a candle is balanced on a horizontal needle placed phenomenon
TRANSCRIPT
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presented by
Belarusian team
Stearin engine
Nankai University, 2009
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A candle is balanced on a horizontal needle placed through it near its centre of mass. When the candle is lit at both ends, it may start to oscillate. Investigate the phenomenon. Maximize the output mechanical power of the system.
Stearin engine
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Stearin engine
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Stearin engine
α
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0 С
N
X
dh
Puncture
Centre of the masses
Origin point
Theoretical explanation
φ
d
xarctgA
d
xarctg
2
2
Δx/2
l
ml
m
mx
Stearin engine
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Complicated Explanation
Δx > 0 when
drops from
right end
φ
Δx/2
φ
00
00
*2/
*2/
d
tgdxarctgA
d
tgdxarctg
Stearin engine
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Puncture near the centre of the masses
Stearin engine
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Change of the height of centre of the masses
Puncture point
dropT
hmgP
hmgA
max
Stearin engine
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α
Plot combustion speed (ξ) against angleStearin engine
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Combustion speed
The candle material is the main source of energy
Gazes are mostly burning near the point, where temperature is maximal
Wick is in low temperature area, where it is unable to burn
Under the wick – a puddle of liquid paraffin. The gaze goes up.
Oxygen for the combustion goes from bottom upwards
Stearin engine
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LevelingStearin engine
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Leveling oscillogrammStearin engine
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Plot mass of drop against angle
Stearin engine
α
α
α
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Oscillations fadeStearin engine
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Oscillations fade
1
)*(
0
17.0
s
eAA TN
N
Stearin engine
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Computer ModelInput parameters (mass, length,
angle, puncture)
Constants (viscosity, combustion speed)
Combustion speed is thought to berandom with average value equal to
measured
Time is changed for small periods, for each we recount
position of the candle
When the mass on one of the ends reaches critical, it drops
Stearin engine
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Stearin engine
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ComparingStearin engine
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DropsStearin engine
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Period of oscillations
gd
l
mgd
IT
32
Free oscillation period of a candle:
Stearin engine
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ResonanceStearin engine
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Stearin engine
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Stearin engine
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Stearin engine
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Stearin engine
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Plot ξ against angle
α
Stearin engine
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We’ll suggest, that resonance occurs, when Тfree = Тdrop, and will find
conditions, needed for the resonance.To do this, we’ll find Тdrop:
dropdrop TT
id dttAdtm0
0
0
))sin(25.085.2(
Stearin engine
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sml
d
marctg
gd
lm
TA
Tm
l
d
d
d
250
;8
cos)2
(
85.23
;8
)2cos(85.2
0
0
d=0.001 m R=0.003 m
Stearin engine
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Stearin engine
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Plot ξ against diameterStearin engine
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Plot V against diameterStearin engine
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Massive candlesWe will separate a class of massive candles. Massive candles are such ones, which can’t move when one drop falls. It means that the moment of the force is less than moment of frictional forces. Such candle may not oscillate in basic mode, even if punctured at the center of the masses.
Stearin engine
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«Scoops»Stearin engine
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«Scoops»Stearin engine
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22
22
12
)*2
(3/*
sin2cos
)*2
(
*
)(
tgdx
dglN
xdtgd
xdmg
TN
A
T
AP
hhgmА
i
drop
ii
ci
φ
Δx/2
φ
Δx > 0
right
Stearin engine
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Power in ModelStearin engine
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Usage of Power
220
2
~;~~;
APATR
P
Stearin engine
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Usage of PowerStearin engine
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Output Power
2
22
)2
(
~~
R
mx
l
dd
xarctg
AP
Stearin engine
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xd 7.0
Stearin engine
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Power in resonance modeStearin engine
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Stearin engine is not a heat machine
We need to use candles from paraffin of about 1sm wide.
The resonance effect is the basic of getting maximal power.
The optimal puncture is needed for the power to be maximal.
The best way of using Stearin engine is transforming its mechanical energy into electromagnetic.
Stearin engine
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The effect of oscillations was explained
We created a computer model, which lets us imitate effect of the problem
We found the parameters, which the oscillations depend on.
We defined optimal parameters for achieving maximal output mechanical power of the system.
We created a device, transforming the power of oscillation into electromagnetic oscillations.
Stearin engine
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Slobodjanuk A. I. “Advance high school physic”
Slobodjanuk A. I. “Computer model of physical processes for high school students”
Y. A. Smorodinsky “Temprature”
Stearin engine
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Stearin engine
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Стеариновый двигатель
Температура плавления воска находится в пределах
от 61 до 65 градусов.
При повышении температуры воска на один градус
плотность воска уменьшается на 0,0008. При
нормальных условиях плотность чистого воска
колеблется от 0,96 до 0,98
Поверхностное натяжение - парафин 18-28 мН/м
Плотность парафина – 0.9
МFтр = 1*10-4 Н*м
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*04.0*50 eR
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rRlmgrrNM
R
kk
ml
kl
I
kl
lkdllkldlkVM
fr
л
l l
ires
2
22
33
32/
0
2/
0
2
*
*12
8*322*2
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)cos(
cos2/
sin
22
аo
frresо
m
mg
frresmmg
xdmgM
MMMI
mglM
mgdM
MMMMI