Os laboratórios didáticos de física experimental, tanto no ensino médio quanto no ensino superior, não costumam abordar experimentos didáticos que contemplem a medida do coeficiente de atrito de rolamento. Aliás, o próprio conceito de atrito de rolamento é sistematicamente ignorado nas coleções de ensino médio e até mesmo naquelas de ensino superior. Neste artigo propomos um experimento de baixo custo usando apenas uma pilha média comum, uma câmera de smartphone e o software livre Tracker para vídeo-análise. Além disso, integramos em uma só experiência didática a medida de duas grandezas físicas distintas, a saber, o coeficiente de atrito cinético e o coeficiente de atrito de rolamento. De fato, a vídeo-análise do movimento completo da pilha, lançada manualmente sobre uma superfície horizontal plana, permite dividir o movimento em duas partes: rolamento com deslizamento seguido de rolamento sem deslizamento. O software Tracker provou ser uma ferramenta eficiente para a obtenção de medidas de posição do centro de massa e de tempo, nas duas fases do movimento. Com esses resultados foram calculados diversos parâmetros da teoria, em especial os dois coeficientes de atrito, com bastante acurácia e precisão.
O presente trabalho é o resultado de um estudo pioneiro visando aplicar uma metodologia de aprendizagem ativa de inspiração construtivista para abordar algumas concepções alternativas mais presentes em mecânica, em turmas de jovens e adultos da rede pública do Estado do Rio de Janeiro. A metodologia utilizada foi a chamada POE (Previsão-Observação-Explicação), baseada no conflito cognitivo, isto é, para cada assunto abordado, os alunos são estimulados a expor seus conhecimentos e posteriormente, confrontá-los com vídeos de experimentos e simulações. Para avaliar a metodologia utilizou-se um teste padronizado com as seguintes finalidades: identificar as ideias prévias dos alunos referentes às diferentes temáticas abordadas e possibilitar a verificação do ganho de aprendizagem global das turmas sendo aplicado antes (pré-teste) e após (pós-teste) às aulas. Os resultados obtidos para o ganho de aprendizagem global mostram um desempenho inferior ao esperado para esse tipo de metodologia descritos na literatura em turmas de graduação, porém, existem indícios claros de que elementos sociais, tais como a faixa etária dos estudantes e a necessidade ou não de realizarem-se atividades laborais remuneradas influenciam no processo de ensino-aprendizagem. A análise quantitativa dos resultados dos testes separados por temas abordados indica um significativo incremento na compreensão de alguns tópicos pontuais, em especial a lei da ação e reação e a relação entre força resultante e aceleração. Além disso, as anotações realizadas pelos alunos nas chamadas fichas de aula mostraram qualitativamente uma evolução da compreensão de alguns conceitos básicos da mecânica, como velocidade, aceleração e força resultante.
This work address the preconceptions of first year engineering students about the kinematic graphs and the outcomes of a pedagogical strategy that relies on Predict – Observe – Explain learning method mediated by a video analysis software. The whole learning procedure was accompanied by a written material as students’ worksheets which enabled a formal record of the students’ conceptions throughout the process. The Test of Understanding of Kinematics Graphs was utilized to evaluate the students’ preconceptions and learning gains. It was found that first year engineering students had serious difficulties in drawing and interpreting kinematic graphs. Although interpretation of graphs and the understanding of the velocity and acceleration concepts improved, the preconceptions were quite resilient.
In the present work, we develop a low-cost and simple experiment to visualise Fourier’s synthesis using a short, soft, and light plastic coiled spring oscillating in a horizontal plane, and a basic camera (120 fps). It is shown that the spring obeys a linear wave differential equation, as gravitational influence is neglected. A nonlinear criterion is evaluated to determine if magnitudes of the parameters in the initial conditions satisfy the linear wave equation. Our setup promotes some desirable characteristics that make Fourier’s synthesis experiments feasible, visual, and enlightening: (i) it requires few, common, and cheap resources, and the experiment can be carried out even in a high-school laboratory; (ii) since the spring’s tension is small (∼1 N, on average), the frequencies of normal modes are low (close to 2 Hz), and therefore, it is possible to record the oscillations just with the camera and extract a considerable number of position and time data in just one cycle; (iii) when the video is loaded in the Tracker free software, it can be reproduced in slow motion. Since the frequencies involved are low, an interesting and instructive temporal sequence of images of the spring displaying the typical trapezoidal shape appears clearly; (iv) the tools associated with the Tracker software tools can yield the relevant oscillation parameters, such as the damping constant, amplitudes, frequencies, and phases; and (v) it is possible to carry out superposition of a snapshot of the spring in Tracker at any time, and to draw the related Fourier synthesis graphs. The visual match between the shape of the spring and the theoretical graph is remarkable, and can be enhanced by adding the damping term.
