1功和动能(Work.pdfVIP

Chapter (5-1)work and energy 1.功和動能(Work and energy) 當某 力對物體施力而產生平行力方向的位移時，我們說某力對物體施 了功。該功的大小定義為: → → → → F $d s F d s coscoscos 那麼力所施的功跑到被施力物體的那裡去了呢 ? (1).變成了動能 (Kinetic Energy) 動能定義為 只要有速度就有動能: T 1 mv2 2 Note: 淨力合力( 只能產生動能) → → → → 1 2 1 2 F $d s m a $d s mads mvdv mdv d( mv ) 2 2 (2).變成了位能 (Potential Energy) 施力如果遇到了重力，電力，彈力..等保守力場所作的功就變成了位 能。 (A).重力位能 (Gravitational Potential Energy) V (h) mgh g (B). 彈力位能 (Elastic Potential Energy) 1 2 V (x) kx s 2 (C). 應變能 (Strain Energy) 1 (3).變成了熱能 施力如果遇到了摩擦力，撕裂力..等非守力場時，所作的功就變成了 熱流失。 2. 機械能守衡定理 (Conservation of Mechanical Energy) 如果施力所作的功如上所示，那麼下式一定成立： → F $ds T + V + V + Q ¶ ¶ ¶ ¶ ¶ g s (T −T ) +(V −V )+(V −V )+Q 2 1 g2 g 1 s2 s 1 當施力為零時 (無外力) ，上式改為: T +V +V T =+V +V +Q 1 g 1 s 1 2 g 2 s 2 稱之機械能守衡定理 例 1: The gantry structure is used to test the response of an airplane during a clash. The plane of mass 8-Mg is hoisted back until θ = 60 °, and then pull-back cable AC is released when the plane is at rest. Determine the speed of the plane just before clashing into the ground, θ = 15 °. Also, what is the maximum tension developed in the supporting cable during the motion? 2 解 因為無外力，故可用機械能守衡定理: (1) 求B位之速度 由 T +V +V