本研究從大自然中之「蓮花效應」引發學習興趣與研究動機，在蒐集相關資訊與文獻後，發現疏水功能不只是防水，還關係著日常生活品質之許多材料特性，包括防水、撥水、防潮、防銹、防蝕、抗菌防污、自清潔…等。而影響固體表面疏水性之兩大特性，包括物理之表面粗糙度與化學之超低表面能，本研究針對物理之表面粗糙度與疏水性之關係做探討，以相同之化學特性來比較不同號數之工業用砂紙之疏水行為，並就廣泛被引用之兩種模擬表面粗糙度與疏水性關係之模式：Wenzel and Cassie model，比較現有文獻對兩種模式之特性，選擇Cassie model 來進一步實驗驗證，以量測之平均接觸角 Θ 推算Cassie model 之表面粗糙係數Φ 值，並簡化不同砂紙顆粒模型為相同粒徑之球狀，以簡化之方程式來求得水珠與砂紙顆粒之實際接觸面積與球心夾角 θ，以提供高中學校能在經費與設備之限制下，仍能有效應用與印證Cassie model，獲得砂紙顆粒直徑與球心夾角 θ 自然對數值之關係。並就疏水性之生活應用，建立接觸角與 Φ 之關係曲線，驗證實驗之方程式，與延續過去之科展成果，以實驗成果提出可行性應用之建議。The interest and motivation of the present work was introduced from “lotus effect” in nature. After we collected related literature and information, we found that the function of the so-called “superhydrophobicity” behaves not only water repellency, but also a variety of real-life applications, including anti-fog, anti-corrosion, anti-bacteria, anti-fouling, self-cleaning, and so on. Pervious studies have pointed out that two criteria affecting the performance of hydrophobic surfaces are physical (roughness) and chemistry (surface tension) properties. This study focused on influence of physically surface roughness on hydrohyphobicity. Based on an identical surface chemistry, we employed different types of industrial sandpapers to mimic the lotus leaf, and investigated the relationship between roughness and hydrophobicity by using two famous models: Wenzel and Cassie models. Comparing with their basic assumptions to our study, we applied Cassie model to confirm our experimental results, in where one Cassie parameter (?) was proposed to simplify the Cassie equation. This superhydrophobic behavior can be well predicted by the Cassie model. This study continues previous achievement and offers some practical utilization according to our\r experimental results.

本文研究風洞中之風帆在不同條件下，受風吹拂所產生之升力與阻力關係，並探討及成功 的以數學模型解釋其原因，此研究結果可應用於帆船帆面之設計。其主要探討之變因為以下 之五種： (一) 風速大小對帆船帆面之受力關係：當帆面與風向垂直時，在低風速時，實際測值較接近 風速的一次方的函數關係。高風速時，實際測值接近為風速的二次方的函數關係。 (二) 帆面積大小與受風推進力之關係：當帆面與風向垂直時，在風速固定風速下實驗，得到 面積與風對帆推力成正比。 (三) 順風航行時，帆面之攻角(θ)與受風推進力之關係：航行方向的力與sin 2θ 成正比關係。 (四) 側風航行時，帆面之攻角(θ)與受風推進力之關係：帆面在攻角大於 45°時，航行方向的力與sin θcosθ 有相當程度的吻合，而在攻角0°~45°之間則與飛機攻 角升力資料相接近。 (五) 初步探討雙桅帆與單桅帆面受風推進力之不同：發現其在側風時能有效的減少失速的現 象，在帆面高攻角時，能減少失速現象，依然可以持續穩定的航行，我們也可推想出飛機 的機翼前段的縫翼功能也是如此。 This article is derived from our research of relation between lifting power and its resistant power produced via wind-blow in a wind tunnel under different terms and condition, also to discuss and to explain their causes successfully via mathematics models, thus, the result of this study may be applied in designing of sail-surfaces of sails boats. Its major discussion can be included into the below 5 kinds: - Relation of (1) Relation of sizes of wind-speed against reacceptance of aerodynamic forces over sail-surface: When sail-surface and wind direction becomes horizontal, under low coin-speed, practical measured-value is rather close to wind-speed's linear function relation. When in nigh wind-speed, the practical measured-value is rather close to wind-speed's quadratic function relation. (2) Relation of size of sail-surface and pushing power of wind: When sail-surface and wind direction becomes horizontal, an experiment was made under fixed wind speed, the result obtained is sail-surface size and pushing wind power