物理與天文學

It is always fascinating to see water droplet’s dancing around on a Japanese teppanyaki hotplate surface. The water usually does not evaporate immediately, but form interesting shapes, dance around and follow by evaporation of gaseous water and disappear. In this experiment, we designed a very simple experimental set-up to observe the little water droplets dancing on a heated hotplate. A homemade stainless plate and a small heater attached to the plate, and a thermal couple was assembled. With this simple setup, we observed the variation of water droplet’s shape as a function of the hotplate temperatures. The temperature of the water droplets, the duration of the water on the hotplate, and the shape number were measured. The shape formation mechanism was proposed. We found when the water droplet was subject to high heat due to the contact of the surface and the hotplate, the abrupt evaporation of the water molecules and violent vibration cause the formation of the various shapes to reach thermal equilibrium; the number of the shapes and the oscillation can be described by Laplace’s equation,Using a high-speed camera, we found the higher the temperature of the water, the more variations of the water droplet shapes can be observed. In addition, at a certain temperature range, the number of the water shapes did not change, suggesting a similar phase transformation behavior on the shape formation. 緣起： 邂逅專題研究、水珠漫舞、剪輯影片，引起我們想更進一步揭開它的神秘面紗。 緣續： 了解熱平台上水滴大小的變化及水珠基本的形狀及變化律動。 緣繫： 進一步研究水珠多變的面貌，並探討水珠的大小、溫度、停滯時間及變化規律相關機制。 緣定： 糾纏在水珠圓舞曲中有如大珠小珠落玉盤的曼妙，其中埋藏了平均圓與能量量子化的律動。

本實驗主要是探究雙圈圈簡單飛機的飛行原理，歸納圈圈結構對飛行距離、升力的影響，以及氣流流經機體時發生的作用。研究結果如下：一、實際發射，歸納影響滑行距離的變因。1. 前後圈直徑比值約為0.8 時滑行距離為最大。2. 前後圈寬度比值越接近1 時，滑行距離越遠，但影響不大。3. 圈圈間隔在21cm 時，滑行距離最大。二、設置風洞，模擬飛機飛行，測量升力1. 圈圈寬度越大，升力越大。2. 升力最大值出現在圈圈仰角25 度左右，風速越快，升力越大。3. 鋁片仰角在20°時升力最大，升力與角度的關係式為 F = 5×10?7θ4 + 4×10?5θ3 ? 0.0083θ2 + 0.2615θ + 0.13744. 風速越快，升力越大，在仰角20°時升力與風速的關係大約為F = 0.4579V2 - 0.9231V +1.4772 。5. 鋁片面寬每增加1cm，升力也增加0.1513gw。前後長每增加1cm，升力即增加0.1263gw。三、設置蒸汽氣流，觀察簡單飛機的氣流場1. 蒸汽流通過圈圈時，會發生附壁現象，而且簡單飛機使氣流往下偏折，飛機得到升力。四、理論演繹︰1. 以康達效應的理論推算出升力，與實際測量得的升力約相等，驗證升力確實由康達理論造成。2. 墊高簡單飛機前圈，使得軸線提高，確實影響了飛行距離，墊高1cm 以內，飛行距離均增加了，以實際的改進證實升力確實是康達效應。This experiment mainly discusses the flying principle of the simple plane which is made up of a straw with two paper circles, one bigger than the other, stuck on both two ends of it. We first launched the simple plane actually and concluded the factors which influenced the sliding distance of the plane, including the distance between two circles, diameter and width of the two circles. Second, we set up a simple wind-tunnel and simulated the flight, in order to measure the strength of lift. Third, we set up the steam air flow and observed the change of the air current in the steam flow while flowing through the plane. The Phenomenon of Wall Enclosing happened and made the flows downward, and the plane gained the lift at the same time. Finally, we deduced that there are two sources of lift and Benoulli's law is not suitable for it. The Coanda Effect can be applied to figure out 54 percent of lift. And the current, blocked by the plane, also offers some lift. In order to prove that the Coanda Effect does effect, we padded the first circle to enlarge the angle of elevation of the axis of the two circles. It really affected the sliding distance of the plane. While the first circle is padded up within 1 cm, the sliding distance of the plane increases. Practical improvement proves that Coanda Effect accounts for the lift.

