The Science of Energy
The so-called fundamental quantities in the study of motion (mechanics) are usually taken to be distance, mass, and time, from which the other concepts can be derived or intuitively rationalized; velocity, acceleration, force, and momentum. Each of these helps to describe motion and to understand the cause-andeffect relationships in motion. However, these quantities still do not provide a complete understanding of motion.
Recall the arguments about colliding bodies that led us to the concept of momentum, or quantity of motion. The cannonball striking the rock wall redistributes its momentum to the rocks of the wall, and they are set into motion. But momentum does not account for the destructive capabilities of the cannonball. For example, if we double the velocity of the cannonball, we find that it doubles the impulsive force necessary to set the stones into motion but has fou r ti mes the destructive capability. So the concept yet needed is that of energy. No concept in science is more important than that of energy and its conservation principle.
Defining Energy
The historical development of the concept of energy was long and laborious. It took more than 150 years
m the first attempts at quantitative formulation, by the Dutch contemporary of Galileo, Descartes, and ewton, Christian Huygens (1629-1695), to the point, which the appropriate terminology was established. In general, energy does not have properties like those atter, such as size, shape, and color. Also unlike matter, it cannot in general be said to occupy space. Nevertheless, matter is but one more manifestation of energy so that we must qualify our statements by saying "in general.
How then do we define this somewhat abstract concept? We can say that energy is a measure of the of a physical system to perform work when the system undergoes a change. ("Change" implies that we should be able to describe the system accurately before and after in order to be able to say that it has changed.) Yet change alone is not a sufficient means of defining energy: As human beings, we are physical systems, but changing our feelings for other human beings does not perform work. A genuine example of energy is what happens when a stream turns a waterwheel as it flows over a dam; the stream performs work on the waterwheel, which rotates a grindstone, which grinds grain. The energy of the stream is a measure of the ability of the stream to perform useful work
Although energy does not in general have the properties of matter, it can be measured and quantified. One unit used by astronomers is the erg, the amount of energy needed to accelerate a mass of 1 gram at a rate of 1 centimeter per second squared as it moves a distance of 1 centimeter.
Conservation of Energy
The most important of all physical laws is the law of conservation of energy:
LAW OF CONSERVATION OF ENERGY: Energy may be neither created nor destroyed but only transformed from one form to another.
Motion involves mechanical energy, which has two forms: one is kinetic energy, and it is the energy a body has because of its state of motion; the other form is potential energy, and it is the energy a body has because of its position in a field of force. A stone at the top of a hill, for example, can be said to have energy by virtue of its position in the earth's gravitational field. If it is pushed, the stone will roll down the hill, converting potential energy to kinetic energy.
We commonly refer to such other forms of energy as chemical energy and electrical energy. We can also understand these forms in terms of kinetic and potential energy; but in most of this book we shall be less specific about it and just say "energy." The form of energy with which we are most concerned in astronomy is radiant energy. The important point to remember throughout is that the conversion of energy from one form to another does not create energy or destroy energy.
TRANSPORT OF ENERGY: WAVES
Energy can be moved from place to place, and thus it must be transported in some form. Waves are one way of transporting energy. What is a wave? It is the transport of a disturbance; that is, a wave is a disturbance that moves. How does this account for the transport of energy? Imagine that two people several feet apart hold the ends of a rope; when one jiggles the rope, a wave will travel from one end to the other. No particles are moving from one end of the rope to the other, but a disturbance is traveling along it. We know that energy is transported by the disturbance since, when the distu rbance arrives, the receivi ng hand is jiggled. That is, the wave in the rope does work on the hand, giving it kinetic energy. Another example of a wave is the disturbance that propagates across the surface after a stone is dropped into a pond. A Wave can thus be defined as a disturbance capable of transferring energy from one place to another.
To understand waves better, consider how scientists describe them quantitatively. The distance between successive crests or troughs is called the wavelength. The number of complete cycles of the disturbance passing a fixed point per second is called the frequency. The speed of the waves the distance it travels per unit of time; this is just the length of each wave (its wavelength) multiplied by the number of waves passing a fixed point per unit of time (its frequency). Thus the speed of the wave is the product of its wavelength and frequency. The last quantity used to describe a wave is its amplitude. This is the greatest height the crests reach or the greatest depth to which the troughs fall. The greater the amplitude, the more energy the wave transports from one to another. In fact, the energy of the wave is measured by the amplitude squared.
Waves are one means of transporting energy but, as we have mentioned, not the only one: The collision of bodies is another way to transfer energy and thus transport it from one place to another. The best common example of this process is the behavior of atoms and molecules in a gas. Therefore let us next focus the ssion of motion on the world of the atom.
