788 Work and Energy 例质量为10kg的质点,在外力作用下做平面曲线运动,该质 点的速度为=427+167,开始时质点位于坐标原点 求在质点从y=16m到y=32m的过程中,外力做的功。 解 4t dx= tdt dt y=16时t=1 D,=中=16一y=16y=32时t=2 du du 80t F=m 0 dt w=Fdx+F, dy=I320t'dt=1200J
7&8 Work and Energy 质量为10kg 的质点，在外力作用下做平面曲线运动，该质 点的速度为 t i j 4 16 2 v = + 解 2 4 d d t t x vx = = dx 4t dt 2 = 16 d d = = t y vy y =16t t t F m x x 80 d d = = v 0 d d = = t F m y y v 320 d 1200 J 2 1 3 = t t = 求 在质点从 y = 16m 到 y = 32m 的过程中，外力做的功。 例 ,开始时质点位于坐标原点。 y =16时 t =1 y = 32时 t = 2 W F x F y x y = d + d
788 Work and Energy 例已知用力F缓慢拉质量为m的小球,F保持方向不变 求日=的时,F作的功。 解F- SIne=0 Tcos6 -mg =0 T F=mg tane W=「Fd=「 Fcos eds mg tan cose d Lmg tan 0 cos ede 1-mgL cose o
7&8 Work and Energy F L 缓慢拉质量为m 的小球， 解 F −T sinθ = 0 T cosθ − mg = 0 F = mg tanθ = mg tanθ cosθ ds x y θ G T 0 =1− mgLcosθ 例 求 = 0 时， 已知用力 F F 保持方向不变 F 作的功。 = 0 0 tan cos θ Lmg θ θdθ W = F dr = F cosθds
788 Work and Energy P164:37 37. For a variable force, we find the work by integration W=|F·ds= +ar+bx)dx
7&8 Work and Energy P164:37
788 Work and Energy §8-8 Power(功率)(P188) Instantaneous power. The instantaneous power P is defined as the rate at which work is performed dn F dr =F…= Lycos6 t dt The sI unit of power is the watt, 1W=1J/s I horsepower=l hp=746 w
7&8 Work and Energy F v Fv cos dt F dr dt dW P = = = = Instantaneous power: The instantaneous power P is defined as the rate at which work is performed. The SI unit of power is the watt, 1 W = 1 J/s 1 horsepower=1 hp = 746 W §8-8 Power (功率) (P188)
788 Work and Energy 87-2 Kinetic Energy and the work-Energy Priciple(P156-p160) 1 Kinetic Energy(动能)P156 Kinetic energy动能) K is energy associated with the state of motion of an object. (The faster the object moves, the greater is its kinetic energy. p156) K o When the object is stationary, its kinetic energy is zero OSI unit of energy is joule(D)
7&8 Work and Energy §7-2 Kinetic Energy and the work-Energy Priciple (P156-p160) Kinetic energy(动能) K is energy associated with the state of motion of an object. （The faster the object moves, the greater is its kinetic energy. p156） When the object is stationary, its kinetic energy is zero. ●SI unit of energy is joule (J) 1 Kinetic Energy (动能) P156 2 2 1 K = mv