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    -----------------------------------------------------------------------------*
    | --------------| A COLLECTION OF IDEAS | by Raheman Velji |
    -----------------------------------------------------------------------------*

    CONTENTS:

    (1) Inventions
    Two inventions that propel themselves using "self-suffiecient
    propultion". A third invention which is an interesting dynamo.

    (2) Law of Conservation of Energy
    A few reasons why the Law of Conservation of Energy is wrong.

    (3) Work
    Redefining work intuitively, with the knowledge that the Law of
    Conservation of Energy is wrong.

    (4) Electricity
    An attempt at explaining electricity with the knowledge of "(3)
    Work".


    * must use a fixed-size font to view diagrams properly

    -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
    -|-|-| (1) INVENTIONS -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
    -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-

    Inventions:
    1) The Seesaw Newton Motor
    2) The Simple Newton Engine
    3) The Gravitational-density Dynamo

    Devices which use "self-sufficient propulsion" work on Newton's law
    that "every action has an equal and opposite reaction." The idea is
    to harness the "action" and eliminate the "reaction", or convert the
    "reaction" into useable energy. Thus, within the device, the
    "reaction" is lost allowing the "action" to propel the device. All
    devices that use "self-suffiecient propulsion" work without affecting
    the environment. That is, they don't need a road to push off of like
    cars, they don't have to push air like planes or spew out gases like
    space shuttles. Thus, they get the name "self-sufficient propulsion"
    because they are self-sufficient. In other words, you can put a box
    around the entire device and the box would move, and nothing would
    enter or exit the box, and the device itself wouldn't react with the
    environment that comes inside the box. It only reacts to the
    environment in the box, which it creates, which it uses to propel
    itself. (I propose that any device that uses self-suffiecient
    propulsion should have the name "Newton" added to its full-name so
    that we remember how it relates to Newton's third law.)

    Whether the Seesaw Newton Motor or the Simple Newton Engine are
    feasible is uncertain. However, the idea of "self-suffiecient
    propulsion" will have a lasting effect on transportation.

    The third invention is an interesting dynamo which generates
    electricity.

    (must be read using a "fixed-size font" to view diagrams)

    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
    =-=-=-1) The Seesaw Newton Motor=-=-=-=-=-=-=-=-=-=-=-=-=
    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

    Top view:


    M1a---M2a <--front
    electromagnets
    m1
    \
    \ /\
    \ ||
    o <--seesaw ||
    \ forward
    \
    \
    m2

    M1b---M2b <--back
    electromagnets


    Ideally, "M1a", "M1b", "M2a", "M2b", "m1", "m2" are all
    electromagnets. (Some of the electromagnets can be changed into
    permanent magnets where it is deemed fit.) "M1a", "M1b", "M2a", and
    "M2b" are fastened to the base, while "m1" and "m2" are connected to a
    "seesaw" whose pivot ("o") is connected to the base. (It is possible
    to construct this without the back electromagnets.)

    The way this invention works is somewhat hard to understand. Here is
    a simplified version:

    When "M1a" and "m1" are nearly touching an electric current is sent
    through "M1a", "M1b", and "m1". "M1a" should repel "m1" while "M1b"
    should attract "m1". Thus, both "M1a" and "M1b" will experience a
    force in the forward direction, while the seesaw swings around
    bringing "m2" close to "M2a". As "M2a" and "m2" are close now, an
    electric current will pass through "M2a", "M2b", and "m2". "M2a"
    should repel "m2" while "M2b" should attract "m2". Again, the
    electromagnets connected to the base, "M2a" and "M2b", will experience
    a force in the forward direction while the seesaw swings back to its
    starting position to repeat the cycle. Since all the electromagnets
    that are connected to the base experience a force in the forward
    direction, the entire device will be propelled forward as the seesaw
    keeps swinging about. Notice that the seesaw does *not* rotate, it
    simply moves back and forth, like a seesaw.

    It should be noted that as the seesaw swings about, a bit of the
    "backward" energy of the electromagnet on the seesaw will be conveyed
    to the base via the pivot, thus slowing down the entire device. That
    loss of speed, though, is negligible.

