力學能守恆理論形成的歷史探究及其在科學史融入教學上的意義

The Investigations on the Theoretical Development of Conservation of Mechanical Energy and Its Implications on Physics Teaching

姚珩(Herng Yao) ； 孫治平(Chi-Ping Sun) ； 李秉書(Pin-Shu Lee)

《科學教育學刊》 24卷4期 (2016/12) Pp. 379-416

https://doi.org/10.6173/CJSE.2016.2404.03

摘要

科學史可協助學生瞭解科學知識的形成、及提升在科學本質上的素養，對科學史做進一步的研究，有助於發揮科學教育的功能。為此本文以文獻分析及歷史研究方法，探討物理學上相當重要的主題—功、動能、位能與力學能守恆律的理論發展歷程。研究發現功與動能的概念最早是由牛頓提出，他為了想瞭解物體在受向心力，而非拉力作用下，求得任意位置處的速度而引入，故功並非是出於工程的需要而發生。其想法隨後由白努利加以擴充，他除了首次寫下f = ma的數學式，還提出了力與位移內積之概念。牛頓所開啟的微小增量及累積求和的分析運算，也為力學論證方法樹立起新里程碑。1743年克來若認為當外力為一函數的正合微分，則此力所作的功與路徑無關，率先提出位能概念。最後拉格朗日統合這些，創建出力學能守恆定律。透過這些原始文獻的探討，得提供教師珍貴資料，將此結果直接融入授課教材，可消除學生常見的迷思，達到更佳的教學目標。文中並輔以扼要的教學模組，以供實務參考。這些物理學家對自然現象問題的選擇，反映出運動問題為古典物理的核心，他們將經驗知識與數學理論統合的物理學方法，亦可深化科學史在瞭解科學方法上之教學效能。

關鍵字

力學能 ； 物理教學 ； 科學史 ； 科學方法 ； 科學本質

並列摘要

We investigate the theoretical developments of work, kinetic energy, potential energy and the conservation of mechanical energy. Our study finds that the concepts of work and kinetic energy originally appeared in Newton’s Principia. These concepts were proposed due to the fact that Newton wanted to find the speed of an object at any position under the action of centripetal force, rather than the external force exerted by the machine. His idea subsequently was expanded by J. Bernoulli, who established the work–energy theorem for an object under the elastic force, and also wrote down the famous mathematical formula f = ma for the first time. He also proposed the concept of inner product between the force and the displacement of a body. Their analytical methods of manipulating the tiny increments and cumulative sums set up the cornerstone for the arguments in mechanics. Clairaut then found that the work done by gravity on a body around the Earth was independent of the path due to the fact that the gravity could be expressed as the differential of a state function. The state function is the so-called potential energy. Combining the work–energy theorem and the concept of potential energy, Lagrange finally established the conservation of mechanical energy. The results of the investigation on the development of mechanical energy can help students avoid the common misconception about work and energy. They may also be good references for teachers to guide students to construct deep scientific thinking, and to comprehend the essence of nature of science.

並列關鍵字

Mechanical Energy ； Physics Teaching ； History of Science ； Scientific Method ； Nature of Science

參考文獻

Suppe, F. (1977). The structure of scientific theories (2ed ed.). Urbana, IL: University of Illinois Press.

Burtt, E. A. (1994)。近代物理科學的形而上學基礎(The metaphysical foundations of modern physical science : A historical and critical essay；徐向東譯)。成都市：四川教育。(原著出版於1924 年)

Duhem, P. (1999)。物理學理論的目的和結構(La théorie physique: Son objet et sa structure；李醒民譯)。北京市：華夏。(原著出版於1906年)

Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2013)。教育研究法—研究設計實務(How to design and evaluate research in education；楊孟麗、謝水南譯)。臺北市：心理。(原著出版於1970 年)

Galilei, G. (2005)。兩門新科學的對話(Discorsi e dimostrazioni matematiche: Intorno à due nuoue scienze attenenti alla mecanica i movimenti locali；戈革譯)。臺北市：大塊文化。(原著出版於1638年)