~ 第八章 ~ 功與能
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~ 第八章 ~ 功與能
8-1 功及其單位 8-2 功率及其單位 8-3 動能與位能 8-4 能量不滅定律 8-5 能的損失及機械效率
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• 功– 當一物體沿著施力的方向作直線運動時,作用力的大小與物體之運動位移的乘積,稱為這個作用力對物體作功。
8-1 功及其單位
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– 若作用力與位移之方向不一致時,則作用力作用於物體上的功,應為作用力之有效力與物體位移的乘積。
8-1 功及其單位
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– 若 Ɵ =0° 時, cos Ɵ =1 ,即作用力之方向與位移一致。 – 若 0° < Ɵ < 90° 時, 0 < cos Ɵ < 1 ,則作用力對物體作
正功。 – 若 Ɵ = 90° 時, cos Ɵ =0 ,即作用力與位移垂直,此時作用力不
作功。 – 若 90° < Ɵ < 180° 時, 1 < cos Ɵ < 0 ,則作用力對物
體作負功。 – 若 Ɵ = 180° 時, cos Ɵ = 1 ,即作用力之方向與位移相反,如摩擦
力所作的功。 – 功是純量。功雖有正負之分,但此正負之分並非指功之方向。 – 若有數個力同時作用於物體上時,此物體所得之功為所有力之合
力與其位移之乘積。 – 單位換算:
• 1J( 焦耳 ) = 107erg( 爾格 ) • 1g-cm = 980erg • 1kg-m = 9.8J
8-1 功及其單位
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8-1 功及其單位
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8-1 功及其單位
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8-1 功及其單位
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8-1 功及其單位
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• 功率– 單位時間所作的功,即稱為功率。
8-2 功率及其單位
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– 在工程應用上,我們習慣用馬力來作為功率的單位。
– 1 公制馬力 (PS) 是指每秒作功 75kg-m 。– 1 英制馬力 (HP) 則為每秒作功 550 ft-lb 。– 其單位換算如下:
• 1PS = 75kg-m/sec = 736W
• 1HP = 550 ft-lb/sec = 746W
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8-2 功率及其單位
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8-2 功率及其單位
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• 能– 凡物體具有作功的本領者,則此物體具有能。– 能與功之單位相同,絕對單位之 MKS 制中均以焦耳為其單位。
– 機械能又分為動能及位能兩種。 – 運動中的物體,具有作功的能力,這種運動中的物體所具有的能量,稱為動能。
8-3 動能與位能
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• 動力位能– 物體因位置改變所具有的能即為重力位能。
8-3 動能與位能
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• 彈力位能– 因形狀改變所具有的能量,稱為彈性位能。
8-3 動能與位能
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• 能量不滅定律– 在一個系統中,能量的總量是不會改
變的。能量可以轉換成另一種形式,或是由某處轉移到另一處,但是在整個系統中的 能量總和是維持不變的。
• 機械能不滅定律– 若在整個系統中,只考慮 機械能,
也就是只考慮動能與位能,而不予考慮摩擦時,則稱為機械能不滅定律。
8-4 能量不滅定律
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• 能的損失– 各種機械於運轉過程中,由於各機件接觸面間的摩擦力,會消耗一些能量,使得輸入的能量,無法完全有效利用使其作功,這種音機械運轉而消耗的能量,稱為能的損失。
8-5 能的損失及機械效率
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• 機械效率– 機械輸出之功 ( 或功率 ) 與輸入機械之能 ( 或功率 ) 的比值,稱為機械效率。
– 若有數個不同機械之組合,其總機械效率為各個機械之機械效率的連乘積。
8-5 能的損失及機械效率
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8-5 能的損失及機械效率