    The above explanation of the workings of the Seesaw Newton Motor is
    incomplete. One must understand the following:

    Every action has an equal and opposite reaction. The main idea of the
    Seesaw Newton motor is to harness the "action" by converting the
    "reaction" into useable energy. When the front electromagnets and the
    electromagnet on the seesaw are activated, the front and back
    electromagnets experience a "positive" force by being forced forward.
    The electromagnet on the seesaw, however, experiences a "negative"
    force as it moves in the backward direction. One must get rid of the
    "negative" energy of the electromagnet on the seesaw. If the
    "negative" energy is not rid of, then it will somehow be transferred
    to the entire device, thus not allowing the device to gain velocity
    and move forward. The Seesaw Newton Motor does not only get rid of
    the "negative" energy, it in fact uses it to propel the device
    further. Consider the following scenario: a Seesaw Newton motor at
    rest, and set-up similar to the diagram above. Now, let us initiate a
    current through "M1a", "M1b", and "m1". The electromagnets on the
    base ("M1a" and "M1b") will experience a "positive" force by being
    forced forward. The electromagnet on the seesaw ("m1"), however, will
    experience a "negative" force by being forced backward. However, at
    the other end of the seesaw, the electromagnet ("m2") seems to be
    approaching the front electromagnet ("M2a") and receding from the back
    electromagnet ("M2b"). Thus, at the other end of the seesaw, when
    those electromagnets are activated, the repulsive force between the
    electromagnet on the seesaw and the front electromagnet will be
    greater, thus propelling the device further forward. Also, at the
    other end of the seesaw, when those electromagnets are activated, the
    attractive force between the electromagnet on the seesaw and the back
    electromagnet will be greater, again propelling the device further
    forward. The fact that both magnets ("M2a" and "M2b") experience a
    greater forward force is due to the the initial "negative" energy of
    the electromagnet ("m1"). Thus, both the "action" and the "reaction"
    are harnessed to propel the entire device forward.

    If both "action" and "reaction" are to be harnessed, one must ensure
    that the electromagnets on the seesaw should not hit either the front
    electromagnets or the back electromagnets. That is because if, as the
    seesaw swings, "m1" hits "M1b" or "m2" hits "M2b", then the collision
    will slow the forward motion of the entire device. It may seem that
    if the seesaw swings so hard that "m1" hits "M1a" or "m2" hits "M2a"
    then the force of the collision will cause the base to experience a
    force in the forward direction. This is wrong. Only the "forward
    momentum" of the seesaw will "push" the base forward. However, when
    the seesaw hits the front electromagnets, the entire seesaw will stop
    moving and the "backward momentum" of the electromagnet on the seesaw
    will be conveyed to the base via the pivot. Thus, such collisions are
    undesirable.

    One must avoid collisions by ensuring that the electromagnets are
    activated such that the seesaw never has a chance to collide. Thus,
    input sensors would need to be used to calculate the speed of the
    seesaw so that the electromagnets can be perfectly timed to avoid
    collisions. By avoiding collisions, both "action" and "reaction" are
    harnessed.

    Notice that for this invention to actually move, the electromagnets
    must be very strong and the entire device must be light. Otherwise,
    the device will stay in the same spot and just wiggle about instead of
    moving. In any case, this invention can definetely compete with
    devices that use ion propulsion.

    Also, the entire Seesaw Newton Motor can (with a battery) be put into
    a box and the box would move without interacting with the environment
    outside the box. Thus, it moves using "self-sufficient propulsion".

    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
    =-=-=-2) The Simple Newton Engine-=-=-=-=-=-=-=-=-=-=-=-=
    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

    The Simple Newton Engine works using "self-sufficient propulsion".

    The engine is a cylinder with a piston in it. The piston may require
    wheels to move inside the cylinder.


    STEP 1:
    \-----------\-----------\-----------\-----------\
    Every action has an equal and opposite reaction. The main idea of the
    Simple Newton Engine is to harness the action by getting rid of the
    reaction. How do we get rid of the momentum of the reaction? One way
    is by using friction, which is discussed in "Step 3".

    The idea is to force the piston in the backward direction, down the
    cylinder. Since every action has an equal and opposite reaction, the
    cylinder will then experience a force in the forward direction. This
    force is ideally created by using electromagnets. Let us say that
    there is an electromagnet on the piston ("#") which repels the magnet
    ("X") that is connected to the front of the cylinder. (Also, one
    could make this similar to a Linear Induction Motor, with the piston
    as the projectile.)

    Side-view (cross-section):

    | ___cylinder
    | ||
    | \/
    |/-------------
    || #X| <--magnet ("X") forward -->
    |\-------------
    | /\
    | ||__piston ("#")
    |
    |<--start
    /-----------/-----------/-----------/-----------/

    STEP 2:
    \-----------\-----------\-----------\-----------\
    Now, activate the electromagnet on the piston. Thus, the piston,
    which is repelled by the magnet, moves down the cylinder, as the
    magnet and the cylinder accelerate forward.

    | ___ The magnet and the cylinder
    | || move forward...
    | \/ -->
    | /-------------
    | | # X|
    | \-------------
    | /\ <--
    | ||__ ...as the piston moves backward
    | through the cylinder
    |<--start
    /-----------/-----------/-----------/-----------/

    STEP 3:
    \-----------\-----------\-----------\-----------\
    In fractions of a second, the piston will have arrived at the back of
    the cylinder. The piston must be stopped before it slams into the
    back of the cylinder because, if it does, then the energy of the
    piston will cancel out the forward velocity that the cylinder has
    gained. So, the energy of the piston must be removed (by friction,
    e.g. brakes on the wheels) or harnessed (a method which converts the
    "negative" energy of the piston into something useable).