Currently, the number of smartphones with an embedded gyroscope sensor has been increasing due games whose performance relies on 3D augmented reality. In general, teaching papers on the gyroscope sensor address very simple spatial configuration, where the fixed rotation axis coincides to the z-axis of the smartphone. This work presents five experimental setups with different spatial orientations of a smartphone on a turntable. The total angular velocity vector of the turntable is constant, but its projections on the three fixed Cartesian axes of the smartphone varies for the five spatial orientations investigated. For the sake of consistency, the magnitude of the vector sum of the three angular velocities components yielded by the gyroscope sensor was checked by video analysis using the free software, Tracker. The internal consistency between the results provided by this video analysis technique and data from the gyroscope assures us this sensor is reliable for teaching proposals. The main goals of this paper are (i) encourage teachers to effectively incorporate the gyroscope sensor of smartphones in to their classrooms, especially in high schools and undergraduate physics and engineering courses; (ii) spread in the academic syllabus the Tait–Bryan convention, a very intuitive way to perform 3D rotations and; (iii) explain how to interpret data of the three components of angular velocity obtained by the gyroscope sensor in different spatial orientations.
The abelian Chern-Simons theory is perturbed by introducing local gauge-invariant interaction terms depending on the curvature. The computation of the correlation function γ 1 dx µ A µ γ 2 dy ν A ν for two smooth closed nonintersecting curves γ 1 , γ 2 is reported up to four loops and is shown to be unaffected by radiative corrections. This result ensures the stability of the linking number of γ 1 and γ 2 with respect to the local perturbations which may be added to the Chern-Simons action.
Nowadays, in almost any country in the world, it is difficult to find a young person who has never played with, seen, or heard of the most famous toy in 2017: the fidget spinner. According to Wikipedia: “The fidget spinner is a toy that consists of a ball-bearing in the center of a multi-lobed flat structure made from metal or plastic designed to spin along its axis with little effort.” Articles on educational proposals related to fidget spinners have been presented recently. Naturally, an issue arises from this polemic context: can fidget spinners be used to illustrate or explain physics concepts such as moment of inertia, torque, and angular momentum? This paper presents a simpler, cheaper, and easier experimental setup to obtain moments of inertia of the fidget spinner by using the free software Tracker for video analysis. A consistency test with an aluminum cylindrical shell ensures the reliability of the experimental setup.
Neste trabalho propomos e investigamos uma proposta didática para o ensino de espelhos esféricos baseada na associação entre uma metodologia de aprendizagem ativa com a estratégia de analogias ponte e conceitosâncora. A atividade era constituída por dois experimentos sucessivos sobre as características de imagens virtuais conjugadas por um espelho esférico côncavo e a dependência de seu tamanho relativo com a posição do observador (ângulo visual). O público-alvo era composto por quatro turmas distintas de ensino médio de uma escola da rede federal. Todo o procedimento foi acompanhado de um material escrito na forma de questionário. Para analisar qualitativamente os diferentes tipos de resposta e também a evolução dos estudantes foi utilizada a taxonomia de reações de Chinn e Brewer. Os resultados obtidos revelam as seguintes conclusões: (i) Ratifica a crítica presente na literatura que o emprego isolado do conflito cognitivo não conduz a mudanças significativas nos conceitos prévios da grande maioria dos alunos. (ii) A estratégia de associar uma metodologia de aprendizagem ativa que provoque o conflito cognitivo com as analogias ponte foi bem sucedida em viabilizar uma mudança da teoria da maioria dos alunos (iii) A necessidade de pesquisas quantitativas complementares para avaliar ganhos de aprendizagem. Palavras-chave: Aprendizagem ativa, conflito cognitivo, analogias, espelhos esféricos.In this paper we propose and investigate a teaching proposal about convergent mirror based on the association between an active learning methodology and method of bridge analogies and anchorings concepts. The activity consisted of two successive experiments on the characteristics of virtual images formed by the concave spherical mirror and dependence on their relative size with the observer position (visual angle) were. Four high school distinct classes of the federal system of education formed the target audience. The whole procedure was accompanied by a written material as worksheets. To evaluate qualitatively their different types of reaction and also the evolution facing the anomalous data from the first experiment, we used the reactions taxonomy created by Chinn and Brewer was used. The results show the following conclusions: (i) it ratifies the present criticism in the literature that the isolated use of cognitive conflict does not lead to significant changes in the previous conceptions of most pupils; (ii) The strategy of associating an discrepant experiment causing cognitive conflict with another bridge experiment, of predictable result that rescue anchoring correlated ideas by analogy, has been successful in achieving a theory change in the most of students; (iii) The need for further quantitative research to evaluate learning gains.
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