The Use of Mobile Phones for the Study of Periodical Movements

Transcription

1 The Ue of Mobile Phone for the Study of Periodical Movement Marin Oprea Faculty of Phyic, Univerity of Bucharet, Bucharet-Magurele, Romania Abtract Nowaday, mobile device hold an extraordinary didactic potential which i jut beginning to be explored and graped by the Phyic teacher community. The high-accuracy enor that mobile phone are equipped with enable one to integrate thee mobile device in the experimental area of Phyic leon, a analyi and meaurement intrument. Thi tudy i deigned to demontrate how the accelerometer of a mobile phone can be ued to record and tudy the periodical movement, uch a the uniform circular motion and the harmonic ocillation. The quantitative and qualitative analyi of the data recorded by the acceleration enor i facilitated by a mobile application which provide a real-time viualiation of the value component of acceleration. Keyword: Smartphone, Accelerometer, Harmonic ocillation, Pendulum 1 Introduction Smart phone are not only communication and entertainment portable device, but alo valuable tool that engage tudent in learning and motivate them to invetigate Phyic related concept (Goad, 01). The acceleration enor integrated in the martphone ha a remarkable importance for the modern approach to the teaching of Phyic, particularly in the field of Mechanic (Vogt and Kuhn 01; Kuhn and Vogt, 013; Vogt and Kuhn, 014; Gonzale et al, 014). Thi enor enable the tudent to trace, with a fairly accurate degree of preciion, the evolution of the value of the Carteian component of a body acceleration in time. That i why the ue of thi enor i adequate for a broad range of dynamically oriented Mechanic experiment, uch a the one involving periodical movement. Several tudie have hown the enor application for the tudy of circular motion (Balleter et al, 014; Catro-Palcio et al, 014; Chevrier et al, 013; Viridi et al, 013; Vogt and Kuhn, 013) which the tudent generally find more difficult to undertand when the teaching take place on a purely theoretical level (Martinez, 014). Thi tudy however focue on the way the accelerometer can be ued to quantitatively and qualitatively tudy the periodical movement of a gravitational pendulum. Pendulum experiment In thi tudy we aim to illutrate data acquiition experiment performed both in the Phyic Laboratory, a well a outdoor. In both cae we determined, baed on the analyi of the recorded acceleration graphic, the following parameter of the ocillation of the body upended by the wire: the ocillation period T, the angular frequency, the frequency, the angular E and the imum amplitude, the imum peed v, the imum kinetic energy c potential energy E p. Moreover, taking from the graphic the imum value of the recorded acceleration a we performed determination of the value of the gravitational acceleration g, when knowing the length l of the pendulum. The value obtained for g wa compared to the

2 The 11 th International Conference on Virtual Learning ICVL tandard value ued to etablih the level of experimental preciion given by the acceleration enor..1 Laboratory Experiment The gravitational pendulum ued in the Phyic laboratory i illutrated in Fig.1. It wa made from a cylindrical homogenou object (a can) which had a upenion wire at the top end and a rectangular frame for fitting the martphone on it bottom end. The ma of the upended body, including the mobile phone, wa m 0,58kg and, from the total length of the wire L 0,5m the value employed wa l 0, 44m (the difference in length wa ued for fatening the end of the wire). Figure 1. Gravitational pendulum experiment in the Phyic laboratory The upended body wa taken out from it equilibrium poition under a θ angle and left to ocillate relative to the vertical ymmetry axi of the experimental etup. The angular amplitude of the ocillation wa gradually reduced, until a harmonic ocillation regime pecific for mall angle wa reached (5 6degree). The movement of the pendulum took place on a yoz level, a the phone yoz accelerometer axe were ituated in thi plane. Due to the reduced angular amplitude of the ocillation, the mot ignificant contribution to the tangential acceleration wa brought by the component a y.we elected, from the recording performed with the application Linear Accelerometer intalled on the phone, the area which correpond to the harmonic ocillation regime (Fig.). Figure. Graphic of tangential acceleration component

