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Use of an Arduino to study buoyancy force To cite this article: P R Espindola et al 2018 Phys. Educ. 53 035010

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Paper Phys. Educ. 53 (2018) 035010 (4pp)

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Use of an Arduino to study buoyancy force 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 The study of buoyancy becomes very interesting when we measure the apparent weight of the body and the liquid vessel weight. In this paper, we propose an experimental apparatus that measures both the forces mentioned before as a function of the depth that a cylinder is sunk into the water. It is done using two load cells connected to an Arduino. With this experiment, the student can verify Archimedes’ principle, Newton’s third law, and calculate the density of a liquid. This apparatus can be used in fluid physics laboratories as a substitute for very expensive sensor kits or even to improve too simple approaches, usually employed, but still at low cost.

1. Introduction

a commercial dynamometer and/or a scale [5, 6]. Then the buoyant force is calculated by the dif­ ference between the weight in air and the weight of the body completely immersed, it is also called apparent immersed weight. In this paper, we propose a simple, low cost, and more profit­ able experiment to explore this phenomenon. An Arduino board and two load cell sensors were employed to measure the buoyancy.

The Archimedes principle is a fundamental law of physics used to describe fluid mechanics. This principle states that an upward force (called buoyant force), acts on a body fully or partially immersed in a fluid. The force acts at the cen­ ter of mass of the displaced fluid and its modu­ lus is equal to the weight of the displayed fluid. An interesting phenomenon observed due this principle is the fact that the weight of the body completed immersed in a fluid is reduced when compared with its real weight in air. Many experiments can be done at low cost in the physics laboratory [1, 2], but they may become, at some point, poor in result analysis due to the lack of experimental data collected. With the advent of the Arduino Board, these limitations are overcome and many experimental approaches arise with interesting possibilities for exper­ imental physics classes [3, 4]. Usually, at the physics laboratory, a simple experiment can be done by measuring the weight of a body completely immersed in a fluid by using 1361-6552/18/035010+4$33.00

2.  Experimental setup For the experimental setup, we use two 1 kg range load cells connected to an Arduino. One is fixed in a support stand, and the other is fixed to two plastic plates to make a balance. A cylinder of mass m, length l = (72.0 ± 0.5) mm , and diam­ eter d = (28.0 ± 0.5) mm is attached to the load cell with a paper clip hanger. The cylinder has marks, in steps of ∆l = (10.0 ± 0.5) mm , used to measure the depth of it in liquid. This load cell is responsible for measuring the apparent weight. The other load cell is used as an balance and we 1

© 2018 IOP Publishing Ltd

P R Espindola et al put a becker with water on top of it. The scale with the becker are put on a lift table. Figure 1(a) shows the complete experimental setup, and the scale in detail can be seen in figure 1(b). The load cells require their own amplifier (we have used in our apparatus the model HX711). Its four wires: red, black, white, and green; are con­ nected to the amplifier electrical pins E+, E −, A−, and A+, respectively. GND and VCC pins of both HX711 are connected to ground and 5 V pins of the Arduíno Nano board. The DT and SCK are connected, respectively, to the Arduíno digital ports D3 and D2, for the stand fixed load cell. For the scale, we use the Arduíno pins D5 and D4. Figure 2 shows the circuit diagram used. The data are collected from the Arduíno board is shown on the computer using the Serial monitor of Arduino IDE 1.8.5 [8]. The source code is presented in the supplementary informa­ tion, available at. When the routine begins, the Arduíno asks the students to start the calibra­ tion procedure of both load cells. A known mass is used as reference (the cylinder, for example). Using  +  and  −   on the keyboard we change the CALIBRATION_FACTOR until the value presented coincides with the reference. If the CALIBRATION_FACTOR is far from expecta­ tion, it can be changed on the source code. This modification of the source code makes the new calibrations faster. After each measurement, the height of the lift table needs to be changed. The routine wait for a command prior to getting the new data set. The complete data was copied from Serial Monitor and saved as text file (ASCII) to analyze in a graphical software.

