1 Chapter Five Work, Energy, and Power

2 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.

3 Work Work down by a constant force F acting on a body is where F s 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

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5 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,

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7 Potential Energy Work down against the gravitational force is independent of the choice of path between any two fixed endpoints. See Fig The potential energy E p is defined as where y is the height in a gravitational field.

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9 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.

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11 Work Done by a Variable Force See Fig 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

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13 Kinetic Energy 1. The force is constant: The initial position is x = 0, we have By Newton's second law Since where v 0 is the velocity at x = 0 and v is the velocity at x. Thus

14 The work done on a body that changes its velocity actually changes the quantity, which is called the kinetic energy E k. The applied force is not constant:

15 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.

16 Energy Conservation For a mechanically conservative system ( one in which no energy enters or leaves the system): –(E k + E p ) initial = (E k + E p ) final –Let us launch an object of mass m from a point y 1 above the floor with an initial velocity v 1. Sometime later, the velocity of the object will be v 2 and its position y 2. See Fig We have

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18 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 = 90 o. For an accountability of energy system we have

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20 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 :

21 Example 5-3 A skier is on a 37 o 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.

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24 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.

25 A kilowatt-hour is the energy dissipated by a device that uses 10 3 W for a period of 1 h, that is,

26 Example 5-4 A tractor can exert a force of N while moving at constant speed of 5 m/sec. What is its horsepower? Sol :

27 Homework 2, 4, 8, 12, 13, 15, 16, 17, 18, 20.