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When a hovercraft accelerates, it builds up kinetic energy. When approaching a steep landing area, the kinetic energy is often more effective than the propeller or fan thrust in helping the hovercraft to climb the landing. In the hovercraft’s engine, chemical energy stored in the fuel is converted to other forms of energy that allow the hovercraft to lift and to propel itself along the ground. Understanding energy is the key to understanding the Universe.
Energy, as you have learned, is the capacity of a system to do work. Another definition of energy is that energy is the amount of heat a system can exchange with its environment. Heat is defined as the transfer of energy between objects due to temperature differences. The astute reader has no doubt observed a degree of circularity within these definitions. Scientists understand a great deal about the forms and behavior of energy, yet no one has been able to define exactly what energy is. However, scientists usually can tell what aspects of a given situation involve energy in an active role.
There are three types of energy: kinetic energy, potential energy, and energy contained in a field of some kind.
The kinetic energy of an object is the energy with which it is moving, and the idea was first developed by the German physicist, mathematician, and philosopher Gottfried Leibniz. He believed that the fundamental quantity of motion was equal to the product of the mass and the square of the velocity, and that this quantity could not increase or decrease. Leibniz named this quantity vis viva, or living force. This theory directly opposed the accepted scientific view of the time as supported by René Descartes and Isaac Newton, which stated that the basic conserved quantity of motion was momentum, the product of mass and velocity. It is interesting to note that while the scientists of the time, who were known as natural philosophers, were debating which was the appropriate quantity, engineers were using Leibniz’s formula – because it worked. The current formulation of kinetic energy is different from Leibniz’s by a factor of 1/2, giving the present formulation as 1/2 × m × v2. You will recognized the old Cartesian quantity as momentum, which it is still useful in many physical situations because momentum is always conserved in physical interactions, while kinetic energy can be converted to other forms of energy. As you might expect, linear kinetic energy, like the other linear quantities, has a rotational equivalent. The formula for this rotational kinetic energy is identical in form to the linear one, with the appropriate counterparts to mass and velocity. This gives the formula 1/2 × I × ω2.
Potential energy exists in a number of different forms. You will recall that three of these forms are gravitational, elastic, and chemical potential energy. Two other forms of potential energy are electrical potential energy and rest mass energy. Gravitational potential energy is based on the mass of an object and the distance of that object from a reference point. Gravitational potential energy is meaningful only in that it represents a capacity to change in position — there is no inherent potential energy in an object. What this means is that you can choose the point of reference to be whatever you want, since a constant offset will vanish when the two potential energies are subtracted to get the difference. Common reference points are the center of the Earth, the surface of the Earth, and infinity. Elastic potential energy can be determined from Hooke’s Law, because it is based on the difference between the length of the elastic material being measured and its natural length. Chemical potential energy is energy stored when chemical bonds are formed and released when they are broken again. Since it is the principle behind fossil fuels, chemical potential energy provides much of the energy used by modern society. Since chemical potential energy is based on mass, it is similar to gravitational potential energy, but different in that it uses temperature difference rather than height difference and the specific heat of the material rather than a general gravitational constant. Electrical potential energy is similar to gravitational potential energy, but is based on charge and electrical constants rather than the masses of objects and Newton's gravitational constant. The electrical potential energy per unit charge in a system is the electric potential, or voltage. As is the case with gravitational potential energy, it is the difference between two states that matters, so the most convenient reference point may be chosen for any given situation. The form of potential energy known as rest mass energy is based on relativity and states that matter is basically an extremely dense form of energy. This energy is released in nuclear reactions and, in very small quantities in laboratory experiments, antimatter reactions. The energy released is based on the change in the mass of the system and the square of the speed of light. The speed of light is a large number, so the square of the speed of light is very large. This means that a small amount of mass can be converted to a large amount of energy.
Formulae for the five different forms of potential energy are listed in the following table:
| Form | Equation | ||
|---|---|---|---|
| Gravitational | Ugravitational = − G ×
m1 × m2 / r or Ug = m × g × h as a special case on Earth | ||
| Elastic | Uelastic = 1/2 × k × x2 | ||
| Chemical | Uchemical = m × ΔT × specific heat | ||
| Electrical |
| ||
| Rest Mass | E = mc2 |
The third category of energy, the energy of a field, is similar to potential energy in that it stores energy to be used at some time. The primary fields in which energy is stored are electric fields and magnetic fields. The energy density of these fields is given by equations. In an electric field, the energy density is equal to 1/2 × ε0 × E2; in a magnetic field the energy density is equal to 1/2 × B2 / µ0. E represents the electric field strength (N/C [lb/C]) and B represents the magnetic field strength (T). The energy in the field is the product of the space in which the energy is being measured and the energy density of the field. The quantities ε and µ represent the permittivity and permeability of free space, respectively. The permeability of free space is 4π × 10-7 N/A2 [2.83 × 10-7 lb/A2 ]. The permittivity is 1/(c2 × µ0) s4A2/(m3kg) [0.00024 / (c2 × µ0) s4A2/(in3slug)], where c is the speed of light in a vacuum (exactly 299 792 458 m/s [118 028 290 71.46 in/s]). These factors exist so that the SI can correctly describe quantities the formulas of which were far too simple in the cgs system.
There are numerous methods by which energy can be changed in position, character, or basic type. A simple method is to use a fixed pulley or symmetrical first-class lever to change the direction of the total kinetic energy of the system. When a weight falls toward the ground, gravitational potential energy is converted to kinetic energy directed toward the ground. Consider a situation where the weight falls and hits the elevated end of a lever, causing the other end of the lever to rise and stretch a spring attached to the end of the lever and to the ground. We can follow the energy conversions here:
Note that all the steps, except the first step, occur simultaneously.
