Work and Kinetic Energy Big Ideas

7 Big Work and Kinetic Energy Ideas Work is force times 1 distance. Kinetic energy is one-half mass times 2 velocity squared. Power is the rate at 3 which work is done. ▲ The work done by this cyclist can increase his energy of motion. The relationship between work (force times distance) and energy of motion (kinetic energy) is developed in detail in this chapter. n this chapter we introduce the idea that force times distance energy. Together, work and kinetic energy set the stage for a Iis an important new physical quantity, which we refer to as deeper understanding of the physical world. work. Closely related to work is the energy of motion, or kinetic 195 M07_WALK6444_05_SE_C07_pp195_222.indd 195 28/08/15 4:25 PM 196 CHAPTER 7 WORK AND KINETIC ENERGY 7-1 Work Done by a Constant Force In this section we define work—in the physics sense of the word—and apply our definition to a variety of physical situations. We start with the simplest case—namely, the work done when force and displacement are in the same direction. Force in the Direction of Displacement When we push a shopping cart in a store or pull a suitcase through an airport, we do work. The greater the force, the greater the work; the greater the distance, the greater the work. These simple ideas form the basis for our definition of work. > To be specific, suppose we push a box with a constant force F , as shown in > > FIGURE 7-1. If we move the box in the direction of F through a displacement d , the work W we have done is Fd: Definition of Work, W, When a Constant Force Is in the Direction of Displacement W = Fd 7-1 SI unit: newton-meter (N # m) = joule, J Work is the product of two magnitudes, and hence it is a scalar. In addition, notice that a small force acting over a large distance gives the same work as a large force acting over a small distance. For example, W = 1 N 400 m = 400 N 1 m . 1 21 2 1 21 2 A constant force of cacting in the direction of a cdoes work magnitude F, c displacement of magnitude d, c W = Fd on the object. > d > > F F > ▲ FIGURE 7-1 Work: constant force in the direction of motion A constant force F pushes a > box through a displacement d . In this special case, where the force and displacement are in the same direction, the work done on the box by the force is W = Fd . The dimensions of work are newtons (force) times meters (distance), or N·m. This combination of dimensions is called the joule (rhymes with “school,” as commonly pronounced) in honor of James Prescott Joule (1818–1889), a dedicated physicist who is said to have conducted physics experiments even while on his honeymoon. We define a joule as follows: Definition of the joule, J 1 joule = 1 J = 1 N # m = 1 kg # m s2 # m = 1 kg # m2 s2 7-2 To get a better feeling for1 work >and2 the associated> units, suppose you exert a force of 82.0 N on the box in Figure 7-1 and move it in the direction of the force through a distance of 3.00 m. The work you have done is W = Fd = 82.0 N 3.00 m = 246 N # m = 246 J Similarly, if you do 5.00 J of work1 to lift21 a book2 through a vertical distance of 0.750 m, the force you have exerted on the book is W 5.00 J 5.00 N # m F = = = = 6.67 N d 0.750 m 0.750 m M07_WALK6444_05_SE_C07_pp195_222.indd 196 28/08/15 4:25 PM 7-1 WORK DONE BY A CONStaNT FORCE 197 TABLE 7-1 Typical Values of Work EXERCISE 7-1 WORK DONE Equivalent One species of Darwin’s finch, Geospiza magnirostris, can exert a force of 217 N with its beak Activity work (J) as it cracks open a Tribulus seed case. If its beak moves through a distance of 0.42 cm during Annual U.S. energy use 19 this operation, how much work does the finch do to get the seed? 8 * 10 Mt. St. Helens eruption 1018 REASONING AND SOLUTION The work the finch does is force times distance. In this case, the force is 217 N and the dis- Burning 1 gallon of gas 108 tance is 0.42 cm 0.0042 m. Thus, = Human food intake/day 107 W = Fd = 217 N 0.0042 m = 0.91 J Melting an ice cube 104 This is a relatively small amount of work1 for 21a human, but2 significant for a small bird. Lighting a 100-W bulb for 6000 1 minute Just how much work is a joule, anyway? Well, you do one joule of work when Heartbeat 0.5 you lift a gallon of milk through a height of about an inch, or lift an apple a meter. Turning a page of a book 10-3 One joule of work lights a 100-watt lightbulb for 0.01 second or heats a glass of water Hop of a flea 10-7 0.00125 degree Celsius. Clearly, a joule is a modest amount of work in everyday terms. Breaking a bond in DNA -20 Additional examples of work are listed in Table 7-1. 