameter Ω@BULLET. Note that the ages of open models are always greater than the ages of flat (Ω@BULLET=1) and closed models. The vertical axis is in units of the flat model age, namely, 2/(3H@BULLET). 
Open (Ω@BULLET=0.5), flat and closed (Ω@BULLET=2) Friedmann's models are now shown in the range that includes R(t@BULLET)=1, right in the middle of the vertical axis. The age of the flat model is shown in the diagram, t@BULLET= 9 Gyr, for H@BULLET= 72 km/s Mpc −1 [6]. Note that, according to eq. 1 and irrespective of Ω@BULLET, the three curves share the same slope dR/dt at R = 1 (i.e., now ), for each model, and consequently, the same Hubble parameter ˙ R/R = H@BULLET. 
The relative differences between the closed and open models and the flat model as a function of time. The differences at t → 0 are easily calculated from eq. 7. Note the crossover times with the flat model, marked by the horizontal dotted line. The vertical dotted line points to the age of the flat model (t=1).
Open (Ω•=0.5), flat and closed (Ω•=2) Friedmann's models have the same slope-or Hubble's constant-at R = 1 (now ). Different ages t• appear along the time axis: t•= 1.0 +0.13 −0.14 for the closed (−) and open (+) models (see also Fig. 2).
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.
 
First phase of a vertical jump, during which there is still contact with the ground.
Moving block on a horizontal surface with friction, under the action of a pulling force.
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.
 
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.
 
Neste texto fazemos um apanhado inicial e geral das principais id¥eias relacionadas a teoria dos sistemas complexos.
 
Hyperfine splitting for quarkonium ground states (M eV ).
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
The rotatory power [ α ( λ )] and the ellipticity parameter [ Ψ ( λ )] as a function of the wavelength λ . 
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.
 
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.
 
Número de usos literais e metafóricos da expressão buraco negro nos portais jornalísticos Folha de São Paulo Online, Estado de São Paulo Online e Portal G1 no período 2008-2009.
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
 
Λ-shaped diagram: the potential energy-in arbitrary units-for the 
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.
 
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.
 
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.
 
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
 
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.
 
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.
 
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.
 
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.
 
This is the problem considered in the article: a projectile is launched from a cliff with an initial speed V0. It moves under the action of the gravitational force mg and a drag force F d that is proportional to a power n of the speed. It is convenient to choose the angle θ as the independent variable.
The projectile velocity v as a function of the angle θ (in radians) for two different initial velocities: v0 = 2 (upper curve) and v0 = 0.5 (lower curve). In this case, n = 1. Notice that the terminal velocity (v = 1) is different from the minimum one. The projectile trajectory is bounded in the region 0 ≤ θ ≤ π/2.
This figure is the same as Figure 4 but for a drag force that goes as F d ∼ V 3 . The minimum velocity shows the same 
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.
 
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.
 
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.
 
Diagrama conceitual sobre texto "Estudo da física" elaborado pelo grupo X.
Um diagrama de referência elaborado sobre o texto "Estudo da física". Demonstra as relações julgadas válidas e significativas conceitualmente.
Diagrama conceitual sobre experimento de refração, elaborado por grupo Y.
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.
 
Resonador Helmholtz insertado lateralmente en un tubo abierto en ambos extremos.
Circuito eléctrico equivalente del sistema acústico de la figura 1.
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.
 
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.
 
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.
 
Top-cited authors
Eliane Angela Veit
  • Universidade Federal do Rio Grande do Sul
Ives Solano Araujo
  • Universidade Federal do Rio Grande do Sul
Daniel Guilherme Gomes Sasaki
  • Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)
Cecilia Cabeza
  • Universidad de la República de Uruguay
Martín Monteiro
  • Universidad ORT Uruguay