3 368 Univerity of Bucharet and Univerity of Craiova We need to mention the fact that the application Linear Accelerometer tore the recorded data into a.cv format in order for it to be proceed in Excel.The diturbance factor during the experiment (vibration from the acoutic pectrum, typical for a chool laboratory during clae) caued light local ditortion of the tangential acceleration a tg graph variation with time t. Still, thi apect did not have a major influence on the value of the meaured parameter. During the time interval elected t (7 7 ) there are N 15 ocillation. Therefore, their t 0 ocillation period i T 1, 33. The angular frequency of thee ocillation ha N 15 the value 4,71 rad 1 and their frequency i 0, 75Hz. From the relationhip [1] T g we calculated that: l 1. g l 0, 44 m (4,71 ) 9,76 m Thi value i cloe to the known value 9,81 m (the difference in value i within the 1% limit). From the graphic we can notice the fact that the amplitude of the tangential acceleration ha light fluctuation around the value of m. By averaging it ium value from the elected m time interval we calculated atg 1, 7. Form the relationhip a tg g in g we determined that the angular amplitude pecific for mall ocillation i m a 1, 7 tg 0,17rad. Thi value correpond to an angle g m 9,76 arcin(0,17) 9, 78 degree, which i within the mall ocillation range where the harmonic ocillation regime of the pendulum i predominant. The length of the angular ector aociated with thi angular amplitude ha the value l in 0, 44m 0,17 0,075m 7,5cm. The imum peed attained, deducted from the law of the conervation of mechanical energy applied in the cae of mall ocillation, wa: m cm [] v g l (1 co ) 0,358 35,8. The aociated kinetic energy had the value: m 0,58 kg (0,358 ) mv [3] E c 0,037J. T

4 The 11 th International Conference on Virtual Learning ICVL Due to the fact that the tudied ytem ocillated in a harmonic regime, it i placed in a conervative force field, o thi value of kinetic energy i to be found in the value of the imum potential energy of the tudied gravitational pendulum.. Outdoor Experiment The experiment for analying the periodical motion uing a gravitational pendulum continued outide the Phyic laboratory, on the chool port field. The experimental device wa modified o that the movement could be tabilized in order to avoid the error produced at the interference of the ocillating motion with mechanical vibration from the urrounding environment. Figure 3. Gravity pendulum - experimental etup outdoor (1) Uing a ealed cylindrical platic container filled with water we contructed a bifilar pendulum with the effective length of l 1, 55m.The ma of the upended body wa m 3,1kg. The body wa upended from the horizontal bar of a handball goal preent on the chool port field. The mobile phone wa placed at the bottom of thi body uing a plexigla interface (Fig.3). After performing the horizontal alignment tet of the device uing a balance level, we tarted the experimental determination. From the large area of acceleration recording taken with the martphone, we elected for analyi the one which correpond to the harmonic ocillation regime, a Fig.4 illutrate.

5 370 Univerity of Bucharet and Univerity of Craiova Figure 4. Graphic of recorded tangential acceleration (bifilar pendulum) A we can notice from the diagram, the a y component weigh the mot in the tangential acceleration of the pendulum. The time interval of the recording which bet approximate the harmonic ocillation regime i t 0, ituated between t 1 80 and t 100 (Fig.5). Figure 5. Graphic of recorded tangential acceleration (harmonic ocillation) By cancelling the a z component of the tangential acceleration due to it inignificant value, the graphic ha the following form: (Fig.6). Figure 6. Graphic of recorded tangential acceleration ( component)

6 The 11 th International Conference on Virtual Learning ICVL The number of ocillation preent in thi time interval i N 8 which lead to the concluion 0 that T,5. The average of the imum ocillation value of the tangential 8 m acceleration wa atg 0,97, given the fact that the fluctuation between the firt and the lat peak from the analyed time interval wa 8, %. The value of the determined phyical quantitie are illutrated in the table below (Table 1). Phyical quantity Determined value Table 1. Value of phyical quantitie Frequenc Angular m Variati y frequency g( ) on of ( Hz) rad g (deg.) ( m ) Length of E v travelled c ector E ( ) ( ) p J (%) The determination of the phyical quantitie from Table 1 wa alo performed during an outdoor experiment in an amuement park for children. We ued the wing preent on the ite a pendula and the data recording proved to have both a fun and a cientific factor (Fig.7). Figure 7. Gravity pendulum - experimental etup outdoor () A ample of the acquired experimental data i illutrated in Fig.8.

