Working through this chapter of the study guide will enable you to:

1. Understand how work and energy are defined.
2. Perform calculations using the concepts of work, energy, and power.
3. Differentiate among the various types of energy, and tell how they are alike and how they differ.
4. Deal with the conservation of energy law and understand its importance in the overall scheme of physical science.
5. Determine the amount of power required to do a certain amount of work in a given period of time.
6. Describe the uses and sources of energy in the United States today.

Discussion

Work and energy are important topics that influence our everyday lives. How many times have you heard conversations start like this? "How are things going at work?" or "I was sick last week, and I just don't seem to have much energy anymore." Every time you drive a car, turn on an electric light, or even just get up out of a chair, you are doing work and using energy. The first two references to work and energy presented above are not well-defined ones in the physical sense, but if you really want to know how much work it takes to accelerate your car from rest to 50 mph or how much energy it takes to get up out of a chair, you will be able to find out after you have studied the material in this chapter.

First, we must learn the technical definitions of the terms work, energy, and power. Work is defined as the applied force times the parallel distance through which the force is applied. Don't let this bias your thinking. There are other ways to calculate work. Later in the chapter, work is discussed as the change in energy that occurs when some physical process takes place. This is typical of many concepts in physical science. There are often several ways that a given quantity can be calculated, and in certain situations (or problems), one method is usually much easier to apply than another. Just remember, any of the appropriate methods can be used, and the results will be the same in all cases if you apply them correctly.

Power is defined as the amount of work done per unit time. Power is calculated by dividing the amount of work done by the time interval during which the work was completed. Because time is involved in this concept, the amount of work done can be the same, but the power exerted must be greater if that work is done in a shorter time interval. That is why a sprinter must have more powerful legs than a long-distance runner. The sprinter must attain top speed in a short time period, hence the need for powerful leg muscles, while the long-distance runner must have more stamina to maintain a lower level of work output for a much longer interval of time.


Section   4.1Work

Using its most basic definition, work can be calculated by multiplying the unbalanced force acting on an object by the parallel distance through which that force is applied. Notice that no work is done if no motion takes place or when no component of the motion is parallel to the direction of the applied force. Even though vector quantities are used in these calculations, work is itself a scalar quantity. This means that no specific direction is associated with work. In SI units, work is expressed in newton-meters. This set of the derived units is given a special name, the joule. In the British system, the unit of work is the foot-pound (ft-lb).

When work is done against friction, as when a large box is pushed across a rough floor, some of its energy is dissipated as heat. Work is also done when a massive body is accelerated to a higher speed, or for that matter, when one is slowed down. Such an acceleration is referred to as doing work against inertia. Lifting an object requires that we exert an upward force equal to the object's weight, so as we lift an object, work is being done against gravity. In these cases, we must do work on the object by applying a force through some parallel distance to change either its height above Earth's surface, or its velocity, or its position. A second way to calculate the amount of work being done is to determine the change in energy of the object under study. It is important to remember that there are often several ways to solve a problem, and both "force times distance" and "change in energy" should be considered when choosing how to calculate the amount of work that is being done in any particular physical situation.


Section   4.2Kinetic Energy and Potential Energy

Many kinds of energy exist, such as heat energy, nuclear energy, solar energy, mechanical energy, and so forth. We will study some of these later in the course, but in this chapter we concentrate on mechanical energy, which can be further divided into two main types known as kinetic energy and potential energy.

Kinetic energy (E_k) is the energy of motion. Any object of mass possesses a kinetic energy equal to ¹/₂ mv² when it is moving with a velocity v. In our discussions, the mass will normally remain constant, so we can simply say that as a general rule, the faster an object is moving, the more kinetic energy it possesses. Because the velocity is squared in this calculation and mass can never have a negative value, E_k is always a positive quantity. As you know, it is necessary for your car's engine to do work to make your car speed up. This leads us to the conclusion that one way a change in kinetic energy can be accomplished is when work is done on an object.

