AN APPROACH TO PHYSICS OF EVERYDAYLIFE EVENTS WITH PORTABLE SENSORS AND A GRAPHIC CALCULATOR IN A LAB COURSE FOR THE FORMATION OF PHYSICS TEACHERS

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1 AN APPROACH TO PHYSICS OF EVERYDAYLIFE EVENTS WITH PORTABLE SENSORS AND A GRAPHIC CALCULATOR IN A LAB COURSE FOR THE FORMATION OF PHYSICS TEACHERS GIREP seminar on «Quality developments in the formation and training of physics teachers» Udine September 200 Antonella Cuppari, Liceo Scientifico Galileo Ferraris - Torino (Italy) Tommaso Marino, Istituto Tecnico Industriale Edoardo Amaldi - Orbassano (Italy) Giuseppina Rinaudo, Gianna Rovero, Department of Experimental Physics of the University of Torino (Italy) rinaudo@ph.unito.it Abstract The introduction of the basic physics concepts and the discussion of physics laws are often done in a rather formal way, assuming idealized situations which rigorously follow the theoretical predictions. In general, this approach does not excite an enthusiastic interest in the students, the main reason being that the spontaneous ideas related to many physical concepts are based on everyday life experience and are therefore rather far from the ideal simplification of the theoretical laws. An example is the concept of acceleration, which is approached through kinematics in formal teaching, while for the student the dynamical aspects are generally more interesting, in particular those connected with impulsive and transient forces, such as the acceleration of a Ferrari formula one car, or the initial sprint in a 100 meters competition. In this context, the use of a portable graphic calculator connected with portable sensors can be very useful, because the measurements of real events can be acquired with sufficient accuracy to allow a subsequent analysis, which can relate them to the theoretical laws. Also the possibility of an immediate graphic display helps to develop a first interpretation and understanding of the underlying physics. In a lab course for the initial preparation of future physics teachers we have carried out an experimentation of a systematic use of a portable system of this type to help the students to rethink the physics they learned in their university courses, starting from a real life event rather than from an abstract law. This is very important in our case, because the majority of our future physics teachers did not graduate in physics but in mathematics and thus tend to privilege the formal mathematical aspects rather than the physical ones. In the presentation, examples will also be given of the results of two experimentations that followed the didactical lab, the first, during the practical training of the students in High School classes, the second, during a three days stage of high school students in a Casa Alpina in the Italian Alpes. Introduction In Italy the Scuola di Specializzazione per l Insegnamento Secondario (SIS) for the preparation of future secondary school teachers has a duration of two years and consists in courses, didactical labs and practical training. With regards to physics, an important aim is to help the future teacher to rethink the physics that he has learned in his university courses, which very often are formal and abstract, by approaching it from a different point of view, more suitable for the transfer at the level of a secondary school. We found that a powerful support in this direction is given by the use of a graphic calculator connected with portable sensors (Fig.1) to obtain a simple, portable, low cost Real Time Laboratory (RTL), not only because the system allows a rapid collection of a large amount of high quality data from different experiments and the immediate analysis and graphical representation of data, but also because it favors the operation of rethinking basic physics concepts by exploring aspects of real life events which are not accessible with conventional means, while being very rich of hints to reflect on the underlying physics [1]. 1

