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Solution of the problem "Stearin engine"

Stearin engine. Solution of the problem "Stearin engine". presented by Belarusian team. Nankai University, 200 9. Stearin engine. Formulation of the problem.

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Solution of the problem "Stearin engine"

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  1. Stearin engine Solution of the problem "Stearin engine" presented by Belarusianteam Nankai University, 2009

  2. Stearin engine Formulation of the problem 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.

  3. Stearin engine Demonstration of the effect

  4. Stearin engine Oscillogramm α

  5. Stearin engine Theoretical explanation Puncture N Centre of the masses d h φ Origin point 0 С Δx/2 X

  6. Stearin engine Complicated Explanation Δx > 0 when drops from right end φ h d φ Δx/2

  7. Stearin engine Puncture near the centre of the masses

  8. Stearin engine Maximal Power Change of the height of centre of the masses Puncture point

  9. Stearin engine Plot combustion speed (ξ) against angle α

  10. Stearin engine Combustion speed Gazes are mostly burningnear the point, where temperature is maximal Wick is in low temperature area, where it is unable to burn Under the wick– a puddle ofliquid paraffin. The gaze goes up. Oxygen for the combustion goes from bottom upwards The candle material is the main source of energy

  11. Stearin engine Leveling

  12. Stearin engine Leveling oscillogramm

  13. Stearin engine Plot mass of drop against angle α α α

  14. Stearin engine Oscillations fade

  15. Stearin engine Oscillations fade

  16. Stearin engine Computer Model Input parameters (mass, length, angle, puncture) When the mass on one of the ends reaches critical, it drops Constants (viscosity, combustion speed) Time is changed for small periods, for each we recount position of the candle Combustion speed is thought to berandom with average valueequal to measured

  17. Stearin engine Slim candle

  18. Stearin engine Comparing

  19. Stearin engine Drops

  20. Stearin engine Period of oscillations Free oscillation period of a candle:

  21. Stearin engine Resonance

  22. Stearin engine Experiment: Resonance

  23. Stearin engine Resonance

  24. Stearin engine Resonance in model

  25. Stearin engine Resonance in model

  26. Stearin engine Plot ξ against angle α

  27. Stearin engine Resonance conditions We’ll suggest, thatresonance occurs, when Тfree= Тdrop,and will find conditions, neededfor the resonance. To do this, we’ll find Тdrop:

  28. Stearin engine Resonance conditions d=0.001 mR=0.003 m

  29. Stearin engine Resonance on multipleperiods

  30. Stearin engine Plot ξ against diameter

  31. Stearin engine Plot V against diameter

  32. Stearin engine Massive candles We 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 offrictional forces. Such candle may not oscillate in basic mode, even if punctured at the center of the masses.

  33. Stearin engine «Scoops»

  34. Stearin engine «Scoops»

  35. Stearin engine Counting output power Δx > 0 right φ h d φ Δx/2

  36. Stearin engine Power in Model

  37. Stearin engine Usage of Power

  38. Stearin engine Usage of Power

  39. Stearin engine Output Power

  40. Stearin engine Optimal puncture

  41. Stearin engine Power in resonance mode

  42. Stearin engine Conclusions: • 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.

  43. Stearin engine Results: • 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.

  44. Stearin engine Literature: • Slobodjanuk A. I. “Advance high school physic” • Slobodjanuk A. I. “Computer model of physical processes for high school students” • Y. A. Smorodinsky “Temprature”

  45. Stearin engine Thanks for your attention!

  46. Стеариновый двигатель Some theoretical data 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

  47. How fast the candle burns

  48. Viscosity

  49. The equation of candle movement

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