The second kind of mechanical energy is potential energy (E_p). Potential energy is stored energy that is often related to the position of an object. When we change the vertical height (h) of an object near Earth's surface, we must do work against gravity. We can then define gravitational potential energy in equation form as E_p = wh = mgh, where w is the weight of the object and h is the vertical height. Remember from Chapter 3 that the weight and mass of an object are related to each other. When the object is near Earth's surface, we can calculate the object's weight by using the equation w = mg. Raising an object requires that work be performed on it, and lifting the object gives it an increase in its potential energy. This means that once again work must be done to change the energy, in this case the potential energy. Dropping an object releases some work and, therefore, decreases its potential energy. Once a reference level is chosen where h is set equal to zero, an object will have a positive E_p if it is located at a height above this level and a negative E_p if it is below this reference level.


Section   4.3Conservation of Energy

When no work is done on a system, there can be no change in its total mechanical energy. For our purposes we define total mechanical energy as the sum of an object's kinetic and potential energies. Even though under this condition the total mechanical energy must be conserved, energy can change form. As an example, kinetic energy can be converted into potential energy, and vice versa, but the sum of the two (total mechanical energy) will not change unless outside work is done on the system. The law of conservation of mechanical energy is very powerful and is explained in detail in Section  4.3 of the textbook. This is an important concept, so look it over very carefully. Remember, when no external work is done on the system, the total energy of that system will always be conserved, even though energy may change form in the process and this may lead to difficulties in tracking these changes or even in determining just what types of energy are present. Nevertheless, in many cases the changes in energy can be carefully traced from one form to another, and in the process much can be learned by applying the ideas of energy conservation to real physical situations.


Section  4.4Power

Completing work always requires a certain amount of time. The rate at which work is done is known as power. The faster a certain amount of work is performed, the more power is required. A sports car and an economy sedan can each transport you up a steep hill, but because of its more powerful engine, you expect your trip to be concluded in a much shorter time when in the sports car than when you are driving in the sedan.

Once you have calculated the amount of work, as outlined in Sections 4.1 and 4.2, you can divide the work by the amount of time that it takes to complete it. Such a calculation gives you the power expended. In SI units, power is expressed in watts (W). Because power is equal to work/time, 1 W = 1 J/s. In the British system the unit of power is the ft-lb/s. A larger unit for power is the horsepower (hp), where one horsepower is defined such that 1 hp = 550 ft-lb/s = 746 W.


Section   4.5Forms and Sources of Energy

Energy comes in several different forms. In this chapter, we are dealing with two types of mechanical energy, kinetic energy and potential energy. We are also studying why conservation of energy is one of the most powerful computational tools available to us in physical science. The study of the various forms of energy will not end when we complete this chapter. Chapter 5 deals with heat energy, and later in the course, we will apply the concept of energy to stretched springs, as well as to nuclear processes, electricity, and other physical phenomena.

All of these kinds of energy are important in our everyday lives and nearly all of them come, either directly or indirectly, from nuclear reactions in the core of our Sun. Once solar energy is received by Earth, it is not easily lost, but it is possible to waste energy by not using it efficiently. Energy usually cannot be recovered once it has been converted into waste heat through inefficient processes that produce thermal pollution. Because the energy available to us is limited, it is important that we learn how we can best utilize it. This Section, together with some later chapters in the textbook, gives a good basis for the understanding required to produce well-informed citizens who can behave responsibly in our energy-intensive world.

Both work and energy are calculated from vector quantities but are themselves scalar in nature. This often makes them much easier to deal with because we do not need to worry about the direction associated with them, as we had to do when dealing with force or momentum. We must, however, still be careful to specify the correct units for each quantity and to remember to follow the rules for rounding and for significant figures when formulating our answers.

Remember that there are several new derived units to learn when dealing with the concepts of work and power. The joule (newton-meter) and the foot-pound are used for work and the watt (joule/s) and horsepower apply to our calculations of power. In the British system, new terms for combinations of units are not as common as in the SI, so power is simply expressed in foot-pounds/second. Horsepower is often used in both systems of units when larger amounts of power are being considered.

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