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4.1 energy: the capacity to do work Energy and Energy Transformations Without light and other radiant energies that come to us from the Sun, life on Earth would not exist. With these energies, plants can grow and the oceans and atmosphere can maintain temperature ranges that support life. Although energy is difficult to define comprehensively, a simple definition is that energy is the capacity to do work. The word energy comes from the Greek prefix en, which means “in,” and ergos, a Greek word which means “work.” Thus, when you think of energy, think of what work is involved. For example, energy must be supplied to a car’s engine in order for the engine to do work in moving the car. In this case, the energy may come from burning gasoline. Forms of Energy heat: the transfer of energy from a warmer body or region to a cooler one It took many years for scientists to develop a system of classifying the various forms of energy. Table 1 lists nine forms of energy and describes them briefly, and Figure 1 shows examples of these forms. Notice in Table 1 and Figure 1 that eight of the energy forms listed involve particles (atoms, molecules, or objects). The other form is radiant energy. Visible light and other types of radiant energy belong to the electromagnetic (e.m.) spectrum. Components of the electromagnetic spectrum have characteristics of waves, such as wavelength, frequency, and energy, and they all can travel in a vacuum at the speed of light, 3.00 108 m/s. (Refer to section 9.1 to review the e.m. spectrum.) Notice also that heat is not listed as a “form” of energy. Heat is the transfer of energy from a warmer body or region to a cooler one. Various methods of heat transfer are described later. In this chapter, we focus on gravitational potential energy, kinetic energy, and thermal energy, which will be defined formally in the appropriate sections. Later in the text, you will study more about the other forms listed. Table 1 Several Forms of Energy Form of energy Description Example thermal The atoms and molecules of a substance possess thermal energy. The more rapid the motion of the atoms and molecules, the greater the total thermal energy. Figure 1(a) electrical This form of energy is possessed by charged particles. The charges can transfer energy as they move through an electric circuit. Figure 1(a) radiant Radiant energy travels by means of waves without requiring particles of matter. Figure 1(b) nuclear potential The nucleus of every atom has stored energy. This energy can be released by nuclear reactions such as nuclear fission and nuclear fusion. Figure 1(b) gravitational potential A raised object has stored energy due to its position above some reference level. Figure 1(c) kinetic Every moving object has energy of motion, or kinetic energy. Figure 1(c) elastic potential This potential energy is stored in objects that are stretched or compressed. Figure 1(c) sound This form of energy, produced by vibrations, travels by waves through a material to the receiver. Figure 1(d) chemical potential Atoms join together in various combinations to form many different kinds of molecules, involving various amounts of energy. In chemical reactions, new molecules are formed and energy is released or absorbed. Figure 1(d) 124 Chapter 4

4.1 (a) (b) (d) (c) Figure 1 Examples of forms of energy (a) Electrical energy delivered to the stove heats the water in the pot. Thermal energy in the boiling water transfers to the pasta to cook it. (b) The Sun emits radiant energies, such as infrared radiation, visible light, and ultraviolet radiation. The Sun’s energy comes from nuclear fusion reactions in its core. (c) At the highest position above the trampoline, this athlete has the greatest amount of gravitational potential energy. The energy changes to kinetic energy as her downward velocity increases. The kinetic energy then changes into elastic potential energy in the trampoline to help her bounce back up. (d) Chemical potential energy is released when fireworks explode. Some of that energy is changed into sound energy. What other forms of energy are involved in this example? Practice Understanding Concepts 1. Give three examples of energy use available today that your grandparents would not have had when they were your age. 2. Name at least one form of energy associated with each object in italics. (a) A bonfire roasts a marshmallow. (b) A baseball smashes a window. (c) A solar collector heats water for a swimming pool. (d) A stretched rubber band is used to launch a rolled-up T-shirt toward the audience during intermission at a hockey game. (e) The siren of an ambulance warns of an emergency. Energy Transformations The forms of energy listed in Table 1 are able to change from one to another; such a change is called an energy transformation. For example, in a microwave oven, electrical energy transforms into radiant energy (microwaves), which is then transformed into thermal energy in the food being cooked. Undoubtedly you can give many other examples of energy transformations. We can summarize these changes using an energy transformation equation. For the microwave oven example described above, the equation is energy transformation: the change from one form of energy to another electrical energy radiant energy thermal energy Energy, Work, Heat, and Power 125

