problem 09 magnet and coin
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Problem 09 Magnet and coin. reporter: Bárbara Cruvinel Santiago. Problem 09 Magnet and coin. - PowerPoint PPT PresentationTRANSCRIPT
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Team of Brazil
Problem 09Magnet and coin
reporter:
Bárbara Cruvinel Santiago
![Page 2: Problem 09 Magnet and coin](https://reader035.vdocuments.us/reader035/viewer/2022062501/56816359550346895dd418ae/html5/thumbnails/2.jpg)
Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 2
Team of BrazilProblem 9: Magnet and coin
Problem 09Magnet 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.
![Page 3: Problem 09 Magnet and coin](https://reader035.vdocuments.us/reader035/viewer/2022062501/56816359550346895dd418ae/html5/thumbnails/3.jpg)
Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 3
Team of BrazilProblem 9: Magnet and coin
Introduction
• Threshold angle
• Rotational motion
• Oscillations
Experiments
• Experimental data
• Theory validation
Conclusion
• Analysis• Comparison
Contents
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 4
Team of BrazilProblem 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
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 5
Team of BrazilProblem 9: Magnet and coin
Threshold angle
Threshold angle is defined
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 6
Team of BrazilProblem 9: Magnet and coin
Threshold angle
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 7
Team of BrazilProblem 9: Magnet and coin
Threshold angle
The regions taken must be small enough to be considered single points, as “point magnetic charges”.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 8
Team of BrazilProblem 9: Magnet and coin
• In the equilibrium:
Threshold angle
Threshold angle:
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 9
Team of BrazilProblem 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/r1
•The coin is in instable equilibrium.tan³θ1 = r2/r1
•The coin comes back to the original position.tan³θ1 > r2/r1
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 10
Team of BrazilProblem 9: Magnet and coin
Rotational motion
Moment of inertia:
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 11
Team of BrazilProblem 9: Magnet and coin
Rotational motion
• Angular acceleration:
Dependent on the inclination angle and on the magnetic properties.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 12
Team of BrazilProblem 9: Magnet and coin
Rotational motion
Angular velocity approximately constant near the normal line to the magnet.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 13
Team of BrazilProblem 9: Magnet and coin
Oscillations
Angular velocity
approached to
constant
Amplitude that
decreases with time
A < 15°
Under-damped
Harmonic Oscillatio
n
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 14
Team of BrazilProblem 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!
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 15
Team of BrazilProblem 9: Magnet and coin
A
θ1
α
A
θ1 α
1st case: on the poles
2nd case: on the sides
Eddy currents: source of dissipative force
Variation of magnetic flux
Induction of electrical currents
Dissipative force generated
1st case: 2nd 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.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 16
Team of BrazilProblem 9: Magnet and coin
Material
1. Magnets2. Real coins3. Steel coins4. Protractor (±0,5°)5. Acrylic ruler• Iron filings• White paper• Dynamometer (±0.05N)• Support for the dynamometer• Camera
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 17
Team of BrazilProblem 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.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 18
Team of BrazilProblem 9: Magnet and coin
Experiment 1: weight analysis
Force (N)
1st 7.9
2nd 7.7
3rd 7.6
4th 7.8
5th 7.6
Average 7.72
Standard Deviation 0.13
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 19
Team of BrazilProblem 9: Magnet and coin
Experiment 1: weight analysis
Total force (N) 7.72
Weight (N) 0.04
Magnetic force (N) 7.68
The weight represents 0.52% of the magnetic force
The weight can actually be neglected.
![Page 20: Problem 09 Magnet and coin](https://reader035.vdocuments.us/reader035/viewer/2022062501/56816359550346895dd418ae/html5/thumbnails/20.jpg)
Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 20
Team of BrazilProblem 9: Magnet and coin
Experiment 2: threshold angle analysis
• 8 coins are used.• They are inclined 1 by 1 degree.• This is repeated 10 times for each coin.• The points are averages.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 21
Team of BrazilProblem 9: Magnet and coin
Experiment 2: threshold angle analysis
Precision of the protractor: ±0,5°
0.020.04
0.060.08 0.1
0.120.14
0.160.18 0.2
0.2215.017.019.021.023.025.027.029.031.033.0
Ratio r2/r1 X Threshold angle
TheoreticalExperimental
Ratio r2/r1
Thre
shol
d an
gle
(in d
egre
es)
θ = arctan³√(r2/r1)
Average deviation: 4%
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 22
Team of BrazilProblem 9: Magnet and coin
Experiment 3: different magnets
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 23
Team of BrazilProblem 9: Magnet and coin
Experiment 3: different magnetsThreshold angle in degrees
Magnet 1 Magnet 21st 26 302nd 25 263rd 24 274th 27 265th 26 286th 25 277th 25 258th 25 249th 26 26
10th 27 24Average 25.6 26.3
Standard deviation 1.0 1.8
The angles are the same considering the standard deviation.
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 24
Team of BrazilProblem 9: Magnet and coin
Experiment 4: oscillation analysis
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 25
Team of BrazilProblem 9: Magnet and coin
Experiment 4: oscillation analysis
0 0.02 0.04 0.06 0.08 0.1 0.12
-15
-10
-5
0
5
10
15
Angular displacement x Time
r1 = 30 mmr1 = 35 mm
Time (s)
Angu
lar d
ispl
acem
ent (
degr
ees) Resembles an under-damped
harmonic oscillation, but the period varies.
Coin with larger area
Greater damping
Evidence of eddy currents
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 26
Team of BrazilProblem 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).
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 27
Team of BrazilProblem 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_conteudo=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
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Team of BrazilProblem ## Title
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg Bad Saulgau, 20th – 29th July, 2012Reporter: Bárbara Cruvinel Santiago 28
Team of BrazilProblem 9: Magnet and coin
Thank you!