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保守力(未完成)

Jul 28, 2008 陳 tinper3

科學家把力分為兩種—保守力與非保守力,

什麼是保守力?

¦ 若是將物體從A移到B (物體在A點與B點動能相同條件下) ,

  若 所需做的功 和路徑無關,則A B所在區域為保守力場

  也因此, 從 A移到B ,再從 B 移回A 時, 即使路徑不同淨功為零, 
  基本上以上兩個敘述意義相同

  因為 A 到B ,物體的能量只與 起點 終點 位置有關 ,與路徑無關,
  因此可以定義 :只與位置相關的能量 ,也就是所謂的 位能

  所以 ,保守場 可以定義位能 ,且有位能的也必然是保守場    ¦

  .......取自黃福坤老師(寫的真好!!若是找到節路網址會再貼上)

從上述可知:保守力提供了位能的概念!

再來要講的是保守力一個非常重要的特性: 保守力只能當成外力

對物體作功或者是提供物體位能 ,兩者只能選其一. 也就是說:保

守力若對物體做功,那麼就不能再提供物體位能(也就是這時物體沒

有位能的概念) ; 而若是保守力提供物體位能,則保守力就不能再對

物體作功.

 

好,接下來我們就要來看看科學家們如何把concept轉化成數學式,

使我們在運算過程中仍能符合所有的concept.  

已推導出W=ΔEk 及W保=-ΔU  (以後再貼上其證明)  現在我們就

來詳細的說明這兩個式子如何在數學運算中完全照著之前所定義的

concept走!

 

p.s. 下列括號()均是在說明式子中所代表的情形.

W=W非保+W保=ΔEk (作用在物體上的外力有保守力及非保守力) 

W=W非保+W保=ΔEk+ΔU+(-ΔU)=ΔEk      

上述這個式子是這樣解讀的: 因為保守力已做工,所以不能提供物體位

能的concept,所以物體沒有所謂的位能,所以合力所做的功只會影響

物體的動能.

 

W非保=ΔEk+ΔU  (作用在物體上的外力只有非保守力)               

仔細瞧瞧!發現了嗎?  這個式子並不是在說非保守力作功會影響物體動

能及位能, 上述的ΔU是保守力提供的!   因為此時我們所用的觀點是保

守力不當外力作功,那麼既然保守力不做功,那麼它就會提供物體位能.

 

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