在日常生活中，靜電無所不在，但是在一般的情況下，我們所能觀察到的靜電現象，卻是少之又少。偶然經過冷氣機，冷氣機的水滴滴答答的滴出，吵雜的水聲，這些水滴是否能被利用?又將應用在哪一方面?引發我們的興趣，偶然間發現的凱氏滴水器，也許能解答我們的疑惑，進而促成此次的科展研究。

依據拉午耳定律，在稀薄溶液的條件下，其熔點下降溫度△T恆與溶質之重量莫耳濃度Cm成正比，亦即△T=KfCm，Kf被定義為莫耳熔點下降常數。又前人實驗出，純水熔點亦會因侷限在孔洞中而下降，稱超冷水。探討論文後發現熔點下降量與孔徑有之關係，我們便思考水溶液在空間侷限下是否也會有類似現象？於是我們將不同濃度的葡萄糖水溶液置於孔洞中測量其熔點。實驗發現葡萄糖水溶液在固定的孔洞中，熔點亦隨溶質之莫耳濃度上升而下降，符合拉午耳定律。改變孔徑的大小，進一步發現莫耳熔點下降常數k會隨著孔徑縮小而增大。顯然水溶液的熔點可同時受到空間侷限與溶質的莫耳濃度所影響，因此加入葡萄糖後，水溶液除遵循拉午耳定律的影響外，又使其熔點進一步下降。如何將拉午耳定律從單純的溶質的莫耳濃度函數，推導含蓋侷限空間R因子的通一公式，亦即更廣義的拉午耳定律:△T=k(R)×Cm是本計劃的主要目標。

如果將各種形狀不一的中空框架放入肥皂水中，框架上會結構出不同形式的\r 肥皂膜。本研究中包含了許多不同的實驗以探討各種常見錐體、柱體的肥皂膜形\r 狀，其邊數對肥皂膜面數的影響，及肥皂膜面積和模型邊長的比例關係。\r 第一部分的實驗中，我們探討不同的溶液、不同濃度對形成肥皂膜面數、模\r 式的影響；第二部分的實驗討論了n 角錐所形成的肥皂膜模式，並且得到其形成\r 的肥皂膜面數與角錐邊數n 存在著「肥皂膜面數= 3n - 3 」的關係；第三部分的實\r 驗討論了n 角柱所形成肥皂膜的模式，得到肥皂膜面數與柱體邊數n 存在著「肥\r 皂膜面數= 3n +1」的關係，其中三角柱為例外，一共只形成九面肥皂膜；第四部\r 分則討論了正八面體等其他形狀的模式；第五、第六部分的實驗則分析了肥皂膜\r 的大小與框架比例間的關係。

很多人都有泡奶粉的習慣，卻偶爾會發現在舀完奶粉後，會有少許奶粉殘留於桌面上,仔細的觀察後發現~舀奶粉時塑膠匙上有叢狀奶粉聚集，且部分奶粉會噴射出去,若奶粉是一般的電偶，理應在排列好後維持穩定的位置，相反的，若奶粉有帶上與塑膠匙面同性的電荷，它應該不會沾附於匙面，而是被斥離。但我們的觀測結果卻同時包含以上兩種現象，我們對此感到好奇而展開研究。

The starting point of this experiment is to study the structure of soap-film. By changing the height of the triangular prisms, cuboids and pentagonal prisms, I observed the patterns set by the soap within the frameworks. It is surprised that when the proportion of prism is in a specific range, the phase in the middle of the structure will overturn 90 degree and then transmitted into another kind of balance pattern. I named this process “phase transition”. According to the experiment ,we can conclude the change of film patterns within variable prisms are all applied to this regular cycle:： We know the soap films are forever attempting to minimize their energy. It stands to reason that surface tension tend to set up the film in its minimal surface. From the point of Mathematic, each structure should have only one single balance pattern, which is set up on the base of Fermat point and this pattern should stand to the minimize of it’s energy. However, we discovered that in some specific cases, one structure can allowed two kinds of balance films-patterns to exist. In these cases, any small vibration can cause the happening of “phase transition”. To sum up, I presume some structures have two different types of balance film-patterns: one of which stands to the local minimum (in this condition the pattern’s surface area isn’t the smallest); the other stands to the absolute minimum (in this condition the pattern’s surface area is the smallest). There is an energy valley separate local minimum from absolute minimum. The second pattern (local minimum) will appear when the structure is blocked from attaining its absolute minimum, but surface intention is not powerful enough to support the film jumping over the energy valley. In this condition, if we works on the structure (such as blowing), which would provide the film of energy to cross the valley, and then phase transition take place. Vice versa, we can also force the film to jump from absolute minimum to local minimum and phase transition will occur as well. In a word, phase transition can happen in each two way, which connects the two types of balance pattern. This report lays stress to find out the condition of phase transition. We also analyze the structure of soap-film by its included angles and surface area in hope to go deep into the science of soap-film. 我們實驗的出發點在於研究泡膜的立體結構。藉由改變正立方柱的高，觀察其平衡薄膜形式，意外的發現當正立方柱的邊長比在某個範圍時，泡膜結構中央會瞬間90 度翻轉，形成另一種平衡型式，我們將這個過程命名為面轉變(Phase Transition)。為了進一步了解面轉變發生的相關因素，我們設計了一連串的實驗，針對正三角柱、正四角柱、正五角柱、正六角柱發生面轉變的時機和條件分析討論。此外，我們還分析了泡膜結構中膜與膜夾角的特性、最小表面積和表面能之間的相關性，對於泡膜的立體結構做了一系列深入的探討。

