Overview
Energy is generally a difficult subject for many nonscience students because it is an abstract concept. This chapter begins with the more easily visualized concepts of work and power, develops two general aspects of energy (position and motion) based on concepts learned in previous chapters, and then uses these aspects as a basis for a conceptual scheme for understanding energy. This scheme is then applied in considering the energy sources used today.
Work and energy are closely related concepts. Work is defined in this chapter by using the second class of equations (defining a concept; see chapter 1). Work is defined as the product of a force moving through a distance, or W = Fd. Both metric units and English units are presented because both are in everyday use today. The metric unit of work is the newton-meter, which is called a joule. The English unit of work is the foot-pound, which does not have another name. Along with learning the scientific meaning of work, students will need to become accustomed to using the terms in the sense of work accomplished or the potential for doing work, for example, “How much work was done on . . .?” and “How much work can the object now do?”
The energy of position, or potential energy, can be measured by how much work is done on an object to give it energy of position or by how much work it can now do because of its position. Since work involves forces and movement through a distance, the variables involved are the force, the movement (acceleration = change of motion), and the mass of the object (a measure of inertia, or resistance to a change of motion). Thus a non-calculus calculation of potential energy can begin with Newton’s second law of motion, or F = ma. To obtain an expression of work, both sides of this equation are multiplied by distance, h (for height, which is a vertical distance), which gives Fd = mah. For gravitational potential energy, the acceleration is g and the relationship is W = mgh or PE = mgh. The potential energy unit turns out to be joules, which is the same unit used to do work to create the potential energy to begin with. Thus from this analysis comes the first idea that work = energy = work, or that both are fundamentally the same thing.
The energy of motion, or kinetic energy, can also be measured by how much work is done on an object to give it energy of motion or by how much work it can now do because of its motion. Again, work involves forces and movement through a distance such as is involved in throwing a baseball. The non-calculus relationship again involves the variables in Newton's second law of motion, F = ma. As before, both sides are multiplied by distance to obtain an expression of work, which in this case is the energy of motion, and KE = mad. Now we need to put the distance quantity (d) in terms of a final velocity (vf) for kinetic energy. This requires the use of the first three equations presented in chapter 2:
The kinetic energy unit turns out to be a joule, which is the same unit used to do the work to create the kinetic energy to begin with. Again you can see that work = energy = work, that is, both energy and work are fundamentally the same thing.
The similarities between energy and work are discussed throughout the presentation of the energy flow scheme. Note that many textbooks define heat as a form of energy rather than energy in transit between two forms. Either definition is correct. Considering heat as a form of energy, however, is a conceptual level akin to considering a dog as the animal that lives across the street.
Energy is generally a difficult subject for many nonscience students because it is an abstract concept. This chapter begins with the more easily visualized concepts of work and power, develops two general aspects of energy (position and motion) based on concepts learned in previous chapters, and then uses these aspects as a basis for a conceptual scheme for understanding energy. This scheme is then applied in considering the energy sources used today.
Work and energy are closely related concepts. Work is defined in this chapter by using the second class of equations (defining a concept; see chapter 1). Work is defined as the product of a force moving through a distance, or W = Fd. Both metric units and English units are presented because both are in everyday use today. The metric unit of work is the newton-meter, which is called a joule. The English unit of work is the foot-pound, which does not have another name. Along with learning the scientific meaning of work, students will need to become accustomed to using the terms in the sense of work accomplished or the potential for doing work, for example, “How much work was done on . . .?” and “How much work can the object now do?”
The energy of position, or potential energy, can be measured by how much work is done on an object to give it energy of position or by how much work it can now do because of its position. Since work involves forces and movement through a distance, the variables involved are the force, the movement (acceleration = change of motion), and the mass of the object (a measure of inertia, or resistance to a change of motion). Thus a non-calculus calculation of potential energy can begin with Newton’s second law of motion, or F = ma. To obtain an expression of work, both sides of this equation are multiplied by distance, h (for height, which is a vertical distance), which gives Fd = mah. For gravitational potential energy, the acceleration is g and the relationship is W = mgh or PE = mgh. The potential energy unit turns out to be joules, which is the same unit used to do work to create the potential energy to begin with. Thus from this analysis comes the first idea that work = energy = work, or that both are fundamentally the same thing.
The energy of motion, or kinetic energy, can also be measured by how much work is done on an object to give it energy of motion or by how much work it can now do because of its motion. Again, work involves forces and movement through a distance such as is involved in throwing a baseball. The non-calculus relationship again involves the variables in Newton's second law of motion, F = ma. As before, both sides are multiplied by distance to obtain an expression of work, which in this case is the energy of motion, and KE = mad. Now we need to put the distance quantity (d) in terms of a final velocity (vf) for kinetic energy. This requires the use of the first three equations presented in chapter 2:
The kinetic energy unit turns out to be a joule, which is the same unit used to do the work to create the kinetic energy to begin with. Again you can see that work = energy = work, that is, both energy and work are fundamentally the same thing.
The similarities between energy and work are discussed throughout the presentation of the energy flow scheme. Note that many textbooks define heat as a form of energy rather than energy in transit between two forms. Either definition is correct. Considering heat as a form of energy, however, is a conceptual level akin to considering a dog as the animal that lives across the street.