Team of Brazil Problem 09 Magnet and coin reporter: Bárbara Cruvinel Santiago.

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1 Team of Brazil Problem 09 Magnet and coin reporter: Bárbara Cruvinel Santiago

2 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago2 Team of Brazil Problem 9: Magnet and coin Problem 09 Magnet and coin Place a coin vertically on a magnet. Incline the coin relative to the magnet and then release it. The coin may fall down onto the magnet or revert to its vertical position. Study and explain the coin's motion.

3 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago3 Team of Brazil Problem 9: Magnet and coin Introduction Threshold angle Rotational motion Oscillations Experiments Experimental data Theory validation Conclusion Analysis Comparison Contents

4 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago4 Team of Brazil Problem 9: Magnet and coin Magnetization of the coin Magnetization is the main cause of the phenomenon. Difficult to predict mathematically for ferromagnetic material. Equivalent to “magnetic charges” for simplification. Considered constant as just one position is taken. Acts as kind of an average for the magnetic momentum

5 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago5 Team of Brazil Problem 9: Magnet and coin Threshold angle Threshold angle is defined

6 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago6 Team of Brazil Problem 9: Magnet and coin Threshold angle

7 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago7 Team of Brazil Problem 9: Magnet and coin Threshold angle The regions taken must be small enough to be considered single points, as “point magnetic charges”.

8 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago8 Team of Brazil Problem 9: Magnet and coin In the equilibrium: Threshold angle Threshold angle:

9 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago9 Team of Brazil Problem 9: Magnet and coin Threshold angle Magnetic properties: – Condition for effect occurrence. – Have no influence in the threshold angle determination. Weight: can be neglected as it is going to be showed. The coin falls over the magnet. tan³θ1 < r2/r 1 The coin is in instable equilibrium. tan³θ1 = r2/r 1 The coin comes back to the original position. tan³θ1 > r2/r 1

10 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago10 Team of Brazil Problem 9: Magnet and coin Rotational motion Moment of inertia:

11 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago11 Team of Brazil Problem 9: Magnet and coin Rotational motion Angular acceleration: Dependent on the inclination angle and on the magnetic properties.

12 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago12 Team of Brazil Problem 9: Magnet and coin Rotational motion Angular velocity approximately constant near the normal line to the magnet.

13 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago13 Team of Brazil Problem 9: Magnet and coin Oscillations Angular velocity approached to constant Amplitude that decreases with time A < 15° Under- damped Harmonic Oscillation

14 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago14 Team of Brazil Problem 9: Magnet and coin Oscillations Dissipative force of type –bv. However, magnetic force does not vary linearly and so does the damping. Hence, the period varies. So, that’s just a first approximation!

15 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago15 Team of Brazil Problem 9: Magnet and coin A θ1θ1 α A θ1θ1 α 1 st case: on the poles 2 nd case: on the sides Eddy currents: source of dissipative force Variation of magnetic flux Induction of electrical currents Dissipative force generated 1 st case:2 nd case: A≈5° Case of our experiments In our case, the eddy currents have their maximum influence in relation to the position on the magnet.

16 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago16 Team of Brazil Problem 9: Magnet and coin Material 1.Magnets 2.Real coins 3.Steel coins 4.Protractor (±0,5°) 5.Acrylic ruler Iron filings White paper Dynamometer (±0.05N) Support for the dynamometer Camera

17 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago17 Team of Brazil Problem 9: Magnet and coin Experimental description Experiment 1: show that the weight is negligible in comparison to the magnetic force. Experiment 2: threshold angle analysis. Experiment 3: magnet analysis. Experiment 4: oscillation analysis.

18 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago18 Team of Brazil Problem 9: Magnet and coin Experiment 1: weight analysis Weight Threshold angle Magnet Oscillations Force (N) 1 st 7.9 2 nd 7.7 3 rd 7.6 4 th 7.8 5 th 7.6 Average7.72 Standard Deviation0.13

19 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago19 Team of Brazil Problem 9: Magnet and coin Experiment 1: weight analysis Weight Threshold angle Magnet Oscillations Total force (N)7.72 Weight (N)0.04 Magnetic force (N)7.68 The weight represents0.52%of the magnetic force The weight can actually be neglected.

20 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago20 Team of Brazil Problem 9: Magnet and coin Experiment 2: threshold angle analysis Weight Threshold angle Magnet Oscillations 8 coins are used. They are inclined 1 by 1 degree. This is repeated 10 times for each coin. The points are averages.

21 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago21 Team of Brazil Problem 9: Magnet and coin Experiment 2: threshold angle analysis Weight Threshold angle Magnet Oscillations Precision of the protractor: ±0,5° Average deviation: 4%

22 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago22 Team of Brazil Problem 9: Magnet and coin Experiment 3: different magnets Weight Threshold angle Magnet Oscillations

23 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago23 Team of Brazil Problem 9: Magnet and coin Experiment 3: different magnets Weight Threshold angle Magnet Oscillations Threshold angle in degrees Magnet 1Magnet 2 1 st 2630 2 nd 2526 3 rd 2427 4 th 2726 5 th 2628 6 th 2527 7 th 25 8 th 2524 9 th 26 10 th 2724 Average25.626.3 Standard deviation1.01.8 The angles are the same considering the standard deviation.