流體旋轉時，外圍及底部流體，因槽壁及槽底摩擦力的影響，流速較慢，相對的壓力也較大，導致外圍的水流會轉入中心。發現本實驗的渦流為強迫與自由漩渦組成。實驗中，探討f(轉動器的頻率)、H(總水深)、y(?入深度)、R(轉盤半徑)四者與角形數間的關係。若y、R 愈大、H 越小，隨著f 的增大，可觀察到的形狀邊數越多；反之，若y、R 愈小、H 越大，則f 愈高，所形成的圖形半徑愈大，易超過轉盤，不易觀察。依白努利方程式，外層水流的流速較慢，而內層水流的流速較快，故外層壓力大而內層壓力小，水會由外往內流，而此渦動流於轉動液面產生的剪力，可能為產生N 邊形漩渦的主要原因之一。流體旋轉系統中，因轉動而產生流體離心力與內外層壓力差交互作用下，於某特定相關的因素條件下，形成特定角形數漩渦，是本實驗的重要發現。When fluids are in rotation, fictitious force given by the container brings about the relative decrease of speed of the bottom and outer layer of water, which causes its pressure to increase, and water to spin inward, resulting in a vortex motion with N-corner polygons formed at the surface of the rotating plate. During this experiment, we discover that the vortices consisted of free and forced vortex and the polygons vary as control parameters f(rotation frequency), H(height of fluid), y(depth of the plate), and R(radius of the plate) change. The larger y and R are,the smaller H is, the more corners show up as f increases. On the contrary, the smaller y and R are,the larger H is, few polygons are identified since the rotating radius of polygons are larger than the plate. According to Bernoulli’s principle, smaller velocity of the outer-layer water causes water pressure to increase and water to spin inward. During this process, shear force is developed at the surface of the rotating fluid, which we believe is the main cause of N-corner polygons. In a rotating system, the interaction of centrifugal force and differential pressure causing a certain Ncorner polygon to be formed under different controlled parameters is our main discovery.

本研究探討運用磁場來達到非接觸煞車的功能，本實驗採用兩種方式來探討磁煞車力，分別為馬達有外加電流及沒有外加電流的情況。首先本實驗提供一穩定的電源使鋁盤轉動，觀察加上磁場及把電源切掉後鋁盤轉速的變化。實驗發現，當馬達沒有外加電流時，磁煞車力與轉速及磁場平方皆成正比；馬達有外加電流時，電流差會與轉速平方差成正比。探討磁煞車力與厚度及介質的關係，實驗結果發現，渦電流常數與厚度成正相關，且當兩片鋁片中夾有介質時，渦電流常數較小。 This experiment is based on the magnetic brake’s practical uses and braking forces. We want to calculate the braking force, and also examine the factors that cause the braking force to differ.We attached a metal disk to a motor to make the disk rotate, then we control the distance between the magnet and the metal disk, therefore measuring the relativity of the distance and the rotational speed. We discovered that when the metal disk received a large quantity of the magnetic field (close distance), the breaking force and the rotational speed increased. On the other hand, when the metal disk received a small amount of the magnetic field (far distance), the breaking force and the rotational speed decreased. The magnetic braking force will convert into kinetic energy, thus, by using this connection and also by increasing the electric current to measure the resistance, we calculated the magnitude of the magnetic braking force. Hence we perceived an inverse ratio between distance and the braking force, that is to say, the closer the distance, the stronger the magnetic braking force; the further the distance, the weaker the magnetic braking force.