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3-1. The Meaning of Work
  1. Work equals force times distance.

    W = Fd

    1. When a force is applied to an object, the object must move a distance or no work is done.
    2. When the force is not parallel to the distance d, the projection of the force in the direction of d must be used to find the work.
    3. No work is done when a force is perpendicular to the direction of motion of an object.
  2. The SI unit of work is the joule.

    1 joule (J) = 1 newton-meter (N · m)

  3. Work done against gravity is represented by:

    W = mgh

    where W = work, mg = mass times the acceleration of gravity (9.8 m/s2), and h = total height.
3-2. Power
  1. Power is the rate at which work is being done:
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    where P = power, W = work, and t = time.
  2. The SI unit of power is the watt.

    1 watt (W) = 1 joule/second (J/s)

  3. The kilowatt (kW) is a convenient unit of power for many applications.
3-3. Kinetic Energy
  1. Energy is that property something has that enables it to do work.
  2. The energy of a moving object is called kinetic energy (KE):
    where m = mass and v = speed.

    KE = ½mv2

    1. Since KE is the product of mass and the square of the speed, the greater the mass and/or speed the greater the KE.
    2. KE increases very rapidly with speed because of the v2 factor.
3-4. Potential energy
  1. Potential energy (PE) is the energy an object has by virtue of its position.
  2. The amount of work an object performs as it moves toward the earth under the influence of gravity is its gravitational potential energy:

    PE = mgh

    where m = mass, g = acceleration of gravity (9.8 m/s2), and h = height.
  3. The gravitational PE of an object is a relative quantity because it depends on the level from which it is reckoned.
3-5. Energy Transformations
  1. All forms of energy can be transformed or converted from one form to another; most events in the physical world involve energy transformation.
  2. Energy exists in a variety of forms. Some forms other than kinetic and potential include:
    1. Chemical energy
    2. Heat energy
    3. Electric energy
    4. Radiant energy
3-6. Conservation of Energy
  1. The law of conservation of energy states that energy cannot be created or destroyed, although it can be changed from one form to another.
  2. Matter can be considered as a form of energy; matter can be transformed into energy and energy into matter according to the law of conservation of energy.
3-7. The Nature of Heat
  1. Heat was once thought to be a weightless, invisible, odorless, and tasteless substance called caloric.
  2. James Prescott Joule was the first to demonstrate conclusively that heat is energy.
3-8. Linear Momentum
  1. Linear Momentum is a measure of the tendency of a moving object to continue in motion along a straight line:

    p = mv

    where p = linear momentum, m = mass, and v = velocity.
  2. The greater an object's linear momentum, the harder it is to change the object's velocity, that is, its speed and/or direction of motion.
  3. The law of conservation of momentum states: In the absence of outside forces, the total momentum of a set of objects remains the same no matter how the objects interact with one another.
3-9. Rockets
  1. The operation of a rocket is based on conservation of momentum.
    1. The momentum of the exhaust gases is balanced by the rocket's upward momentum.
    2. The total momentum of the entire system is zero.
  2. Multistage rockets are more efficient than single-stage, and so are widely used.
3-10. Angular Momentum
  1. Angular momentum is a measure of the tendency of a rotating object to continue spinning about a fixed axis; conservation of angular momentum is the description of the tendency of spinning objects to remain spinning.
    1. The greater the mass of an object and the more rapidly it rotates, the greater its angular momentum.
    2. The angular momentum of a spinning object also depends upon how its mass is distributed; the farther away from the axis of rotation its mass is distributed, the more the angular momentum.
3-11. Special Relativity
  1. Albert Einstein (1879-1955) published the special theory of relativity in 1905.
  2. Special relativity is based on two postulates:
    1. The laws of physics are the same in all frames of reference moving at constant velocity.
    2. The speed of light (c) in free space has the same value for all observers (c = 3 x 108 m/s)
  3. According to the special theory of relativity, when there is relative motion between an observer and what is being observed, lengths are observed to be shorter than when at rest, time intervals are observed to be longer, and masses are observed to be greater.
  4. Nothing material can travel as fast or faster than the speed of light.
3-12. Rest Energy
  1. The rest energy of a body is the energy equivalent of its mass:

    EO = mOc2

    where EO = rest energy, mO = rest mass, and c = speed of light.
  2. Rest energy is liberated in all energy-producing reactions of chemistry and physics.
3-13. General Relativity
  1. Einstein published the general theory of relativity in 1916, which related gravitation to the structure of space and time and showed that even light was subject to gravity.
  2. Einstein spent the last years of his life unsuccessfully trying to join together the phenomena of gravitation and electromagnetism into a "unified field theory."
3-14. The Energy Problem
  1. Except for nuclear energy and heat energy from within the earth, all available energy is directly or indirectly derived from the sun.
  2. Coal, oil, and natural gas are called fossil fuels because they were formed from the remains of organisms that lived millions of years ago.
  3. The use of fossil fuels presents several disadvantages.
    1. Oil and natural gas reserves will last about another century.
    2. Although coal reserves will last several hundred more years, mining coal is dangerous, and burning coal creates environmental problems such as acid rain, air pollution, and enhanced global warming.
  4. Nuclear energy presents both advantages and problems.
    1. Nuclear fuel reserves exceed those of fossil fuels, especially with the development of "breeder" reactors.
    2. Properly built and run nuclear power plants are excellent energy sources.
    3. The potential for a large-scale nuclear accident is present.
    4. Discharge of radioactive wastes into the environment from badly run nuclear power plants has occurred.
    5. An unsolved disposal problem of radioactive nuclear waste exists.
3-15. The Future
  1. Nuclear fusion represents a potentially safe, nonpolluting, and inexhaustible energy source; however, the problem is how to manage until nuclear fusion arrives.
  2. Alternate energy sources, such as solar energy, present various technical and environmental problems; some are not economically feasible.
  3. Wise use of alternate energy sources, conservation of energy, and a slowdown in human population growth are necessary to avoid disaster until nuclear fusion becomes a reality.

The Physical Universe, 11eOnline Learning Center

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