All the forms of energy in the above sequence have one thing in common — the objects involved have energy by virtue of either motion or position. These forms are often collectively called mechanical energy. Transformations can also occur between mechanical energy and other types of energy. For example, the turbine in an electrical power plant converts mechanical energy, whether from wind, steam, water, or some other source, into electrical energy. The thrust system in a hovercraft converts the chemical energy in the fuel to forward kinetic energy. It is important to note that when energy is converted from one form into another in energy transformations, some of the energy is lost. The amount of energy lost can range from the small loss due to frictional heating, to the large amount of energy lost in an engine as it produces heat, noise, and vibration. As additional sources of energy loss are produced, less energy is transferred to the thrust of a hovercraft. In fact, the typical energy conversion efficiency of a hovercraft may be as little as 14%
Frequent transformations of energy occur when an object vibrates or oscillates. The object may be a weight hanging from a spring; a Foucault Pendulum swinging back and forth, or a hovercraft undergoing a phenomenon known as skirt bounce, which causes the hovercraft to bounce up and down. In this situation, the system converts between kinetic and potential energy repeatedly with a certain frequency, where the sum of the two is always equal to an unchanging total. When the oscillator is at either end of its motion, the kinetic energy is zero and the potential energy is equal to the total energy of the system. At the midpoint of the motion, the potential energy is zero and all the mechanical energy of the system is in the kinetic energy.
In transformations of energy, there is always a total amount of energy in a closed system, and that amount cannot increase or decrease. This conservation of energy is one of the fundamental principles of physics, since everything in the universe is either matter or energy and relativity says that matter is just another form of energy. On a more mundane scale, it allows people to trace the operation of machines and other devices and to design them to perform tasks effectively, taking into account the transformations and losses in their operation. If a cart rolls down a hill, the potential energy from gravity is converted into the kinetic energy of the cart moving; sound from the squeaky wheels; heat from parts rubbing against one another; slight deformations of the wheel (and surface); kinetic energy from air being pushed aside; as well as into any number of effects with magnitudes that can range from too small to measure to larger than the conversion from potential to kinetic energy. The ratio of the energy in the final state of a series of transformations, to the initial energy of a system, is the efficiency of the machine through which the energy transformations were effected. Remember that the efficiency of a machine is given as the ratio of the work output of the machine to the work put in. The work-energy theorem states that when work is done on a system, the work done is equal to the change in the kinetic energy of the system. This is why the efficiency of the machine can be calculated using energy or by calculating work.
When engines convert fuel to energy, a high-efficiency engine will convert as much of the energy content of the fuel as is possible into thrust, lift, electrical generation, or whatever other function is desired. Another important aspect is the energy density of the fuel itself, but do not confuse this with the energy density of an electric or magnetic field. The energy density of a fuel is the energy that can be extracted from it through appropriate processes. For example, 1 kg [0.0685 slug] of coal can produce 24 MJ [22.748 Kbtu] of energy; gasoline can produce 45 MJ/ kg [622.65 Kbtu/slug]; and hydrogen can produce 130 MJ/kg [1798.81 Kbtu/slug]. The high energy density of hydrogen seems to indicate that it would be a great fuel source because it takes less of it to produce the same amount of energy produced by more conventional sources. Keep in mind, however, that hydrogen has a very low mass density at normal temperatures, which means that it must be stored at either very high pressure, at low temperature, or in very large tanks (or any combination thereof) to be a practical fuel source. Conventionally produced hydrogen requires more energy to produce than it can release, but it is still a good method of energy transport. Another reference is the energy content of food: fats can release 37.7 MJ/kg [521.654 Kbtu/slug] of energy, while proteins and carbohydrates release 16.8 MJ/kg [232.46 Kbtu/slug]. Fuels burning in engines, as well as foods being metabolized by organisms, undergo the same chemical process of combining with oxygen to release energy. Another method by which energy can be released from certain materials is nuclear energy production. The energy density of uranium when used in a nuclear reactor is 560 000 MJ/kg [7748.71 Mbtu/slug]. This difference in the energy density occurs because the energy produced comes from different forms of potential energy. For hydrogen, fossil fuels, and food, the energy is stored in chemical bonds and released via chemical reactions. The nuclear reaction is based on the rest mass energy of subatomic particles in the uranium nucleus (or the nucleus of other fissionable material). The masses involved are small, but the c2 factor more than compensates for that. If a safe, compact, lightweight, durable, and powerful nuclear reactor were developed, then atomic hovercraft would be practical. Due to the principle of conservation of energy, all of the energy in the fuel is released (except for the parts that are not involved in the reaction due to the design of or leaks in the mechanism). Most of this energy is converted to heat, sound, and vibration, but it is not destroyed.
Energy is strongly related to other physical quantities. In mechanics, the quantities of velocity, acceleration, force, work, and power all relate to energy in some form. Velocity, you will recall, is one of the two defining terms in kinetic energy (KE = 1/2 m v2). The relation between work and energy has been discussed — work is a change in the kinetic energy of an object. Since power is the amount of work done in a certain amount of time, it also represents the rate at which energy is transformed in a system. Force is the mechanism by which mechanical energy is transformed, since the change in the kinetic energy of a body is equal to the work, the product of the force and the distance over which the force must operate in order to effect that change in energy. Acceleration, being the quantity directly changed by force for a certain mass, is thus related to mechanical energy.
Quiz Questions:
1. Can mass be converted into energy? How?
2. If mass can be converted into energy, doesn't that violate the Law of Conservation of Energy?
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