Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Kinetic energy wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Internal energy wikipedia , lookup
Gibbs free energy wikipedia , lookup
Centripetal force wikipedia , lookup
Chapter Five Work, Energy, and Power 1 Work, Energy, and Power • Definitions in physics do not always match the usage of the words. • We consider mechanical work, energy, and power, for it is the treatment of these terms from First Principle that will be applied directly to electrical circuits. 2 Work • Work down by a constant force F acting on a body is where Fs represents the component of force in the direction We define a new unit 1 N-m = 1 joule with symbol J. • When force and motion are not in the same direction (see Fig.5-2), we have 3 • 4 Example 5-1 • A box is pushed 3 m at constant velocity across a floor by a force F of 5 N parallel to the floor. (a) How much work was down on the box by the force F, which clearly opposes friction (see Fig. 5-1). (b) How much work is down on the box by the force of friction? • Sol : (a) W = 5 N 3 m = 15 J (b) Because a = 0, 5 • 6 Potential Energy • Work down against the gravitational force is independent of the choice of path between any two fixed endpoints. See Fig. 5-3. • The potential energy Ep is defined as where y is the height in a gravitational field. 7 • 8 • For potential energy a reference level must always be specified. See Fig. 5-4, 5-5. • Only the difference in heights needs to be specified to give the relative difference in potential energy. 9 • 10 Work Done by a Variable Force • See Fig. 5-6. • When , we have • In more general case where F and the general displacement are not in the same direction, the expression for the work becomes or 11 • 12 Kinetic Energy • 1. The force is constant: The initial position is x = 0, we have By Newton's second law Since where v0 is the velocity at x = 0 and v is the velocity at x. Thus 13 • The work done on a body that changes its velocity actually changes the quantity , which is called the kinetic energy Ek. • The applied force is not constant: 14 • Since we have • The work-energy theorem is stated as the work done by the resultant force acting on a particle is equal to the change in kinetic energy of the particle. 15 Energy Conservation • For a mechanically conservative system ( one in which no energy enters or leaves the system): – (Ek + Ep)initial = (Ek + Ep)final – Let us launch an object of mass m from a point y1 above the floor with an initial velocity v1. Sometime later, the velocity of the object will be v2 and its position y2. See Fig. 5-7. We have 16 • 17 • Let us assume an idealized pendulum that swings in a vacuum so that there is no energy lost to air friction and that is no frictional loss at the pivot (see Fig. 5-8). We start the pendulum by pulling it to one side and releasing it with no initial velocity. • the string does no work on the pendulum because of where θ is the angle between the string direction and ds, and θ = 90o. • For an accountability of energy system we have 18 • 19 Example 5-2 • Suppose a ball is dropped from a height h = 10 m. What is its velocity just before it strikes the ground? • Sol : 20 Example 5-3 • A skier is on a 37o slope of length s = 100 m (see Fig. 5-9). The coefficient of friction between his skis and the snow is 0.2. If he start from rest, what is his velocity at the bottom of the slope? • Sol : • No energy is put in, but • Let us tilt our coordinate axis so that the slope becomes the x axis and the normal becomes the y axis. 21 • 22 • 23 Power • Power is defined as • The unit of power is joules per second (J/sec). • New unit: 1 J/sec = 1 watt (W). • A 100-W light bulb uses 100 J of electrical energy each second. 24 • A kilowatt-hour is the energy dissipated by a device that uses 103 W for a period of 1 h, that is, 25 Example 5-4 • A tractor can exert a force of 3 104 N while moving at constant speed of 5 m/sec. What is its horsepower? • Sol : 26 Homework • 2, 4, 8, 12, 13, 15, 16, 17, 18, 20. 27