10 EXAMPLE 7-2 HEADING FOR THE ER An intern pushes an 87-kg patient on an 18-kg gurney, producing an acceleration of 0.55 m s2. (a) How much work does the intern do in pushing the patient and gurney through a distance of 1.9 m? Assume the gurney moves without > friction. (b) How far must the intern push the gurney to do 140 J of work? PICTURE THE PROBLEM Our sketch shows the physical situation for this problem. Notice that the force exerted by the intern is in the same direction as the displacement of the gurney; therefore, we know that the work is W = Fd. a = 0.55 m/s2 REASONING AND STRATEGY We are not given the magnitude of the force, F, so we cannot > apply Equation 7-1 W = Fd directly. However, we are given the F mass and acceleration of the patient and gurney, and from them 1 2 we can calculate the force with F = ma. The work done by the intern is then W = Fd, where d = 1.9 m. Known Mass of patient, 87 kg; mass of gurney, 18 kg; acceleration, a = 0.55 m s2; (a) pushing distance, d = 1.9 m; (b) work, W = 140 J. d = 1.9 m > Unknown (a) Work done, W = ? (b) Pushing distance, d = ? SOLUTION Part (a) 1. First, find the force F exerted by the intern: F = ma = 87 kg + 18 kg 0.55 m s2 = 58 N 2. The work done by the intern, W, is the force times the distance: W Fd 58 N 1.9 m 110 J = = 1 21= > 2 Part (b) W 1401 J 21 2 3. Use W = Fd to solve for the distance d: d = = = 2.4 m F 58 N INSIGHT You might wonder whether the work done by the intern depends on the speed of the gurney. The answer is no. The work done on an object, W = Fd, doesn’t depend on whether the object moves through the distance d quickly or slowly. What does depend on the speed of the gurney is the rate at which work is done, which we discuss in detail in Section 7-4. PRACTICE PROBLEM — PREDICT/CALCULATE (a) If the total mass of the gurney plus patient is halved and the acceleration is doubled, does the work done by the intern increase, decrease, or remain the same? Explain. (b) Determine the work in this case. [Answer: (a) The work remains the same because the two changes offset one another; that is, F = ma = m 2 2a . (b) The work is 110 J, as before.] Some related homework problems: Problem 3, Problem 4 1 > 21 2 M07_WALK6444_05_SE_C07_pp195_222.indd 197 28/08/15 4:25 PM 198 CHAPTER 7 WORK AND KINETIC ENERGY Zero Distance Implies Zero Work Before moving on, let’s note an interesting point about our definition of work. It’s clear from Equation 7-1 that the work W is zero if the distance d is zero—and this is true regardless of how great the force might be, as illus- trated in FIGURE 7-2. For example, if you push against a solid wall, you do no work on it, even though you may become tired from your efforts. Similarly, if you stand in one place holding a 50-pound suitcase in your hand, you do no work on the suitcase, even though you soon feel worn out. The fact that we become tired when we push against a wall or hold a heavy object is due to the repeated contraction and expansion of indi- vidual cells within our muscles. Thus, even when we are “at rest,” our muscles are doing mechanical work on the microscopic level. Force at an Angle to the Displacement In FIGURE 7-3 we see a person pulling a suitcase on a level surface with a strap that makes an angle u with the horizontal—in this case the force is at an angle to the direction of motion. How do we calculate the work now? Well, instead of force times distance, we say that work is the component of force in the direction of displacement times the magnitude of the displacement.

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