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Impulse measurement using an Arduíno To cite this article: P R Espindola et al 2018 Phys. Educ. 53 035005

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Paper Phys. Educ. 53 (2018) 035005 (4pp)

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Impulse measurement using an Arduíno P R Espindola, C R Cena, D C B Alves, D F Bozano and A M B Goncalves Instituto de Física, Universidade Federal de Mato Grosso do Sul, Campo Grande, MS, CEP 79070-900, Brazil E-mail: [email protected]

Abstract In this paper, we propose a simple experimental apparatus that can measure the force variation over time to study the impulse-momentum theorem. In this proposal, a body attached to a rubber string falls freely from rest until it stretches and changes the linear momentum. During that process the force due to the tension on the rubber string is measured with a load cell by using an Arduíno board. We check the instrumental results with the basic concept of impulse, finding the area under the force versus time curve and comparing this with the linear momentum variation estimated from software analysis. The apparatus is presented as a simple and low cost alternative to mechanical physics laboratories. S Supplementary material for this article is available online

1. Introduction

p­ ractical activities in undergraduate physics laboratories, and does not require a high investment in equipment.

The impulse-momentum theorem says that the impulse is equal to the change in the linear momentum of the body. Also the impulse can be calculated by product of the resultant force acting on an object and its time of interaction. The bungee jump is a good example that can be used to discuss the impulse-momentum theorem [1, 2]. In the literature we can find works presenting zero cost experiments [3] related to the impulsemomentum theorem, and experiments that use commercial sensors [4] to demonstrate the relationship using the bungee jump as example. Here we present another way to make a low cost experiment using an Arduíno board and a load cell sensor to measure the force that acts during the process. The Arduíno board comes as an alternative to reduce this lack of modern experiments at universities and schools [5–9]. Most of the time it can improve the quality of the 1361-6552/18/035005+4$33.00

2.  Experimental setup The experimental setup for this experiment is very simple. To measure the force, a 1 kg range load cell is connected to a analog–digital amplifier which then outputs to the Arduíno board. The load cell is fixed in a support stand, and a body of mass m is connected to it by a rubber string of length L ( L is minor than height position of the load cell on stand support). A picture of the apparatus can be observed at figure 1. In our case we use a 1 kg micro parallel beam type load cell. It has 4 wires: red, black, white, and green; that are connected to the load cell amplifier (we use the model HX711) electrical pins E+, E−, A−, and A+, respectively. The electrical contacts on other side of the load cell amplifier: GND, DT, 1

© 2018 IOP Publishing Ltd

P R Espindola et al SCK, and VCC are connected to the Arduíno Nano board. The DT and SCK are connected to the Arduíno digital ports D3 and D2, respectively. Figure 2 shows the circuit diagram used. By default, the data collection rate of the HX711 output is 10 Hz. It is slow to do this experiment. Another sample rate (80 Hz) is available but it cannot be done using the software. The change needs to be done by the hardware. Some HX711 boards comes with connections to do it. Others, like the one we have used in this experimental setup, there is not. To change the sample rate it is necessary to disconnect the pin 15 of the IC from the printed circuit board and connect it with the pin 16 (see supplementary info to more details (stacks.iop.org/PhysEd/53/035005/mmedia)). Prior to starting the measurements, the load cell must be calibrated. To do the calibration, we connect the Arduíno board to the computer and open the serial monitor on Arduíno IDE 1.8.5 [11] software. Once the calibration routine is started, a known mass is suspended on load cell (we use the body used to do the experiment as mass reference). Using  +  and  −  on keyboard we change the CALIBRATION_FACTOR until the value presented on the serial monitor coincides with the reference. At first, the CALIBRATION_ FACTOR should be far from the expectation. We recommend after first calibration, to annotate the found calibration factor and substitute it at the source code. This procedure will make the new calibration faster. After the calibration setup, the routine ask for a time used to proceed the measurement. The force, and time are taken by the Arduíno, and the results are presented on the serial monitor. All the data was collected on the serial monitor and saved as a text file (ASCII) to be used in a graphical software. The communication with the sensor was made using the respective libraries [12] (the libraries can be found by a simple Internet search). The complete source code can be visualized in the supplementary info. The code is based on HX711 library examples and can be modified according to user demand. Since HX711 can be used with many types of load cells no drastic changes need to be made to the source code. When another amplifier model is used, the code will probably need to be modified.

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Figure 1.  Picture of the experimental apparatus.

3.  Results and discussion The experiment was conducted as follows: we leave the body to fall from a height of 30 cm relative to the lower position that it can stay fixed to the string. The data was collected until it stops. Figure 3 shows the tension at the string (measured by the load cell) as function of time. Before and after the bounces the force measured is zero since there is no tension on the string. After some bounces the measured force stabilises at the body weight. To analyze the impulse we are interested in the first bounce. It is presented in figure  4. The impulse was calculated from the area below the force curve. Since the impulse is defined as the integral of the net force over time, and the net force is the tension measured by the load cell minus the weight (see the free body diagram, the inset of figure 4), we need to subtract the weight from the tension force data. The impulse measured by the marked area in figure  4 is I = 0.81 N · s. To confirm the impulse-momentum theorem, that says that the impulse is equal to the variation of the linear momentum, we made a video of the experiment.

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Phys. Educ. 53 (2018) 035005

Impulse measurement by using Arduino 4

Net force (N)

T

Figure 2.  Sketch of the circuit with the Arduíno, the load cell amplifier and load cell [10].

