No abstract

De acuerdo al modelo enseñado en los cursos introductorios universitarios, la frecuencia de las oscilaciones libres de un sistema masa-resorte vertical, en el caso de fuerzas disipativas y masa del resorte despreciables, puede calcularse simplemente como la raíz cuadrada de la relación entre la gravedad del lugar y el estiramiento producido por el cuerpo sujeto al resorte. Sin embargo, cuando se utiliza un resorte real, las frecuencias medidas difieren en forma notable por debajo de las previstas por el modelo. El análisis de la respuesta estática del resorte a la carga revela que no obedece la ley de Hooke e impide definir unaúnica constante elástica k E en cualquier condición de carga. Haciendo una aproximación lineal de esta respuesta alrededor del punto de trabajo y definiendo una constante dinámica k D , la resolución de la ecuación diferencial de movimiento predice un valor de la frecuencia mucho más cercano al medido. Una posterior corrección heurística, que toma en cuenta la masa del resorte, hace disminuir aún más la discrepancia relativa. Nuestro análisis concluye que los fenómenos disipativos son insignificantes comparados con la elasticidad y la inercia del sistema estudiado. Este problema y su solución muestran la necesidad de discutir en las aulas la modelización de este fenómeno físico. Palabras clave: oscilaciones, sistema masa-resorte, ley de Hooke, no-linealidad.On university introductory courses, while studying the frequency of free oscillations of a vertical spring-mass system in the case of negligible dissipative forces and massless spring, such a frequency can be simply calculated as the square root of the relationship between the local gravity and the spring elongation. However, when an actual spring is used, the measured frequencies differ markedly below those predicted by the model. The analysis of the static response of the spring to the load reveals that it does not obey Hooke's law and prevents defining a single elastic constant k E in any load condition. By making a linear approximation of this response around the point of work and defining a dynamic constant k D , the resolution of the differential motion equation predicts a value of the frequency much closer to the measured one. A subsequent heuristic correction, which takes into account the mass of the spring, further decreases the relative discrepancy. Our analysis concludes that dissipative phenomena are insignificant compared to the elasticity and inertia of the system studied. This problem and its solution show the need to discuss in the classroom the modeling of this physical phenomenon. Keywords: oscillations, spring-mass system, Hooke's law, non-linearity. IntroducciónEn los libros de texto introductorios de Física de nivel universitario [1-4], la elasticidad de los materiales, en general, es ejemplificada por un resorte helicoidal lineal; es decir, la fuerza ejercida sobreéste es proporcional a la longitud de su estiramiento o de su compresión. La ley de la fuerza como función del estiramiento es conocida como ley de Hooke...

In this paper we review the examples of J H Poynting (1884) on the transfer of electromagnetic energy in DC circuits. These examples were strongly criticized by O Heaviside (1887). Heaviside stated that Poynting had a misconception about the nature of the electric field in the vicinity of a wire through which a current flows. The historical review of this conflict and its resolution based on the consideration of electrical charges on the surface of the wires can be useful in the courses of electromagnetism or circuit theory.

In this work we describe how we designed and built an acoustic system that allowed us to adapt a Kundt’s tube for the measurement of the speed of sound at different temperatures. The air column inside the tube was excited by a speaker at a frequency of 2 kHz. We changed the air column length by moving a piston throughout the tube, and we measured and recorded that length when we observed a resonance signal on the oscilloscope screen. This procedure was repeated at different temperatures, ranging from 19○C to 115○C. Then it was calculated the propagation of the speed of sound based on the temperature. The results were compared with those predicted by the classical model, which assumes that air is an ideal diatomic gas, and that the acoustic phenomenon is an adiabatic process. Finally, it was found a satisfactory agreement between the experimental values and those predicted by the classical model