toward sail is in direct proportion. (3) When it is in “round-the-clock wise” navigation the angle of attack (θ) of sail-surface and the relation with wind's pushing power: Strength of navigation direction and sin2θconforming direct proportion. (4) When it is in side-wind navigation, the angle of attack (θ) and pushing power by wind relation; When the sail surface is in the angle of attack (θ) greater than 45o, the navigation direction power and sinθcosθhas certain extent of conformity, and between angle of attack e 0o-45o, happens to be very appropriate with aircraft's angle of attack and lifting power data. Fundamental discussion of Double Masts Sail boats and Single Mast Sail boats comparing differences of wind-aided pushing power: It was found that stall phenomena could be decreased effectively, when it is side-winded, especially, when the sail-surface is at high angle of attack, it could decrease Stall phenomena, and could maintain stable navigation. We can also assume that the front section of aircraft aide-wing’s function exactly the same.

In this project, we mainly employ the self-made “positioning system for celestial objects” (PSFCO) to investigate the relations among Sun, Moon, and Earth. Based on the observational data, we then construct a three-dimensional (3D) model to further understand the hidden mystery. We first use the PSFCO, which was developed through four generations (see figure 1), to measure the change for a whole year in the North Polar Distance (NPD) of Sun and Moon individually. From the data analysis, we find that: 1. This change in NPD is very close to a sinusoidal function. 2. The date when the NPD of Moon is the largest in a month shifts earlier by 2.26 days every month on average. 3. The angle between the equatorial axis (EA) and the lunar orbital plane (LOP) is about 63.5 degrees, while the angle between the EA and the ecliptic plane (EP) is about 66.5 degrees. 4. The angle between the LOP and the EP is about 5 degrees. This is exactly why the solar eclipse and the lunar eclipse do not happen every month. 5. Time for a celestial object to be above the horizon = 1080 minutes – 4 (minute/degree) x NPD of the object. We geographically prove this empirical formula. With this formula and the PSFCO, we can accurately predict the times when an object rises and sets. We finally make a 3D model for Sun, Moon, and Earth. In this process, we confronted and then solved several difficult questions in mathematics and astronomy. This research dramatically enhances our understanding in our local planetary system. 主要利用自製的“天體定位儀”來詳細探討月亮、太陽及地球之間的位置及軌道關 係，並藉由三度空間模型的製作來進一步了解其中的奧妙。 首先利用天體定位儀 (共研發出四代，見圖1) 來量測月亮及太陽各自與北極的夾角 在1 年內的變化，經數據分析發現： 一、這個變化很像sin 函數。 二、月亮與北極的夾角發生極大值的農曆日數，每月平均提早約2.26 日。 三、白道面與赤道軸的夾角約為63.5 度，黃道面與赤道軸的夾角約為66.5 度。 四、白道面與黃道面之間的夾角約為5 度。這正是日蝕及月蝕不常發生的主要原因。 五、天體在地平線上的時間(分) = 1080 分－４(分/度) x 天體與北極夾角(度)。我們用幾 何定理證明了這個觀測到的關係式，且配合天體定位儀可準確預測任何可見天體 升上及落下地平線的時間。 最後製作月亮、太陽及地球的3D 軌道模型。過程中遭遇並解決了各種數學及天文 難題，使我們對這個行星系統有了更深一層的認識。

