Computer simulation and modeling in virtual physics experiments

Transcription

1 1198 Current Developments in Technology-Assisted Education (006) Computer simulation and modeling in virtual physics experiments W. Tłaczała *,1, G. Gorghiu, A. E. Glava 3, P. Bazan 4, J. Kukkonen 5, W. Mąsior 6, J. Użycki1 and M. Zaremba1 1 Faculty of Physics, Warsaw University of Technology, Koszykowa 75, Warsaw, Poland Science of Systems, Automatics and Informatics Department, Valahia University Targoviste, 13008, Targoviste, Romania 3 Department of Educational Science, Babes-Bolyai University Cluj Napoca, , Romania 4 Teachers Training Center of Zaragoza 1, Zaragoza, Spain 5 Department of Applied Education, University of Joensuu, , Finland 6 Regional In-Service Teacher Training Center WOM in Bielsko-Biała, Bielsko-Biała, Poland This paper describes a set of virtual advanced physics experiments devoted to electrical resonance, heat transportation in metals, Curie temperature for ferromagnetic materials, statistics, beta absorption in matter and Mössbauer effect. Described virtual experiments are equipped with applications, which simulate physical phenomena and processes, model instruments and experimental measurement systems. In contrast to many other simulations, our experiments are based on real experimental data. Keywords e-learning, virtual laboratory, LabVIEW, teacher training, Socrates Project, Comenius Introduction Usually, the virtual instrument (VI) is understood as computer controlled real instrument used for data acquisition, analyses and presentation. In this case the control of the physical instrument, which exists in the background of the computer, may be performed using the computer keyboard, mouse, and display. The VI definition can be expanded for computer-based virtual instrumentation systems (VIS). The VIs and VIS can be also a wide variety of the computer based applications for the physical phenomenon and measurement process modeling or applications which simulate real-world devices, instruments and measurement systems operating. Such peculiarities of the VIs and VIS predestinate them for applications building used for modeling and simulations in the virtual physics experiments. Models of the physical or measurement processes can be built using two methods: one method based on mathematical modeling and the second based on measurements performed with real measurement system regarded as a black box, which input-output relations are only taken into account for particular properties presentation with so-called calibration curve. Below are presented the both methods used for modeling physics phenomena and laws, advanced physic experiments and measurement processes based on the virtual instruments.. Analytical models with VIs The physical phenomena and physical laws can be described analytically using the mathematical equations. As examples of the analytical models using VIs, applications appointed to the Planck s Law and Wien s Displacement Law and the electrical resonance phenomenon are presented below. The Planck s and Wien s Displacement Laws. When the temperature of the object is known, the distribution of the radiating energy is given by the law of black body radiation, the Planck s Law, as shown in equation: * Corresponding author: tlaczala@if.pw.edu.pl, Phone:

2 Current Developments in Technology-Assisted Education (006) 1199 b 1 M (, T ) 5 hc / λ λ e kt λ, (1) 1 where: b10 7 in relative units; λ - wavelength; h - Planck constant; k - Boltzmann constant; c speed of light in vacuum; T - temperature in Kelvin degrees. For the given absolute temperature T (K) the peak wavelength λ p (μm) can be calculated using relationship λ p T897.9, known as the Wien s Displacement Law. Fig. 1 The VI developed for dynamic demonstrating of the Plank s law and Wien s displacement law. The implementations of the equation (1) and relationship λ p T897.9 allow dynamic demonstrating of the Planck s Law and the Wien s Displacement Law with application shown in Figure 1. The electrical resonance phenomenon. The current and voltage as a function of the frequency can be observed in the parallel and series tuned LC circuits. Figure a shows LCR d parallel-tuned resonance circuit. Its equivalent circuit diagram is shown in Fig. b. In this configuration R d denotes a dynamic resistance, and the resistance R consists of the voltage source resistance R S added to the leads resistance R LEAD, so R R S + R LEAD. Fig. The parallel resonance: a) LC parallel-tuned circuit supplied from the voltage source, b) equivalent circuit diagram, c) simulation of the admittance, reactance and susceptance as functions of the frequency in the parallel circuit supplied from the equivalent current source, d) simulation of the ratio yu/u mr as a function of frequency in the parallel-tuned circuit.

3 100 Current Developments in Technology-Assisted Education (006) The admittance absolute value Y of the parallel-tuned LCR d circuit and the phase displacement ϕ P between the current and the voltage as functions of frequency are given by following equations: Y I U m m ( G) + 1 ωc ωl, 1 ωc ϕ arctan ωl P G where: G1/R d. Figure c shows the VI developed for demonstration how the admittance, reactance and susceptance in the parallel-tuned circuit supplied from the ideal current source depend on the frequency. The VI for the resonance phenomena presentation and simulation how the ratio yu/u mr depend on the frequency is shown in Fig. d. This VI allows also the simulation of the phase displacement ϕ P between the current and the voltage U LCP as a function of frequency. 3. Input/output black box model with VIs As examples of the method based on input/output black box modeling can be - described below - virtual physics experiments completed with VIs. These experiments (which user interfaces are shown in Fig. 3) are appointed to the electrical resonance phenomena, Curie temperature determination for the ferromagnetic materials and heat transportation studies based on the Ångström method. The problem of modeling of the electrical resonance phenomenon, described above and based on the analytical model, can be alternatively solved using the input/output black box model with VI implementation (Fig. 3a). () Fig. 3 Users interfaces of the experiments appointed to a) electrical resonance, b) Curie temperature determination for ferromagnetic materials, c) heat conductivity studies with the Ångström method. The model of this experiment is based on the real experimental data. It means that on the stage of the application building, the collection of the output readings (electrical signal amplitudes) recorded in the real experiment as a function of frequencies have been incorporated in the software. The collection of amplitude-frequency couples is next used as references when the virtual experiment is performed. In contrast to the analytical method, the input/output black box takes into account not only the particular physics law, phenomenon etc. and limited set of the parameters, but also the influence of the environment, in which measurement system operate, on the information conveyed by measurement results. This virtual experiment allows user to understand the measurement methodology, experimental set-up functions and operating, and finally, the physics phenomenon to be studied. The instruments, used in the virtual experiments, not only allow users to conduct measurements but also to provide full information concerning experiment, for example: how to switch on instruments, make connections, set correct parameters and run experiment, how to collect and analyze data and verify obtained results etc. Described virtual experiments are equipped with applications, which simulate physics phenomena and processes, model instruments and experimental measurement systems. Before starting data acquiring, the experimenter has to prepare virtual experiment to work. It needs to connect