P

I = 0.81 N · s 0

Fnet = T – P –2 0.2

0

0.4

0.6

0.8

1

Time (s)

Figure 4. The graph shows a close-up of the first bounce. The y-axis now represents the net force applied to the body. The red area represents the impulse produced by the net force. Right is presented a free body diagram with all the forces: tension and weight.

4 Tension (N)

2

2

analog–digital converter (HX711) is not fast enough to provide sufficient data points to determine the impulse from F verus t curve analysis. We believe that an ADC with a faster data collection rate permits a good measurements with non elastic strings.

0 0

2

4 Time (s)

6

Figure 3. Tension measured on the elastic string by the load cell as a function of the time.

4. Conclusion In this work we show a way to measure the impulse due the tension force in a bungee jump experiment. To measure the force a load cell connected to an Arduíno board was used. The impulse was calculated by the integral of net force as a function of time curve. In order to compare, the change in the linear momentum was calculated by video analysis of the body movement. The difference between the results was less than 5% confirming the impulse-momentum theorem.

With the video analysis we can calculate the body velocity before and after the bounce. Using the Tracker video analysis software [13], we measure the position, and velocity (see the supplementary info) of the body as a function of the time. The momentum change is given by ∆p = mvup − mvdown , (1)

where vup is the maximum velocity of the body going up, and vdown is the maximum velocity of the body going down. By the video, we measure to vup =  2.00 m s−1 and vdown = −2.22 m s−1. The value calculated to the linear momentum variation of the body (mass m = 0.201 Kg) was ∆p = 0.85 N · s. The percentual difference between the impulse I = 0.81 N · s and the change in momentum ∆p = 0.85 N · s was less than 5%. It shows a good agreement with the theory. We have tried to make these same measurements with an inextensible string. But the

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Acknowledgments The authors would like to acknowledge the financial agencies: CNPq and FUNDECT by the support.

ORCID iDs A M B Goncalves 0001-7052-4713 3

https://orcid.org/0000-

Phys. Educ. 53 (2018) 035005

P R Espindola et al Cicero R. Cena received his PhD degree in Materials Science in 2013 at UNESP, Ilha Solteira - Brazil. He is currently assistant professor at UFMS. His research fields are focused on the synthesis of ceramic micro and nanofibers with potential application on sensors and photocatalysis. He used to work on development of low cost experimental apparatus to physics teaching. Running and swimming are his favorite sports.

Received 5 January 2018, in final form 12 January 2018 Accepted for publication 19 January 2018 https://doi.org/10.1088/1361-6552/aaa920

References

[1] Martin T and Martin J 1994 The physics of bungee jumping Phys. Educ. 29 247–8 [2] Heck A, Uylings P and Kdzierska E 2010 Understanding the physics of bungee jumping Phys. Educ. 45 63–72 [3] Ganci S and Lagomarsino Oneto D 2017 A zero cost experiment on the ‘impulse-momentum theorem’ Phys. Educ. 52 13002 [4] Horton P 2004 Elastic experiment is licensed to thrill Phys. Educ. 39 326–8 [5] Pereira N S A 2016 Measuring the RC time constant with Arduino Phys. Educ. 51 065007 [6] Atkin K 2016 Using the Arduino with MakerPlot software for the display of resonance curves characteristic of a series LCR circuit Phys. Educ. 51 065006 [7] Kubínová S and Šlégr J 2015 Physics demonstrations with the Arduino board Phys. Educ. 50 472 [8] Goncalves A M B, Cena C R and Bozano D F 2017 Driven damped harmonic oscillator resonance with Arduíno Phys. Educ. 52 043002 [9] Goncalves A M B, Cena C R, Alves D C B, Errobidart N C G, Jardim M I A and Queiros W P 2017 Simple pendulum for blind students Phys. Educ. 52 53002 [10] Image made with Fritzing http://fritzing.org/ home/ [11] Arduíno IDE www.arduino.cc/en/Main/Software [12] HX711 libraries was found https://github.com/ bogde/HX711 [13] Tracker Video Analysis and Modeling Tool https://physlets.org/tracker/

Diego C. B. Alves received his PhD degree in physics from Universidade Federal de Minas Gerais. He is currently assistant professor at Universidade Federal de Mato Grosso do Sul (UFMS). His current research interests include the growth of semiconductor oxide nanostructures and nanodevices, synthesis of graphene oxide and 2D materials via chemical route with applications to photovoltaics and catalysis.

Doroteia F. Bozano bachelor in physics, has been an associate professor at UFMS since 2011. She received her PhD degree in Agronomy at UNESP. Her PhD work was related to synthesis of materials by sol-gel technique and catalysis studies.

Alem-Mar B. Goncalves received his PhD degree in physics from Universidade Federal de Minas Gerais. He is currently assistant professor at Universidade Federal de Mato Grosso do Sul (UFMS). His current research interests include growth and applications of bidimensional (graphene, MoS2, etc.) and semiconductor oxide based nanomaterials to catalysis, photovoltaics, and sensors. He also uses his technical skills to work on the development of physics teaching experimental apparatus.

Paulo R. Espindola is a graduate in physics from Universidade Estadual de Mato Grosso do Sul (UEMS). Now, he is as a physicist at Universidade Federal de Mato Grosso do Sul (UFMS). Master’s student in Material Science at UFMS.

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