The “Insectivorous Plants”﹐ the first historical publication by Charles Darwin﹐contained the detailed observations and meticulous descriptions of various carnivorous plants and had become the most important reference for the study of carnivorous plants﹒ But the prey mechanism and digestive function of the bladder traps of the Utricularia were not well described﹒ The present study has a great success in these fields which include the volume change of bladder traps before and after firing﹐the spontaneous pressure relief of the bladder traps even without being triggered by prey, and the quadriceps visible absorption process﹒ The last two findings are not yet publicated. This laboratory experiment is carried out with Utricularia Gibba﹐a native species of Utricularia in Taiwan﹒ Through static and dynamic observation﹐we find that bladder traps suck in water by 12-25% of body volume change, and the bladder traps release internal pressure spontaneously under long period of waiting, despite not being triggered﹒ We can also easily demonstrate the absorption process of quadriceps by manually triggering the bladder traps to suck food color solutions. All the events above can be clearly seen under microscopy﹒達爾文是最先對食蟲植物作深入且完整研究的科學家，至今他的著作仍是研究食蟲植物的重要資料，但在其內容中對狸藻捕蟲囊捕蟲行為及消化功能的研究觀察並不完整。本實驗使用簡單的方法，在這方面有突破性的進展，包括捕蟲囊捕食前後的體積變化，自發性舒張及囊內腺毛對於食用色素的消化吸收，後兩項發現及實驗均未曾出現在文獻資料中。 本實驗以台灣本土水生食蟲植物絲葉狸藻(Utricularia gibba)為研究對象，由靜態及動態觀察，顯示捕蟲囊捕食前後體積變化為12~25%，且即使在沒有捕到水中生物的情況下，也會有自發性舒張以解除囊內壓力的現象。捕蟲囊內四爪腺毛消化吸收功能的整個過程，可藉由食用色素加以呈現，並清楚的在顯微鏡下觀察到這些現象。

人體表面積在醫學的應用相當重要：燒燙傷的評估是以全身面積被灼傷的百分比 表示；營養狀況的評估，新陳代謝率也以單位表面積表示之；體液或藥物之需求量也 是以體表面積來決定劑量；然而人體是一不規則物體，應用一般幾何面積計算公式有 其困難處，如何快速的計算人體表面積，以作為醫療的指引，有其必要性。而青少年 正處於快速發育期，各部位的成長是否會影響表面積的計算，由於目前鮮少對青少年 之專文報告，尤其缺乏台灣地區之調查。為了探索這些問題，乃進行調查與研究。 本研究以台灣地區國民中小學10 至15 歲青少年為對象，探討在此發育期間體格 之變化及可能之影響相關因子，並建立體表面積之快速計算公式。本研究隨機取樣以 1209 人形成樣本，其中男生623 人，女生586 人，利用尺秤，取得身體各部位的資料， 並以問卷調查運動、飲食與睡眠等問題，以探討影響此成長期發育之因子。結果發現： 台灣青少年體表面積快速計算公式為(身高x 體重 ÷37)0.5；其體表面積九分法計算方 式也有別於一般歐美成年人的計算法；及此年齡層的身高與體重受運動的頻率、運動 持久性、飲食習慣多寡的影響，而與運動種類及主食種類相關性不大，這項研究的發 現，將有助於醫護人員對青少年問題的處理。Body Surface Area (BSA) has been used in many clinical conditions to calculate the percentage of burned area, to evaluate the nutrition status - the unit of the metabolic rate, to determine the need of fluid supply or the medicine dosage requirement. So precise measurement of BSA is very important, however the human body is an irregular shape, a laborious task using the geometrical method. To establish a simple quick formula to guide the therapeutic treatment is a necessity. Also the rapid growth phase during the adolescent stage might change the BSA in some way. BSA has not been established for the teenagers in Taiwan. To investigate this issue, a total of 1209 healthy elementary and junior high school boys (623) and girls (586) aged 10 to 15 in Taiwan were recruited by random selection. By use of anthropometrical measurements and a health questionnaire to the subject simultaneously, the data was analyzed statistically. The results revealed that a quick adequate formula derived from the body height and weight for Taiwan teenagers was determined by the formula, BSA = [ Height (meter ) x Weight (Kg) ÷37 ] 0.5, the Taiwan teenage “rule of the nine” of BSA is different from that of the adult, and that the frequency and the duration of exercise, the diet habit, and the duration of sleep significantly influence both body growth and weight. These findings may provide significant references for the physicians to treat the clinical conditions of teenagers in Taiwan.