4 Current Developments in Technology-Assisted Education (006) 101 instruments, switch on all virtual instruments and set correct operating parameters, to select the experimental conditions. The lasting of each step is also the same as in real. 4. Simulations in the virtual experiments Virtual instruments can be also successfully used for simulation of the device and measurement systems operating and instrument execution. Curie temperature determination for ferromagnetic materials. Figure 4 shows a part of the virtual measuring system (Fig. 3b) used to determine the Curie temperature (T c ) for the ferromagnetic material. The transformer (transducer) with ferromagnetic core as a sample is the main part of the experimental set-up. The primary winding (PC) of the transformer is excited with an AC voltage source (~50 Hz, constant amplitude), inducing voltages in secondary winding (SC), which vary with the temperature of the ferromagnetic sample. In this virtual experiment, the user measures the transformer output voltages as functions of temperature which can be controlled by the heating system. The information about the sample temperature is contained in the voltage level measured at the output of the thermocouple. Fig. 4 The models of: a) the transducer used in the virtual experiment appointed to Curie temperature determination for the ferromagnetic material, b) the experimental arrangement used in the virtual experiment appointed to the heat conductivity studies. The main aim of this experiment is to find the temperature at which transition between two states of the voltage versus temperature waveform is observed. This temperature, called the Curie temperature point, corresponds to the ferromagnetic/paramagnetic phase transition, what can be observed in Fig. 3b. Heat conductivity in metals. Figure 3c shows the user interface of the virtual measuring system used to determine the thermal conductivity coefficient λ for a metallic (copper) rod using the Ångström method. The value of the thermal conductivity coefficient is different for different materials and characterizes, for instance, the isolation characteristics of materials. The model of the experimental set-up used in this experiment is shown in Fig. 4b. The experiment based on the Ångström method demonstrates the damping of temperature in a rod. During measurements the temperature changes are generated by repeatedly switching on/off the heating system installed on the one end of the rod. This produces a temperature wave which penetrates the rod. These changes propagate through the whole sample but with the amplitude decreasing (exponentially) with increasing distance x from the source of heat. The temperature T is then described by a function typical for all damped waves. By measuring the temperature wave amplitudes T1 and T in two points x 1 and x, separated by a distance ΔL (Fig. 4b), it can be calculated the thermal conductivity coefficient λ. This is equal with: ρc( ΔL) λ, (3) Δt ln ( T1/ T )

5 10 Current Developments in Technology-Assisted Education (006) where: ρ denotes the density of the material, c its specific heat, Δt temporal phase shift between oscillations in both points. Nuclear physics experiments. Nuclear radiation is met in many branches of science, technology, medicine and in everyday life. Having these aspects in view, nuclear physics experiments should be an essential part of the education experience in the modern society. Most of works done up to now, concentrated on distance learning, creating links via Internet with real laboratories, situated inside the universities. It was the aim of the presented work to invent the nuclear physics experiments wide available and based on results obtained in real measurements performed earlier in the real nuclear physics laboratory. The set of the virtual nuclear experiments is devoted to studies of beta absorption in matter, the statistical character of nuclear decay and learning Mössbauer effect. Fig. 5 Users interfaces of the experiments appointed to a) beta absorption in matter, b) statistical character of nuclear decay, c) Mössbauer effect. 5. Conclusions Modeling and simulations offer very important tools used in research and techniques for understanding real physical laws and phenomena, measuring methods and processes, also device operating and instrument execution. For this purpose, virtual instruments can be successfully used. With virtual instruments it is relatively easy to build a wide variety of the computer based applications for process modeling, and simulation of the instruments operating and measuring systems execution. Presented virtual experiments can be also attractive models of the measurement processes used in education. The presented set of virtual advanced physics experiments are included in a specific module for training, dedicated for the in-service teachers training, in the frame of a recent approved European Socrates - Comenius three years project: CP RO-COMENIUS-C1, funded by European Commission, School Education: Socrates. The project activities will be developed during October 006 September 009 and the training module consists of 6 face-to-face meetings and provides both technical and pedagogical elements with the view of the implementation in the classroom of the proposed virtual applications. The content of the units is oriented on: basics of virtual instrumentation, teaching methodologies and pedagogical strategies involved in the using of the virtual instrumentation, virtual instruments and specific programming languages, basic steps in developing a virtual instrument, virtual instrumentation application designing and implementing. References [1] D. W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer-Verlag Berlin Heidelberg, [] L. P. Mari, Models of the Measurement Process, Handbook of Measuring System Design, edited by Peter Sydenham and Richard Thorn, 005 John Wiley & Sons, Ltd, pp [3] G. W. Johnson, Graphical programming: practical applications in instrumentation and control, nd ed., McGraw-Hill, [4] W. Tłaczała, Modeling with LabVIEW, Handbook of Measuring System Design, edited by Peter Sydenham and Richard Thorn, 005 John Wiley & Sons, Ltd, pp