Figure 1. (a) Picture of the complete experimental apparatus. (b) Detail on the scale built with the load cell.

on cylinder comes with an increase of the becker weight. The variation on the weights are related to the buoyancy force. The buoyancy force acts in the up direction on cylinder, decreasing its weight. As consequence of Newton’s third law, a force appears in the down direction on the becker, increasing its weight. Another way to see the results is if we sub­ tract the weight of the beaker with liquid. Figure 4 shows these results. Now, we can see directly the increase of the buoyancy force with the cylinder depth. The decrease in the apparent force is equal to the increase in buoyancy. It can be observed when we add the two values. The results of the sum keeps constant with depth. Finally, we can determine from these results the density of the liquid. The Archimedes princi­ ple says that the buoyancy force is equal to the volume of the liquid displaced by the body, B = ρgV, (1)

3.  Results and discussion

where B is the buoyancy force, ρ is the liquid density, g is the gravitational acceleration, and V is the volume of immersed body. In our case, the volume can be described as the area of the cylin­ der times the depth. The liquid density can be found by plotting the buoyancy force as a function of the immersed volume and fitting a linear curve (Figure  5). It is equal to the slope divided by the gravitational acceleration. We have used tap water as the liquid in our experiment, and the value of density found is ρ = (1.03 ± 0.01) × 103 kg m−3.

The cylinder was introduced into the liquid by lifting the support platform of the becker. The depth of the cylinder was measured by the marks made on it. For each depth, we collect the value of the forces, following the routine instructions on the Serial Monitor of Arduíno IDE. The sup­ port platform was lifted until the cylinder was completely immersed. The results of the apparent weight and the beaker (filled with water) weight as function of the depth are presented in figure 3. As expected, the decrease of the apparent weight

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Phys. Educ. 53 (2018) 035010

Use of an Arduino to study buoyancy force

Figure 2.  Sketch of the circuit with Arduino, the load cell amplifier and load cell [7]. The upper load cell has used a scale to measure the buoyancy force, and the bottom is used to measure the apparent weight.

Buoyant force (N)

Force (N)

3.4 Beaker weight Cylinder apparent weight

3

0.4

0.4

0.2

0

0 0

0.02 0.04 0.06 Cylinder depth (m)

0

2 Volume (10–5 m3)

4

Figure 5. The buoyancy force as a function of the cylinder immersed volume. The red line is the linear fit to the data.

Figure 3.  Weight of the beaker and of the cylinder as function of the cylinder depth.

4. Conclusion In this work we use two load cells connected to an Arduíno board to study the buoyancy force on a cylinder immersed in water. We could observe a decrease of cylinder apparent weight due to the upthrust force. The reaction to this force was observed as an increment in the beaker weight. Using the data, we calculate the density of the water and found a value of ρ = (1.03 ± 0.01) × 103 kg m−3.

Force (N)

0.6

0.4

Buoyant force Apparent weight Sum

0.2

0 0

0.02 0.04 0.06 Cylinder depth (m)

Acknowledgments The authors would like to acknowledge the finan­ cial agencies: CNPq and FUNDECT for their the support.

Figure 4. The graph shows the buoyancy force and the cylinder apparent force as a function of depth. The black circles are the sum of the two other forces.

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P R Espindola et al

ORCID iDs A M B Goncalves 0001-7052-4713

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.

https://orcid.org/0000-

Received 10 January 2018 Accepted for publication 19 January 2018 https://doi.org/10.1088/1361-6552/aaa93a

References

[1] Cena C R, Pereira O C N, Pereira V N, Canassa T A and Viscovini R C 2014 Theoretical and experimental approach to the harmonic oscillator using the Lissajous curves Rev. Bras. de Ens. de Fís. 36 2302–1 [2] Brissi D A, Ghirardello D, Cena C R, Goncalves A M B and Canassa T A 2017 Construction of a low cost wave generator and possible approaches in physical education Cad. Fis. da UEFS 15 1402–1 (http://dfis. uefs.br/caderno/vol15n1/s4Artigo02_CiceroGerador-de-Ondas.pdf) [3] Goncalves A M B, Cena C R and Bozano D F 2017 Driven damped harmonic oscillator resonance with Arduíno Phys. Educ. 52 043002 [4] 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 [5] Koenigs F F R 1984 Determination of liquid densities and volumes of solid bodies by the reaction force on a vessel Phys. Educ. 19 413 [6] Moreira J A, Almeida A and Carvalho P S 2013 Two experimental approaches of looking at buoyancy Phys. Teach. 51 96 [7] Image made with Fritzing http://fritzing.org/home/ [8] Arduíno I D E https://arduino.cc/en/Main/ Software

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.

 aulo R. Espindola is a graduate in P 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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