NO.58-06 2019 DEC | 科學研習期刊目錄 本期專題 數學素養 益智遊戲易位棋中的數學思維 | 李源順 「理財素養」生活中的數學素養 | 溫世展 如何從小培養數學創造力 | 溫世展 統計與資料科學中的數學 | 王啟樺 買房裡的數—貸款的數學 | 鄧家駿 教學現場 有數學感的教與學—以周長和面積為例 | 李源順 數學奠基活動「矩形拼板」在國中數學課堂的實施與回饋 | 鄧家駿 有數學感的教與學：以雞兔同籠為例 | 李源順 隱含微積分概念的國小「圓面積」教學 | 陳玉珊 高中數學科展經驗談 —數學探究的樂趣 | 張宮明 科學新知 我們對「颱風假」應有的認知和省思 | 陳正改 臺灣地震測報的發展 | 蕭乃祺 特約專欄 全等 | 游森棚 日本月刊科學繪本初探：走讀福音館『かがくのとも』50週年紀念展 | 劉淑雯 黃明宏 STEAM課程的發展架構與教學活動設計 | 唐偉成 科普活動報導 一個『再發現』的探究歷程：2019自然科學探究式網路競賽得獎作品科學探究經驗分享 | 黃嘉郁 科學家的秘密基地 | 高瑩珊 科教館GO好玩 遊戲化核能知識卡牌桌遊推廣 | 顏慈瑤 李柏翰 蘇萬生 總召集人的話 中小學的數學教育被高度期望培養學生在日常生活中進行數字和空間思考的能力與信心，使能明辨和解決相關問題。本期特別以「數學素養」為專題。 「本期專題」單元共有五篇文章，〈益智遊戲易位棋中的數學思維〉一文介紹如何利用易位棋教學培養學生的數學解題思維。〈「理財素養」生活中的數學素養〉一文介紹數學與理財素養內涵以及理財情境下的數學素養。〈如何從小培養數學創造力〉一文介紹數學創造力的相關理論與研究、教材與教學策略以及教學實踐。〈統計與資料科學中的數學〉一文從數學角度介紹統計與資料科學背後追隨的人工智慧之夢。〈買房裡的數—貸款的數學〉一文討論向銀行「借錢」買房子後，如何「還錢」最划算。 「教學現場」單元刊登五篇文章，〈有數學感的教與學—以周長和面積為例〉一文利用小四學生學習長方形和正方形的周長與面積單元，解說該如何讓學生學得完整的周長與面積概念。〈數學奠基活動「矩形拼板」在國中數學課堂的實施與回饋〉一文介紹數學奠基活動國中組中的「矩形拼板」桌遊活動。〈有數學感的教與學：以雞兔同籠為例〉一文利用類似雞兔同籠問題，說明嘗試錯誤、有規律嘗試錯誤、邏輯推理、代數解法之間的關聯及重要性。〈隱含微積分概念的國小「圓面積」教學〉一文解說如何藉由小五「多邊形」的學習，引導小六連結「逼近」概念以及先備學習經驗，讓圓面積的學習更有脈絡性。〈高中數學科展經驗談—數學探究的樂趣〉一文分享作者多年來帶領高中生從事專題研究，進而形成科展作品的過程。 「科學新知」單元刊登兩篇文章。〈我們對「颱風假」應有的認知和省思〉一文帶領讀者面對「颱風假」課題，省思應如何看待及抱持何種態度才不致失焦。〈臺灣地震測報的發展〉一文則介紹臺灣在集集地震後在地震測報工作的進展。 「特約專欄」單元刊登三篇文章，〈森棚教官的數學題〉一文拋出有關兩個三角形全等條件的問題。〈日本月刊科學繪本初探：走讀福音館《かがくのとも》50週年紀念展〉一文分享走讀日本福音館《かがくのとも》(科學之友)月刊50周年展後對月刊科學繪本的介紹與推薦。〈STEAM課程的發展架構與教學活動設計〉一文則提出對PBL-STEAM課程發展與教學活動設計的見解。 「科普活動報導」刊登兩篇報導：〈一個「再發現」的探究歷程：2019自然科學探究式網路競賽得獎作品科學探究經驗分享〉透過2019年指導學生參與自然科學探究式網路競賽得獎作品實例，說明進行探究活動的歷程；〈科學家的秘密基地—科學好好玩，一起動手做〉報導國研院善用其強項和方式讓孩童愛上科學的展覽活動。 本期「科教館GO好玩」單元刊登〈遊戲化核能知識卡牌桌遊推廣〉一文，則介紹如何透過有趣的卡牌桌遊，讓民眾甚至年齡更小的學童曉得核災的知識。 總召編輯委員 - 李隆盛 關於本刊 出版單位：國立臺灣科學教育館 發行人：陳雪玉 總召集人：李隆盛 編輯委員： 物理科吳仲卿/陳耀榮/李柏翰/盧玉玲 | 化學科古建國/許良榮/王伯昌/林如章/周金城 | 生物科王美芬/蕭世輝/陳建志/郭淑妙 | 地球科學許民陽/王郁軒/李文禮 科技科張玉山/汪殿杰/林育沖/趙珩宇 | 數學科李源順/鄧家駿/溫世展/張宮明 | 跨領域學科李名揚/連信仲 | 特約專欄 游森棚/黃琴扉/劉淑雯 策劃：曾聰邦 主編：錢康偉 本月專題特約主編：李源順 編輯：吳郡怡 網頁設計編輯：蔡婉懿/曾怡/施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

