Work and Energy
一、英文名詞中譯：
Scalar 純量
Vector 向量
Force 力量
Work 功
Displacement 位移
Velocity 速度
Mass 質量
Kinetic energy 動能
Net force 淨力
Conservative force 保守力
Nonconservative force 非保守力
Gravitational acceleration 重力加速度
The work–energy theorem 功–能原理
Gravitational potential energy 重力位能
Elastic potential energy 彈性位能
Electric potential energy 電位能
Mechanical energy 力學能
Conservation of mechanical energy 力學能守恆原理
二、重要觀念整理：
A. 功與能
1. 受到外力作用的質點，如果再外力的方向產生一段位移，則此外力對質點作功
W = F •S = F S cosθ （純量）
2. 變力所作的功，等於 F ‐ S 圖中函數曲線與 S 軸所圍成的面積。
3. 外力的合力對質點所作的功，等於質點動能的變化量。（功–能原理）
W = 1/2 mvf2 – 1/2 mvi2
4. 系統保守力作功的負值，為系統位能的改變量。
Ws = –（1/2 kxf2 – 1/2 kxi2）= 1/2kxi2 –1/2 kxf2
Wg = –（mghf – mghi）= mghi –mghf
5. 非保守力所作的功，等於力學能的改變量。
Wnc = （1/2 mvf2 + mghf + 1/2 kxf2）–（1/2 mvi2 + mghi + 1/2 kxi2）
6. 力學能守恆：
a. 一個沒有外力作用的系統，如果系統內力是重力、彈力、靜電力等保守力時，
此系統動能與位能可等值變化，而力學能總和保持一定。
b. 力學能守恆的系統，其力學能的大小會隨位能零位面的改變而改變。
然而一旦零位面選定後，力學能就保持定值。
1/2 mvf2 + mghf + 1/2 kxf2 = 1/2 mvi2 + mghi + 1/2 kxi2
三、練習題：
1. A desk is pushed across the floor at constant velocity by a 160 N force directed downwards at an angle of 20° to the horizontal. How much work is done in J when it has moved 1.4 m forward?
2. A 0.25 kg mass is located 24 m above the surface of the earth. What is its potential energy in J with respect to the earth’s surface?
3. A 50 kg boy is on a massless swing that has an effective length of 3.0 m. His potential energy is zero when the angle between the swing and the vertical is zero. The maximum angle between the swing and the vertical is ? What is his speed in m/s at the bottom of the swing?
4. A 0.300 kg particle is accelerated from a speed of 7.20 m/s to 11.2 m/s. How much work in J was done on the particle?
5. A projectile of mass 0.750 kg is shot straight up with an initial speed of 18.0 m/s. （a）How high would it go if there were no air friction？ （b）If the projectile rises to a maximum height of only 11.8 m, determine the magnitude of the average force due to air resistance.