7 37 Univerity of Bucharet and Univerity of Craiova Figure 8. Graphic of recorded tangential acceleration (wing) The fluctuation preent in the beginning and at the end of the recording are caued by the mechanical diturbance induced by the peron operating the application Linear Accelerometer intalled on the mart phone. The area of interet for analyi in the graphic i to be found in the interval In thi region one can oberve periodic phenomena of a harmonic type. The a x component of acceleration doe not contribute quantitatively to the total value of the tangential acceleration a tg. The quantitative difference between the imum value of a y and a z i the conequence of the ocillation having a mall angular amplitude. Uing the information from the graphic in Fig.8 we determined the value of g tarting from g l. The value of wa determined uing the relationhip 6,8 rad,51. The meaured value of l wa etimated at T t 15 N 6 l 1, 55m. Therefore, g l 1,55 m (,51 ) 9,78 m 1. The fact that the value i cloe to the tandard one of 9,81 m indicate that the accelerometer ha a good preciion in recording data. 3 Concluion Thi tudy ha hown the reliability of the accelerometer when tudying the ocillating motion of a gravitational pendulum, both in laboratory condition and outdoor. The ucceful experimental reult reflect the importance of thi enor for the precie and quickly attainable meaurement of a body acceleration while ocillating. The graphic that accurately trace the evolution in time of the Carteian component of the pendulum acceleration are very important element that tudent can ue to analye harmonic

8 The 11 th International Conference on Virtual Learning ICVL ocillation. Baed on the data temming from thee graphic, the tudent are able to calculate the value of the phyical quantitie involved: period, frequency, angular amplitude, velocity, energy etc. All in all, the mart phone hould be viewed a a valuable multi-enor tool which can be ued to invetigate a wide range of phyical phenomena and which can be part of many creative Phyic experiment. The ucceful integration of thi portable device into the teaching proce can greatly enhance the qualitative apect of learning and timulate the tudent motivation for the tudy of cience in general and of Phyic in particular. Reference Balleter, E., Catro-Palacio, J.C., Velázquez-Abad, L., Giménez, M.H., Monoriu, J.A., Sánchez Ruiz, L.M. (014). Smart Phyic With Smartphone Senor, 014 IEEE Frontier in Education Conference, 1-4. Catro-Palacio, J. C.; Velazquez, L., Gomez-Tejedor, J. A., Manjon, F. J., Monoriu, J. A. (014). Uing a Smartphone Acceleration Senor to Study Uniform and Uniformly Accelerated Circular Motion, Revita Braileira de Enino de Fiica, 36 (), 315. Chevrier, J., Madani, L., Ledenmat, S., Biey, A. (013). Teaching Claical Mechanic Uing Smartphone, The Phyic Teacher 51, Goad, K.D. (01). The Perception of Teacher Toward the Ue of Mobile Technology a a Tool to Engage Student in Learning, PhD Diertation - Indiana State Univerity, Terre Haute, Indiana. Viridi, S, Moghrabi, T., Nari, M. (013). An Obervation of a Circular Motion uing Ordinary Appliance: Train Toy, Digital Camera, and Android baed Smartphone, Proiding of Simpoium Naional Inovai dan Pembelajaran Sain, 3-4 July, 1-7. Kuhn, J., Vogt, P. (013). Smartphone a Experimental Tool: Different Method to Determine the Gravitational Acceleration in Claroom Phyic by Uing Everyday Device, European Journal of Phyic Education, 4(1), Gonzalez, M., Gonzalez, M.A., Llama, C., Martin, M. E., Vega, J., Martinez, O., Hernandez, C., Herqueda, M. (014). Mobile Phone for Teaching Phyic: Uing Application and Senor, Proceeding of the Second International Conference on Technological Ecoytem for Enhancing Multiculturality, Aociation of Computing Machinery, New York, NY, USA, Martinez, L., Garaizar, P. (014). Learning Phyic down a lide: A et of experiment to meaure reality through martphone enor, 014 IEEE Global Engineering Education Conference (EDUCON), Vogt, P., Kuhn, J. (01). Analyzing free fall with a martphone acceleration enor, The Phyic Teacher, 50, Vogt, P., Kuhn, J. (01). Analyzing Simple Pendulum Phenomena with a Smartphone Acceleration Senor, The Phyic Teacher, 50, Vogt, P., Kuhn, J. (013). Analyzing Radial Acceleration with a Smartphone Acceleration Senor, The Phyic Teacher, 51, Vogt, P., Kuhn, J. (014). Analyzing Colliion Procee with the Smartphone Acceleration Senor, The Phyic Teacher, 5,