20 世紀初，石油的量產造就了人類文明前所未有的繁榮，然而由於運送、廢棄處理等因素，使得油類污染成為環境保護的重大議題。本實驗中，我們的研究主題為在受油污染的土壤中純化並鑑定出可分解油類之土壤菌和綠膿桿菌對可分解油類之土壤菌與這群土壤菌彼此之間的交互關係，藉此了解它們間的互動對環境生物復育的影響。我們由受油類污染的行道樹土壤中分離了約12 種的土壤菌，其中我們得到3 種對油類分解效果效果極佳的非綠膿桿菌(暫時命名為P7A、P7C、P7D)。經過菌種鑑定發現P7A、P7C、P7D 均為格蘭氏陽性菌。為了解這群可分解油類之土壤菌間的互動關係，我們針對分解效果最佳的P7A、P7C、P7D 作為研究對象，將菌落接種至含有鹽類與機油的液體培養基中震盪培養，並每隔一定時間測量其O.D 值。結果發現P7A、P7C、P7D 間的互動會導致其在以機油為單一碳源的培養液中之生長速度的改變，因此在行環境生物復育時須注意土壤菌間交互關係對其分解污染物速率的影響。此外我們由受油類污染的行道樹土壤中亦分離出了一些綠膿桿菌，因文獻指出，綠膿桿菌所分泌的綠膿素降低受油污染土壤中土壤微生物相的多樣性；因此，我們將由行道樹土壤中純化出的綠膿桿菌T3 與可分解油類P7A、P7C、P7D 進行交互作用觀察，發現T3 會侵占P7A、P7C、P7D 的既有菌落區，而平板培養基亦可清楚看出和T3 交接的P7A、P7C、P7D 菌落區寬度有明顯降低，因此我們認為T3 可抑制或殺死P7A、P7C、P7D，可得知綠膿桿菌會對可分解油類之土壤菌產生抑制或競爭關係。In early 20th century, the exploitation of petroleum transformed human civilization into a tremendously prosper stage. Because of the transportation and disposition of petroleum, the oil pollution has become a important issue in environmental protection. Besides, Chloropseudomonas spp. which can survive in many different environments and decompose lots of organic compounds. In this study, we want to find the bacteria which can utilize oil from machine oil-contaminated soil, investigating the interaction relations between Chloropseudomonas spp. and these oil-degrading soil bacteria. First, we classified these oil-degrading bacteria by the book called“Bergey’s Manual of Systematic Bacteriology.”We find three species of oil-degrading bacteria (P7A、 P7C、P7D) which are all grams-positive bacillus, possibly belonged to Aureobactreium、Curtobacterium、Cellulomonas、Oerskovia、Brochothrix、 Caryophanon. Second, in the study of the relationship between Chloropseudomonas spp. and the oil degrading soil bacteria, we found that Chloropseudomonas spp can considerably inhabit the growth of oil-degrading bacteria. Besides, there are also a great variety of interaction between three species of the oil-degrading bacteria. According to the result , the interaction might considerably affect the efficiency of oil bioremediation. Due to our analysis, we suggest that it is necessary to pay more attention to the interaction between bacteria when undertaking oil bioremediation.

