1、Short Version : 6. Work, Energy & Power短版: 6. 功，能和功率,Usefulness for Studying Energy研究能量的好處,Alternative ways to describe motion 提供另一種方法來描述運動:Conservation of energy能量守恆.Hamiltonian formulism漢美頓的做法.Extension to non-mechanical studies延伸至非力學研究: Thermal physics熱學. Electrodynamics電動力學.,6.1. Work功,Work W do
2、ne on an object by a constant force F is一個穩定的力 F 對一個物體所作的功是,rF = displacement along direction of F.沿 F 方向的位移,Note: F need not be a net force.注意：F 不需要是淨力,Fr = force along direction of r .沿 r 方向的力,Work & the Scalar Product功和純量(乘)積,Work is a scalar.功是一個純量,Scalar = quantity specified by a single number純
3、量 由一個在任何座標系统that is the same in every coordinate system. 都一樣的數字所代表的量Scalar has no direction.純量無方向,Scalar (dot) product of vectors A & B : 向量 A & B 的純量(點)乘積：,is a scalar 是個純量,= angle between F & r F & r 的夾角,A,B,BA = B cos,3-D,2-D,Proof,Letbe the unit vectors along the Cartesian axes.,C,A + C,A,AB,CB,
4、( A + C )B,6.2. Forces that Vary會變化的力,位置,力,Tactics 策略 6.1. Integrating作積分,Example 例 :,Since 因,we have 故,See Appendix A for integral table.附錄 A 是一個積分表不定,Stretching a Spring拉長一個彈簧,Example 6.4. Bungee Jumping高空彈跳,Bungee cord is 20 m long with k = 11 N/m.彈跳繩長 20 m，其 k = 11 N/m。At lowest point, cord leng
5、th is doubled.在最低點時，繩長加倍。 How much work is done on cord?對繩所作功為何？ How does work done in the last meter compare with that done in the 1st meter?最後一米所作的功與第一米的比較怎樣？,(a),(b) 1st meter 第一米,Last meter 最後一米,Force & Work in 2- & 3- D二和三維的力與功,Line integral 線積分,1-D,2-D,3-D,Work Done Against Gravity對重力做的功,Only
6、vertical displacement requires work against gravity祇有垂直方向的位移需要對重力做功,W = m g h,6.3. Kinetic Energy動能,Kinetic energy 動能 :,K is relative (depends on reference frame). K 是相對的 (依參考框而定) 。K is a scalar (independent of coordinate system). K 是個純量。,Work-energy theorem :功-能定理,GOT IT 懂嗎? 6.3.,For each situation
7、, tell whether the net work done on a soccer ball is為下列每一狀況，判斷對一個足球所作的淨功是positive, negative, or zero.正的，負的，或是零。Justify your answer using the work-energy theorem.用功-能定理證明你的答案是對的。You carry the ball to the field, walking at constant speed.你以等速行走，把球帶到球場。 You kick the stationary ball, starting it flying
8、through the air.你把靜止的球踢到空中。 The ball rolls along the field, gradually coming to a halt.球在場上滾動，慢慢停下來。,zero 零 (K=0),positive 正的(K0),negative 負的(K0),Energy Units能量單位, energy 能 = work 功 ,= J 焦耳 (SI 公制),CGS:,Other energy units 其他的能量單位 :eV (electron-volt): used in nuclear, atomic, molecular, solid state p
9、hysics. eV (電子伏特) : 用於核子，原子，分子，固態物理。cal (calorie), BTU (British Thermal Unit): used in thermodynamics.cal (卡路里), BTU (英熱單位) : 用於熱力學。kW-h (kilowatt-hours): used in engineering.kW-h (仟瓦-小時) : 用於工程。,See Appendix C請看附錄 C,6.4. Power功率,Average power 平均功率:,(Instantaneous) power : (瞬間)功率,Example 6.7. Climbi
10、ng Mount Washington爬上華盛頓山A 55 kg hiker makes the vertical rise of 1300 m in 2 h.一個 55 kg 的行者用 2 h 完成那1300 m 的垂直距離 。A 1500 kg car takes h to go there.一部 1500 kg 的汽車用 h 就到了。Neglecting loss to friction, what is the average power output for each.忽略摩擦的消耗，每個的平均功率為何？,Hiker 行者:,Car 汽車:,Power & Velocity功率和速度
11、,Example 6.9. Bicycling騎腳踏車Riding a 14 kg bicycle at a steady 18 km/h (5.0 m/s),騎着一部 14 kg 的腳踏車以 18 km/h (5.0 m/s) 的等速前進時， you experience a 30 N force from air resistance.你受到的空氣阻力是 30 N 。If you mass 68 kg, what power must you supply如果你的質量是 68 kg ，on level ground.在平地時 up a 5 slope.上一個 5斜坡時你需要的功率是多少？,(a),(b),Fair,Fg,v,Fair,v,Energy and Society 能量和社會,運輸,住宅,工業,商業,水力,生質,地熱，風力，太陽能,煤,核子,油,氣,2008: 4.71020 J or 1.51013 W,