2 calculator sonar Figure 1 Example of graphic calculator and portable sensor utilised in the real time laboratory. We started to use the graphic calculator and the portable sensors in the didactical labs and in the practical training of the SIS-Piemonte only in 2001, as an experimental trial restricted to a few SIS students who followed a training course for in-service teachers. The reasons of the initial mistrust were mostly due to technical difficulties, in particular the insufficient number of available instruments and the short time allowed to become familiar with the new technology and with the new didactical strategy. However, at the same time, we were sure that this system would be very useful for the formation of our future physics teachers, who, having a prevalent mathematical formation, tend to give more importance to the mathematical aspects rather than to the physics of the event. Some of the SIS students applied what they had learned in the course during their practical training experience in secondary school classes and this gave us a direct feedback of the potentiality of the approach not only for the formation of our SIS students, that is of the future teachers, but also for its transfer to secondary school students. Essentially, the major discovery was that it became evident to the SIS student that real events do not follow exactly the mathematical laws that they studied in their university course and that the deviations from the law are not indication of a poor approximation of the real phenomenon to the perfect mathematical law but rather are hints of a rich underlying physics, which might be even more interesting to study than the expected law. Of course, some difficulties were also found, that we will discuss below. After this encouraging experience, we introduced in the SIS programs a dedicated laboratory using graphic calculators, which was shared with the mathematicians: about half the time was dedicated to program and represent graphically mathematical functions and half the time to physics experiments with portable sensors. The common part concerned modeling with the help of the calculator, essentially relying on the possibility of the powerful and immediate graphical representation, with two complementary approaches, either learning to read the graphs in order to discover the features of the underlying mathematical/physical law or starting from the law and try to figure out the behavior of its graphical representation. A recent experience was the use of the graphic calculator and portable sensors during a three-days stage in a Casa Alpina in the Italian Alps of high school students, with the SIS students acting as tutors and entertainers. The stage was meant to be half way between a discovery experiment and a physics context; different labs were offered to the high school students with very large autonomy given to them for exploration and creative invention; one of the labs was about discoveries with portable sensors and graphic calculators. In the following section we will give some examples which we consider particularly interesting to show the potentiality of this approach to develop physics concepts and to model physical laws. Examples of modeling RTL experiments The simplest experiments involve studies of motion. Typical ideal motions are the uniform, the uniformly accelerated and the oscillatory motion, which are described, in space-time diagrams, respectively by a straight line, a parabola and a sinusoid. Let us examine instead a real uniform motion, such as a simple walk with constant speed. In figure 2 we show the plot obtained with a sonar and a graphic calculator TI-8 plus for a regular walk towards the position of the SONAR [2]. ).. posizione - tempo 2

3 6 steps Figure 2 Data of position versus time taken during a 6 step walk toward the SONAR. The first analysis of the collected data is done using the plot shown on the screen of the calculator to evaluate if the data are reasonable; the plot appears to be rather close to a straight line, time and distances appear to be as expected. The data are then transferred through the serial port to a personal computer and the subsequent analysis is done with a conventional work sheet (EXCEL), to allow an easier analysis with a familiar system. We always ask the SIS students to take note of the number of steps, in order to facilitate the hunt for deviations from the linear behaviour, which is the dream of a mathematician, in particular for indications of the step periodicity in the plots. In this plot there no evident variations indicating the different steps, but they become evident in the plot of the velocity (figure ), calculated as the difference between subsequent positions divided by the time interval (the sign of the velocity was inverted to make the interpretation easier). velocità (m/s) step 1 velocità - tempo step 2 step step step average velocity step tempo (s) Figure Velocity versus time of the data shown in figure 1; the lighter line is the result of smoothing the values. This plot now shows that there are clear deviations from a straight line and that the deviations are roughly periodical, with a period close to the value expected from the count of the number of steps. We can now build a more realistic model of a real walk, which will need many more parameters besides the average velocity, in particular - the initial acceleration, which is very clear and is practically concluded within the first step (about 0.6 s); - its value, which is about 0.7ms -1 / 0.6s 1.1 ms -2, that is a significant fraction of the gravity acceleration;