    If friction is used to stop the piston, the friction must cause the
    piston to lose velocity in decrements; should the brake make the
    piston stop abruptly, then the "negative" momentum of the piston will
    be transferred to the cylinder. Consider the following analogy: if
    I'm on a bike and I stop abrubtly by pushing down hard on my brakes, I
    (my body) will go hurtling forth until I hit a wall. In the presence
    of gravity, I might hit the ground before I hit a wall, but the point
    remains the same. However, if I push on my brakes and slowing come to
    a stop, I can avoid being thrown forward. And moreover, by coming to
    a stop slowing, the momentum of me and the bike is dissipated as heat,
    and perhaps sound. Thus, in the Simple Newton Engine the "reaction"
    is lost due to friction (as heat and possibly sound) while the
    "action" is harnessed to propel the cylinder forward.

    |
    |
    |
    | /-------------
    | | # X|
    | \-------------
    | /\
    | ||__The piston must be stopped before
    | it hits the back of the cylinder
    |<--start
    /-----------/-----------/-----------/-----------/

    STEP 4:
    \-----------\-----------\-----------\-----------\
    When the piston has reached the end, and has been brought to a stop,
    it must then be moved to the front of the cylinder, perhaps by hooking
    it to a chain which is being pulled by a motor. Perhaps the piston
    can slowly move back on its wheels towards the front of the cylinder.
    Or perhaps the piston can be removed from the cylinder when it is
    being transferred to the front, and thus leave the cylinder free so
    that another piston can "shoot" through the cylinder.

    |
    |
    |
    | /-------------
    | |# X|
    | \-------------
    |
    |
    |
    |<--start
    /-----------/-----------/-----------/-----------/


    Return to STEP 1:
    \-----------\-----------\-----------\-----------\
    The piston has been returned to the front. Overall, the engine has
    moved and gained velocity. Now it is ready to restart at STEP 1.

    |
    |
    |
    | /-------------
    | | #X|
    | \-------------
    |
    |
    |
    |<--start
    /-----------/-----------/-----------/-----------/

    Also, like the Seesaw Newton Motor, the entire Simple Newton Engine
    can (with a battery) be put into a box and the box would move without
    interacting with the environment outside the box. Thus, it uses
    "self-sufficient propulsion".

    --------------------------------------------------
    Magnetic Propulsion for the Simple Newton Engine:

    Cross-section:

    mmmmmmmmmmmmmmmmmmmm
    mmmmm ____ mmmmm <-- "m" are magnets
    mmmm /WWWWWW\ mmmm
    mmm /W/ \W\ mmm
    mm /W/ mm \W\ mm
    m W mmmm W m <-- "W" is a wire coil
    m |W| mmmmmm |W| m
    m |W| mmmmmm |W| m
    m W mmmm W m X forward
    mm \W\ mm /W/ mm (into paper)
    mmm \W\____/W/ mmm
    mmmm \WWWWWW/ mmmm
    mmmmm mmmmm
    mmmmmmmmmmmmmmmmmmmm

    If the magnets "m" are arranged such that the field is perpendicular
    to the wire, and if a current is set up in the wire coil, then the
    wire coil will either move forward or backward. This could be applied
    to the Simple Newton Engine. The wire coil would be the "piston" and
    the magnets would be part of the "cylinder".


    --------------------------------------------------
    It should be noted that the Simple Newton Engine creates a small
    amount of force for a relatively minute amount of time. In my mind,
    it would only be effective if many are used simultaneously. For
    example, I imagine that it wouldn't be too hard for the Simple Newton
    Engine to have a burst of 5N for a tenth of a second. Building a unit
    of ten thousand of such Newton engines would create a combined force
    of 5000N, assuming that the engines can "reload" in 0.9 seconds. The
    real problem is getting a good force-to-mass ratio (acceleration); if
    you can get acceleration greater than 10 m/s² then you can pretty much
    launch any vehicle, no matter how massive, into space. If the vehicle
    is too massive, then all you need to do is add more individual engines
    to the unit, and eventually it should lift off the ground. If such
    high accelerations cannot be made, then I'm sure this invention can
    compete with ion propulsion.