我們使用陽極氧化鋁(AAO)模板來製備銅及其氧化物的奈米線。以硫酸銅和乳酸配製電鍍液，利用氫氧化鈉水溶液(NaOH)將其pH 值調整到12，供以不同電壓，可電鍍出銅及氧化亞銅奈米線。在較高電壓下可製備出銅奈米線，而在較低電壓下可製成氧化亞銅奈米線，若使用中間電壓則能製得銅及氧化亞銅的混合態。利用x 光繞射分析儀(XRD)來分析其結晶構造、使用場發射掃描式電子顯微鏡(SEM)以得知其表面形貌。電鍍出的奈米線直徑約60 nm。奈米線的長度可藉由調整電鍍時間或電壓來控制。在製作IC 內部導線方面，銅奈米線深具開發潛能；在提升太陽能電池的轉換效率、製作可見光光觸媒方面，氧化亞銅奈米線極具前瞻性。We electrodeposited copper and cuprous oxide (Cu2O) nanowires with anodic aluminum oxide (AAO) templates. Both Cu and Cu2O nanowires could be prepared with an alkaline cupric lactate solution, which was adjusted to pH 12 using a 6 M NaOH, when supplied with different electrolytic voltages. Cu nanowires could be prepared when a higher voltage was supplied, and Cu2O nanowires could be prepared with a lower voltage. A mixture of Cu and Cu2O nanowires could be prepared with a supply of a voltage in between. X-ray diffraction (XRD) is used to determine the phase composition, and scanning electron microscopy (SEM) is employed to characterize the morphology of the nanowires. The length of nanowires can be controlled by adjusting the time spent on electrodeposition and the voltage supplied. The resultant diameter of the nanowires was about 60 nm. Cu nanowires are promising materials for making the conductive wires in IC, and Cu2O nanowires hold great promise for improving the conversion efficiency of solar cells and manufacturing visible-light photocatalyst.

中文摘要：\r 本文利用溶膠－凝膠法（Sol－Gel method）製備二氧化鈦奈米粒子（Anatase\r 晶相），測定廷得耳效應判斷其是否為奈米粒子，並以二氧化鈦奈米粒子加入水\r 中，以紫外光照射測試其光催化分解水反應的活性，並測試其分解南崁溪河川廢\r 水的能力。結果顯示自製二氧化鈦奈米粒子具有明顯的廷得耳效應，光催化分解\r 水反應因紫外光源功率過低未能呈現，有待改進；分解河川廢水的能力仍在進行\r 中。\r Abstract\r This experiment produces Titanium dioxide nano-particles (Anatase crystal\r phase)by using Sol-Gel method. We prove the particles as nano-order by the Tyndall\r effect And adds Titanium Dioxide into water, illuminate it with special wavelength\r ultraviolet radiation. The activity of its light catalysis reaction to water was tested.\r The capability of the treatment of wastewater in Nancan River by nano-titanium\r particles was also studied. The results show that the powder prepared by this\r experiment has apparently Tyndall effect，the photo-catalysis reaction of water is\r failed due to the weak power of UV light sources. The test of wastewater treatment is\r still processed.