Practice Understanding Concepts 3. Write the energy transformation equation for each example below. (a) Fireworks explode. (b) An arrow is shot off a bow and flies through the air. (c) A paved driveway feels hot on a clear, sunny day. (d) A camper raises an axe to chop a chunk of wood. (e) A lawn mower with a gasoline engine cuts a lawn. 4. Make up an example of an energy transformation involving the creation of your favourite sounds. Then, write the corresponding energy transformation equation. SUMMARY Energy and Energy Transformations Energy is the capacity to do work. Energy exists in many forms, such as thermal energy and kinetic energy. In an energy transformation, energy changes from one form into another. The transformation can be described using an equation with arrows. Section 4.1 Questions Understanding Concepts 1. Show how energy is transformed for each situation by using an energy transformation equation. (a) A hotdog is being cooked at an outdoor concession stand. (b) A truck is accelerating along a level highway. (c) A child jumps on a trampoline. (d) A tree is knocked over by a strong wind. (e) An incandescent light bulb is switched on. work: the energy transferred to an object by an applied force over a measured distance 2. Provide an example (not yet given in this text) of a situation that involves the following energy transformations. (a) electrical energy thermal energy (b) kinetic energy sound energy (c) chemical potential energy thermal energy (d) electrical energy kinetic energy 4.2 Figure 1 The work done in pulling the carts, which are locked together, depends on the force applied to the carts and the distance the carts move. 126 Chapter 4 Work The term work has a specific meaning in physics. Work is the energy transferred to an object by an applied force over a measured distance. For example, work is done when a crane lifts a steel beam for a new building, when a truck’s engine makes the truck accelerate, when an archer bends a bow as the arrow is pulled back, and when the bow releases the arrow. However, when holding a heavy box on your shoulder, you may feel pain and even break into a sweat, but you are not doing any work on the box because you are not moving it. To determine what factors affect the amount of work done in moving an object, consider a situation in which an employee at a grocery store pulls a long string of empty carts at a constant velocity with a horizontal force (Figure 1).

4.2 By fixing the distance that the carts are moved and doubling the applied force required to pull the carts (by adding twice as many carts), the amount of work done is doubled. Similarly, with a constant applied force, if the distance the carts are pulled is doubled, then again the work done is doubled. Thus, the work done by the applied force is directly proportional to the magnitude of the force and directly proportional to the magnitude of the displacement (distance) over which the force acts. Using the symbols W for work, F for the magnitude of the applied force, and d for the magnitude of the displacement, the relationships among these variables are W F and W d Combining these proportionalities, joule: (J) the SI unit for work W F d W kF d where k is the proportionality constant Choosing the value of k to be 1, we obtain the equation for work: W F d Notice that work is a scalar quantity; it has magnitude but no direction. Therefore, vector notations for F and d are omitted. The equation W F d has important limitations. It applies only when the applied force and the displacement are in the same direction. (In more complex situations where two-dimensional motion is analyzed, the equation that is used is W F d (cos v), where v is the angle between the applied force and the displacement.) Since force is measured in newtons and displacement is measured in metres, work is measured in newton metres (N m). The newton metre is called the joule (J) in honour of James Prescott Joule, an English physicist who studied heat and electrical energy (Figure 2). Since the joule is a derived SI unit, it can be expressed in terms of metres, kilograms, and seconds. (Recall that the newton, the unit of force, can also be expressed in these base units: 1 N 1 kg (m/s2).) You will gain a lot of practice with the joule, kilojoule, megajoule, etc., for the rest of this chapter and in other parts of this course. Sample Problem 1 An airport terminal employee is pushing a line of carts at a constant velocity with a horizontal force of magnitude 95 N. How much work is done in pushing the carts 16 m in the direction of the applied force? Express the answer in kilojoules. Solution F 95 N d 16 m W ? W F d (95 N)(16 m) W 1.5 103 J Figure 2 The joule is named after James Prescott Joule (1818 – 1889), owner of a Manchester brewery, who showed that heat was not a substance but, instead, the transfer of energy. He found that thermal energy produced by stirring water or mercury is proportional to the amount of energy transferred in the stirring. DID YOU KNOW ? Joules and Calories Although the joule is the SI unit of energy and work, we still hear of the heat calorie (cal), a former unit of heat, and the food calorie (Cal), a former unit of food energy. These units are related in the following ways: 1.000 Cal 1.000 103 cal 1.000 kcal 1.000 cal 4.184 J 1.000 Cal 4.184 kJ Thus, a piece of apple pie with 395.0 Cal contains 1.652 106 J, or 1.652 MJ, of chemical potential energy. The work done in pushing the carts is 1.5 kJ. Energy, Work, Heat, and Power 127