4 - the variations of velocity at each step, which are also very evident and appear as fluctuations about the average value, with a deceleration followed by an acceleration; - the values of the intermediate accelerations, which are about one half of the initial acceleration. It is thus evident that the walk is quite different from an uniform motion and that the deviations are not the indication of an imperfect uniform motion, which should be smoothed away to obtain the perfect motion, but, on the contrary, they carry the information on the rich physics that underlies the simple walk. Indeed, forces are continually needed, both at the beginning, to reach the average velocity, and at each intermediate step, for the deceleration when to foot hits the ground and for the subsequent acceleration to speed up again. The forces needed are a significant fraction of the body gravity force: this means that the leg and feet muscles are able to apply such forces. Also the minimum energy needed to reach and maintain the average velocity can be evaluated, as well as the power, since the time interval of the acceleration is recorded with sufficient precision []. What is the source of the forces? For the accelerations, it is the static friction with the floor, for the deceleration, the dynamical friction: both can be estimated from the data and the corresponding coefficients can be evaluated. Along a similar line are the data shown in figure. They were obtained with an accelerometer and the graphic calculator during the stage in the Casa Alpina while jumping from a stool. In this case the SIS students were the tutors and the experiment was performed by the high school students who took part in the stage. Of course the SIS students had tested the entire experiment before and had decided that they would focus on the meaning of g, that is on the gravity acceleration. The analysis was done directly on the screen of the calculator, because the idea was to discover first of all how the acceleration changes from the value of the free fall to zero. The two pictures in the figure refer to the same jump: at the left, the cursor is positioned during the free fall and one reads that the value of the acceleration is indeed close to g and the time of free fall corresponds to what expected on the basis of the height of the stool; at the right one reads the peak deceleration, which is about 2. g. The plot displays also the variation of the deceleration with time, which recalls qualitatively the variations of a spring force. Indeed there is a quite complicated spring, with a spring constant which depends on the type of jump, on the muscles of the jumper and on the type of floor. The indicator is the duration of the deceleration, and the students of all kind (high school and SIS) soon discovered how to jump in order to obtain a short duration and, as a consequence, a large peak deceleration! Figure Acceleration as a function of time during a jump from a stool. A completely different example was the analysis of a cooling down plot. The data were taken by the SIS students with the temperature sensor and the object which cooled was simply a thin aluminum foil heated with a phon. The students knew the law, they measured the room temperature around the foil and tried to fit the data to the exponential law. What happened was that they could not find a good fit to the very detailed data obtained with the online sensor, simply because there is no such thing as an ideal room temperature, but they discovered, on the basis of the data, the value of effective room temperature, which happened to be about 2 o C below the measured value. In Fig. we show, at the left the data in logarithmic scale with the measured room temperature and, at the right, the data with the fitted room temperature. Again the students could appreciate the help to develop the feeling for physics that the richness of data of a graphic calculator can provide. biente)/gradi C elsius) 2 ln (T-Tambiente-misurato) biente)/gradi Celsius) ln (T-Tambiente) ln (T-Tambiente-effettivo)

5 Figure Temperatures of a thin aluminum foil shown in a logarithmic scale as a function of temperature after subtraction of the room temperature; in the left hand side plot the measured value of the room temperature was subtracted, in the right hand side plot the value that gave the best fit to the logarthmic dependence. Conclusions Our experience of using graphic calculators and portable sensors with SIS students did show that there are positive but also negative aspects; however, on the overall average, the balance is positive. The main drawback is the time and effort needed to overcome the technical difficulties; the most positive aspect is the push to abandon the stereotyped mathematical modeling of the complex physical event and to look at the experimental data to extract their real meaning. References and notes [1] Preliminary results were presented at the GIREP 2002 conference in Lund ; for details on the experiment with the SONAR, see also A. Cuppari, S. Lombardi, T. Marino, V. Montel, G. Rinaudo, E. Sassi e I. Testa, Contare i passi con RTL, in the tutorial on graphic calculators in the meeting TED 2002, Genova, February [2] Between the portable sensor and the graphic calculator an intermediate device is needed to convert the analog signal to a suitable digital form; a detailed description of the hardware and software needed is given in referen.ce [1]. [] Assuming, for example, a mass of 0 kg, the average energy needed for initial acceleration in this walk is about 10 J and the power about 00 W; for the intermediate accelerations at each step, the energy and the power are between 1/2 and 1/ of the initial values.