24 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago24 Team of Brazil Problem 9: Magnet and coin Experiment 4: oscillation analysis Weight Threshold angle Magnet Oscillations

25 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago25 Team of Brazil Problem 9: Magnet and coin Experiment 4: oscillation analysis Weight Threshold angle Magnet Oscillations Resembles an under-damped harmonic oscillation, but the period varies. Coin with larger area Greater damping Evidence of eddy currents

26 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago26 Team of Brazil Problem 9: Magnet and coin Conclusion Magnetic properties are important for the motion itself and are the initial condition for the effect occurrence. Threshold angle is dependent only on the coins dimensions (exp. 2/3). The fall or reverting motion is due to the torque of the magnetic force. Oscillations resembles an under-damped harmonic oscillations but the period varies (exp. 4). Evidences of dissipation by eddy currents (exp. 4).

27 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago27 Team of Brazil Problem 9: Magnet and coin References 1. http://www.bcb.gov.br/?MOEDAFAM2 2. http://www.infomet.com.br/acos-e-ligas-conteudo- ler.php?cod_tema=9&cod_secao=10&cod_assunto=81&cod_conteu do=123 3. http://www.usmint.gov/mint_programs/circulatingCoins/index.cfm ?action=CircPenny 4. http://geophysics.ou.edu/solid_earth/notes/mag_basic/mag_basic. html 5. PRÄSS, Prof. Alberto Ricardo. Oscilações: Movimento Harmônico Simples – MHS. Física.net

28 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago28 Team of Brazil Problem 9: Magnet and coin Thank you!Thank you!

29 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago29 Team of Brazil Problem 9: Magnet and coin Dynamometer calibration The dynamometer was calibrated with PET bottle full of water, with exact 1 kg, measured with a scale of precision of 0.1 g. The maximum mark of the dynamometer is 10N.

30 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago30 Team of Brazil Problem 9: Magnet and coin Real coin’s table Technical characteristics of the coin Value (R$)Diameter (mm)Thickness (mm)Mass (g)Material 0.01171.652.43Steel covered with copper 0.05221.654.10Steel covered with copper 0.10202.234.80Steel covered with bronze 0.25252.257.55Steel covered with bronze 0.50232.856.80Stainless steel 1.00271.957.00 Stainless steel (core) a steel covered with bronze (ring)

31 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago31 Team of Brazil Problem 9: Magnet and coin Table for experiment 2 Threshold angle (in degrees) Coins0.160.080.040.070.10.130.170.06 13328212526252823 23125222425 3225 33025232224 3421 42924202327303123 5282319242629 22 62824182425283321 72923192325333023 82824192325312922 92824202326272921 102923192427263023 Average29.324.32023.525.627.830.522.4 Theory28.523.318.922.424.926.929.021.4 Standard deviation1.641.491.560.850.972.941.961.26 Percentage error3%4%6%5%3% 5% Average Percentage Error4%

32 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago32 Team of Brazil Problem 9: Magnet and coin Experiment 2 for real coins - table Threshold angle (in degrees) CoinsR$ 1.00R$ 0.50R$ 0.25R$ 0.10R$ 0.05 1252625 2262726 24 32325 2923 42227242523 5242826 25 62229242724 7 27252723 8 282725 92227242723 102126252823 Average23.22725.126.523.8 Theory22.626.524.125.722.9 Standard deviation1.551.150.991.350.92 Percentage error3%2%4%3%4% Average Perc. Error3%

33 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago33 Team of Brazil Problem 9: Magnet and coin Experiment 2 for real coins - graphic Percentage error = 3%

34 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago34 Team of Brazil Problem 9: Magnet and coin Threshold angle: Ampère model consideration Ampère Model:

35 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago35 Team of Brazil Problem 9: Magnet and coin Threshold angle: Ampère model consideration Ampère Model:

36 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago36 Team of Brazil Problem 9: Magnet and coin Experiment 2: threshold angle analysis Weight Threshold angle Magnet Oscillations Precision of the protractor: ±0,5°

37 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago37 Team of Brazil Problem 9: Magnet and coin Coin’s material Used coins: steel (iron + carbon). Ferromagnetic: existence condition for the phenomenon. – Iron, cobalt, nickel and gadolinium; – Magnetic domains are oriented in the direction of the external field. Certain coins cannot be tested, like dollar coins (zinc+ copper).

38 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago38 Team of Brazil Problem 9: Magnet and coin Magnetic properties

39 Team of Brazil Problem ## Title Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara GuinsbergBad Saulgau, 20 th – 29 th July, 2012 Reporter: Bárbara Cruvinel Santiago39 Team of Brazil Problem 9: Magnet and coin Contribution of the weight for the torque Correction factor for systematic error. Without disregarding the weight, the relation without c wouldn’t be gotten.