Practice Understanding Concepts Answers 1. A farmer uses a constant horizontal force of magnitude 21 N on a wagon and moves it a horizontal displacement of magnitude 3.2 m. How much work has the farmer done on the wagon? 1. 67 J 4. 1.8 103 N 2. Express joules in the base units of metres, kilograms, and seconds. 5. 0.73 m 3. Rearrange the equation W F d to express (a) F by itself and (b) d by itself. 6. 12 J 4. A tow truck does 3.2 kJ of work in pulling horizontally on a stalled car to move it 1.8 m horizontally in the direction of the force. What is the magnitude of the force? F (N) 20 5. A store clerk moved a 4.4-kg box of soap without acceleration along a shelf by pushing it with a horizontal force of magnitude 8.1 N. If the employee did 5.9 J of work on the box, how far did the box move? 10 6. Determine the area under the line on the graph shown in Figure 3. What does that area represent? Applying Inquiry Skills 0 0.2 0.4 0.6 d (m) Figure 3 You can analyze the units on this forcedisplacement graph to determine what the area calculation represents. (Only magnitudes are considered.) (a) the system diagram Positive and Negative Work In the examples presented so far, work has been positive, which is the case when the force is in the same direction as the displacement. Positive work indicates that the force tends to increase the speed of the object. However, if the force is opposite to the direction of the displacement, negative work is done. Negative work means that the force tends to decrease the speed of the object. For example, a force of kinetic friction does negative work on an object. Thus, W F d yields a positive value when the force and displacement are in the same direction, and yields a negative value when the force and displacement are in opposite directions. Sample Problem 2 A toboggan carrying two children (total mass 85 kg) reaches its maximum speed at the bottom of a hill, and then glides to a stop in 21 m along a horizontal surface (see Figure 4(a)). The coefficient of kinetic friction between the toboggan and the snowy surface is 0.11. (a) Draw an FBD of the toboggan when it is moving on the horizontal surface. (b) Determine the magnitude of kinetic friction acting on the toboggan. (c) Calculate the work done by the kinetic friction. (b) the FBD FN FK Fg mg 7. (a) Consider a constant force applied to an object moving with uniform velocity. Sketch a graph of the work (done on the object) as a function of the magnitude of the object’s displacement. (b) What does the slope of the line on the graph represent? Solution (a) The required FBD is shown in Figure 4(b). (b) m 85 kg g 9.8 N/kg Figure 4 For Sample Problem 2 128 Chapter 4 mK 0.11 FK ?

4.2 FK mKFN mK F g mKm g (0.11)(85 kg)(9.8 N/kg) FK 92 N The kinetic friction has a magnitude of 92 N. (c) W F d (92 N)(21 m) W 1.9 103 J The work done by the kinetic friction is –1.9 103 J because the force of friction is opposite in direction to the displacement. Practice Understanding Concepts 8. A student pushes a 0.85-kg textbook across a cafeteria table toward a friend. As soon as the student withdraws the hand (the force is removed), the book starts slowing down, coming to a stop after moving 65 cm horizontally. The coefficient of kinetic friction between the surfaces in contact is 0.38. (a) Draw a system diagram and an FBD of the book as it slows down, and calculate the magnitudes of all the forces in the diagram. (b) Calculate the work done on the book by the friction of the table. Answers 8. (a) Fg 8.3 N; FN 8.3 N; FK 3.2 N (b) –2.1 J Work Done Against Gravity In order to lift an object to a higher position, a force must be applied upward against the downward force of gravity on the object. If the force applied and the displacement are both vertically upward and no acceleration occurs, the work done by the force against gravity is positive, and is W F d. The force in this case is equal in magnitude to the weight of the object or the force of gravity on the object, F F g m g . Sample Problem 3 A bag of groceries of mass 8.1 kg is raised vertically without acceleration from the floor to a countertop, over a distance of 92 cm. Determine (a) the force needed to raise the bag without acceleration (b) the work done on the bag of groceries against the force of gravity Solution (a) m 8.1 kg g 9.8 N/kg F ? m g F F g (8.1 kg)(9.8 N/kg) F 79 N The force needed is 79 N. Energy, Work, Heat, and Power 129