本研究主要在探討骨牌脈波在傳遞時的速度變化，並比較在不同的骨牌和不同的排列方式下骨牌的終端速度有何種差異；同時也研究骨牌在鏈鎖反應下能量的放大現象。觀察後發現單列骨牌脈波在傳遞一段距離後，由於空氣阻力的影響，脈波將會達到一終端速度，此終端速度與骨牌高度成反比，而與骨牌質量平方成正比。骨牌的脈波傳遞在鏈鎖反應下仍有一終端速度，但大於單列之骨牌脈波速，且鏈鎖反應具有放大推力之功能。由我們的研究可預測一列物體傾倒時所花費時間和所能達到之終端速度，而鏈鎖反應可比擬為一雷射模型能量集中和釋放的機制，相信可利用骨牌儲存能量的機制應用於需迅速釋能的機械中 This research is mainly discussing the changing of velocity of a domino pulse, and comparing the terminal velocity of various kinds of dominos and arresting modules. Also we focus on the energy-enlarging fact of chain-reaction of domino series. We found that after running a distance, the pulse of a single-series domino will finally reach a terminal velocity by the friction force of air. The terminal velocity will inversely proportion to the height of a single domino, and will proportion to the square of mass of a single domino. During a chain-reaction, the pulse still has a terminal velocity, but it is higher than the terminal velocity of a single series domino .The chain-reaction has an ability to enlarge the original force, too. By the research, we are able to predict the time interval and the terminal velocity while a series of objects are falling. On the other hand, the chain reaction is similar with mechanism of energy concentration and emission of LASER. We also believe that this mechanism is able to explain and apply to those machines which need to release energy rapidly.

A cylinder rolling on an inclined plane and a sphere on grooved tracks are discussed in details.Using elementary mechanics, the formulas are derived for the time interval (t) and the final speed (vas a function of release height (h). (1) A cylinder is rolling down an inclined plane. The speed and time of the center of mass ofthe cylinder which changed with position (x) are recorded by a motion sensor. We can get theplots of v vs. √x and t vs. √ x, and find that the acceleration of the center of mass of thecylinder is constant, whether the cylinder is in rolling or a combination of rolling and slipping. (2) A sphere is rolling down an inclined grooved track. The final speed at the bottom of thetrack can be calculated from the physics of projection motion after the sphere leaves the track to thefloor. The time t for the sphere starting from rest to the bottom can be recorded by using photogate detectors. From the v-√h and t-1/√h graphs, μs between the sphere and track can be obtained. (3) When a sphere is released from the vertical height h of a cycloidal slide, the time tof pure rolling is the same independent of release position. But, when the sphere moves at a combination of rolling and slipping, the time t' will be different from t. We measure t and t' with photogate detectors and get the plot of t vs. h. The value ofμs can be calculated from the t - h graph. 圓柱或鋼珠從斜面或有槽曲面形成的軌道上滾下時，利用基本力學，可推導出時間 (t) 、速率 (v) 隨高度改變的函數關係。 (1) 利用運動感應器記錄圓柱由斜面上滾下時，圓柱質量中心的速度及運動時間隨位置 (x) 的變化，可繪出 v 對√ x 及 t 對 √x關係圖，由v－√x 及 t－√ x圖可知不論圓柱純滾動或滾動兼滑動，其質心均等加速度運動。 (2) 鋼珠由有槽斜板滾下時，到達底端的速率可由從底端至地面的拋體運動算出，而其時間t則可利用光電計時器直接記錄，利用 v－√h 圖及 t－1/√ h 圖可求出鋼珠和軌道的靜摩擦係數 μs。 (3) 鋼珠從旋輪線上方純滾動至底端時，所經歷的時間 (t) 和釋放高度無關，但是當鋼珠滾動兼滑動時，所經歷時間 t' 會改變，利用光電計時器量出 t 及 t'並作圖，利用 t－h 圖可出 μs。