6.Work,EnergyPower功,能和功率.pptVIP

6. Work, Energy Power 功，能和功率 Work 功 Forces that Vary 會變化的力 Kinetic Energy 動能 Power 功率 What’s the speed of these skiers at the bottom of the slope? 這兩個滑雪人抵達山坡底時的速率為何? Does the work of climbing a mountain depend on the route chosen? 爬一個山所作的功會隨路徑而改變嗎？ No 否 Direct application of Newton’s law can be infeasible. 直接使用牛頓定律可能不切實際。 complicated 複雜 Energy conservation to the rescue (Chap 7). 能量守恆來救駕 (第七章) 這滑雪人的加速度固定 simple 簡單 這滑雪人的加速度隨坡度而變 6.1. Work 功 Work W done 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 Example 6.1. Pushing a Car 推一部車 The man pushes with a force of 650 N, moving the car 4.3 m. 這男人用 650 N 的力推，把車移動了4.3 m。 How much work he does? 他作了多少功？ Example 6.2. Pulling a Suitcase 拉一個行李箱 Woman exerts 60 N force on suitcase, pulling at 35? angle to the horizontal. 女人對行李箱用力 60 N，朝與水平成 35? 的方向拉。 How much work is done if the suitcase is moved 45 m on a level floor? 如果行李箱在水平的地板上移動了 45 m，所作的功為何？ ?x ?xF = ?x cos? 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 of ? ?A ?B x y A B Example 6.3. Tugboat 拖船 Tug boat pushes a cruiser with force 拖船推巡洋艦的力為 F = ( 1.2, 2.3 ) MN, displacing the ship by 使之移位 ?r = ( 380, 460 ) m. Find the work done by the tugboat. 求拖船所作功 Find the angle between F ?r. 求 F ?r 的夾角 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