(b) d 0.92 m W ? W F d (79 N)(0.92 m) W 73 J The work done against the force of gravity is 73 J. Practice Understanding Concepts Answers 9. (a) 1.5 N (b) 2.9 J 10. (a) 2.5 103 N (b) 2.6 102 kg 11. 9.1 m 9. A 150-g book is lifted from the floor to a shelf 2.0 m above. Calculate the following: (a) the force needed to lift the book without acceleration (b) the work done by this force on the book to lift it up to the shelf 10. A world-champion weight lifter does 5.0 103 J of work in jerking a weight from the floor to a height of 2.0 m. Calculate the following: (a) the average force exerted to lift the weight (b) the mass of the weight 11. An electric forklift truck is capable of doing 4.0 105 J of work on a 4.5 103 kg load. To what height can the truck lift the load? Zero Work Situations exist in which an object experiences a force, or a displacement, or both, yet no work is done on the object. If you are holding a box on your shoulder, you may be exerting an upward force on the box, but the box is not moving, so the displacement is zero, and the work done on the box, W F d, is also zero. In another example, if a puck on an air table is moving, it experiences negligible friction while moving for a certain displacement. The force in the direction of the displacement is zero, so the work done on the puck is also zero. In a third example, consider the force exerted by the figure skater who glides along the ice while holding his partner above his head (Figure 5). There is both a force on the partner and a horizontal displacement. However, the displacement is perpendicular (not parallel) to the force, so no work is done on the woman. Of course, work was done in lifting the woman vertically to the height shown. Practice Understanding Concepts Figure 5 If the applied force and the displacement are perpendicular, no work is done by the applied force. 12. A student pushes against a large maple tree with a force of magnitude 250 N. How much work does the student do on the tree? 13. A 500-kg meteoroid is travelling through space far from any measurable force of gravity. If it travels at 100 m/s for 100 years, how much work is done on the meteoroid? 14. A nurse holding a newborn 3.0-kg baby at a height of 1.2 m off the floor carries the baby 15 m at constant velocity along a hospital corridor. How much work has the force of gravity done on the baby? 15. Based on questions 12, 13, and 14, write general conclusions regarding when work is or is not done on an object. 130 Chapter 4

4.3 SUMMARY Work Work is the energy transferred to an object by an applied force over a distance. If the force and displacement are in the same direction, the work done by the force, W F d, is a positive value. If the force and displacement are in opposite directions, the work done is a negative value. Work is a scalar quantity measured in joules (J). Section 4.2 Questions Figure 6 An off-road dump truck Understanding Concepts 1. An average horizontal force of magnitude 32 N is exerted on a box on a horizontal floor. If the box moves 7.8 m along the floor, how much work does the force do on the box? 2. An elevator lifts you upward without acceleration a distance of 36 m. How much work does the elevator do against the force of gravity to move you this far? 4. A camper does 7.4 102 J of work in lifting a pail filled with water 3.4 m vertically up a well at a constant speed. (a) What force is exerted by the camper on the pail of water? (b) What is the mass of water in the pail? 5. In an emergency, the driver of a 1.3 103-kg car slams on the brakes, causing the car to skid forward on the road. The coefficient of kinetic friction between the tires and the road is 0.97, and the car comes to a stop after travelling 27 m horizontally. Determine the work done by the force of friction during the skidding. 6 F (N) 3. An off-road dump truck can hold 325 t of gravel (Figure 6). How much work must be done on the gravel to raise it an average of 9.2 m to get it into the truck? 8 4 2 0 0.1 0.2 0.3 d (m) 0.4 Figure 7 For question 7 6. For the equation W F d, describe (a) when the equation applies (b) when the equation yields a nil or zero value of work Applying Inquiry Skills 7. The graph shown in Figure 7 was generated by a computer interfaced to a force sensor that collected data several times per second as a block of wood was pulled with a horizontal force across a desk. (a) Estimate the work done by the force applied to the block. Show your calculations. (b) Describe sources of systematic error when using a force 4.3 Mechanical Energy A constant change our society experiences is tearing down old buildings to make way for new ones. One way to do this is by chemical explosions. However, if that is considered to be too dangerous, a much slower way is to use a wrecking ball (Figure 1). What energy transformations allow such a ball to destroy a building? Figure 1 Several principles of mechanics are applied in the demolition of this large structure. Can you write the energy transformation equation for this situation? Energy, Work, Heat, and Power 131

Energy and Energy Transformations Energy is the capacity to do work. Energy exists in many forms, such as thermal energy and kinetic energy. In an energy transformation, energy changes from one form into another. The transformation can be described using an equation with arrows. 4.2 Work The term work has a specific meaning in physics.

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