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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Atwood machine ： ウィキペディア英語版 Atwood machine The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. The ideal Atwood Machine consists of two objects of mass ''m''1 and ''m''2, connected by an inextensible massless string over an ideal massless pulley. 〔 Chapter 6, example 6-13, page 160. 〕 When m1 = m2, the machine is in neutral equilibrium regardless of the position of the weights. When m1 ≠ m2 both masses experience uniform acceleration. == Equation for constant acceleration == We are able to derive an equation for the acceleration by using force analysis. If we consider a massless, inextensible string and an ideal massless pulley, the only forces we have to consider are: tension force (''T''), and the weight of the two masses (''W1'' and ''W2''). To find an acceleration we need to consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of we can derive a system of equations for the acceleration (''a''). As a sign convention, we assume that ''a'' is positive when downward for $m\_1$, and that ''a'' is positive when upward for $m\_2$. Weight of $m\_1$ and $m\_2$ is simply $W\_1\; =\; m\_1\; g$ and $W\_2\; =\; m\_2\; g$ respectively. Forces affecting m1: $\backslash ;\; m\_1g-T=m\_1a$ Forces affecting m2: $\backslash ;\; T-m\_2g=m\_2a$ and adding the two previous equations we obtain $\backslash ;\; m\_1g-m\_2g=m\_1a+m\_2a$, and our concluding formula for acceleration $a\; =\; g$ Conversely, the acceleration due to gravity, ''g'', can be found by timing the movement of the weights, and calculating a value for the uniform acceleration ''a'': $d\; =\; at^2$. The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion. 〔 Section 1-6, example 2, pages 26-27.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Atwood machine」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.