    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
    =-=-=-3) The Gravitational-density Dynamo-=-=-=-=-=-=-=-=
    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

    Here is the general idea of the Gravitational-density Dynamo:

    First, an object (the object could be a liquid) on the ground is
    inserted into a tall tube which contains a fluid which is more dense
    than the object. Also, the object should be insoluble in the fluid.
    Due to the density difference, the submerged object is displaced
    upwards. When the object reaches the top, it is removed from the tube
    and is dropped. Due to the force of gravity, it will fall. The
    energy of the falling object will somehow be harnessed to create
    electricity. Once the object has reached the ground, it must be
    reinserted back into the tube to repeat the process. (Notice that the
    tube should be as tall as possible so as to maximize the amount of
    energy of the object when it falls.)

    When I first conceived this idea I figured the object would be a log
    of wood, and the fluid would be water. In the following section, I
    will examine a Gravitational-density Dynamo that uses water as the
    object and perfluorooctane as the fluid.

    -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
    -|-|-| (2) LAW OF CONSERVATION OF ENERGY |-|-|-|-|-|-|-|-|-|-|-|-
    -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-


    ---------------------------------------
    Here is a specific, and perhaps practical, version of the
    Gravitational-density dynamo. (The workings of the
    Gravitational-density dynamo was described in the previous section.)


    _________________________
    | |
    semi- __\ |___ _________________ |
    permeable / | | | |
    material | |
    (dialysis | | |
    tubing) | | |
    | | |
    | | ------*------ <--\
    | | | |
    | | | turbine
    | | |
    tube B --> | |
    (contains | | | |
    perfluoro- | | | |
    octane) | | | |
    | | | | <-- tube A
    | | | | (contains
    | |_________________| | water)
    | | |
    |____________|____________|

    /|\
    \_ semi-permeable
    material
    (dialysis
    tubing)


    Tube A contains water. Tube B contains perfluorooctane. Tube A
    and tube B are connected to each other by dialysis tubing, which is a
    semi-permeable material. Water can permeate through the dialysis
    tubing, but perfluorooctane can't. Due to osmotic pressure, the water
    in tube A will pass through the dialysis tubing entering tube B.
    Since perfluorooctane is insoluble in water, and since water is less
    dense than perfluorooctane, the water will rise to the top of tube B.
    The water that has risen will permeate through the dialysis tubing at
    the top of tube B. Once enough water has accumulated at the top of
    tube B, it will fall, turning the turbine, and returning back into
    tube A.

    Notice that this dynamo didn't require any input energy, and it
    will continue to work, creating electricity by turning the turbine
    (and generator, which is not shown), so long as the perfluorooctane
    does not seep into tube A through the semi-permeable material.
    Eventually, the perfluorooctane will seep through the dialysis tubing,
    and so, this invention is not a perpetual motion machine.

    But how can this dynamo generate electricity without any input
    energy? First, let's observe that the water at the top of tube B has
    a gravitational potential energy. When it falls, the gravitational
    potential energy is realized and is converted into electricity by the
    turbine (and generator, which is not shown). But how did the water
    initially get its gravitational potential energy? It got its
    gravitational potential energy from being displaced in a fluid
    (perfluorooctane) that is more dense than it. Thus, we must conclude
    that insoluble objects in fluids that are more dense gain
    gravitational potential energy by being displaced upwards. However,
    where is that energy coming from? By the Law of Conservation of
    Energy, something must lose energy so that another can gain energy.
    Since we cannot find anything losing energy, we must conclude that the
    Law of Conservation of Energy is wrong, and that gravity creates
    forces which then create/destroy energy; in this case it created
    energy in the final form of electricity.

    Energy is being created/destroyed all around us. Gravity and
    magnetism are prime examples. Both create forces. The immediate
    effect of the forces on the system is nothing (the vectors of the
    forces cancel each other out). However, after the immediate effect,
    and after a minute amount of real time, the forces will do work on the
    system. If "positive work" is done, then the system will gain energy.
    If "negative work" is done, then the system will lose energy.
    Whether energy seems to be added to the system or removed depends on
    your inertial frame of reference. Should these forces be sustained
    for a longer duration of real time, then the forces might be found to
    have not done any work on the system (that is, it added the same
    amount of energy that was removed).

    ---------------------------------------
    Suppose we have two magnets with like-charges "q" and "q0". The
    space between the two charges is "r". Let the potential energy
    between the charges be "U". So,

    1 q*q0
    U = ------ ------
    4*pi*E r

    where pi = 3.14
    E is the permittivity of free space

    As the two magnets are moved closer to each other, potential
    energy will be gained and kinitic energy will be lost. As the two
    magnets move away from each other, potential energy will be lost and
    kinitic energy will be gained.

    Say, initially, that both magnets are far apart. Now, let us do
    work by moving the charges closer together. When we are done, and the
    magnets are close to each other, the potential energy will have
    increased. The increase will be equivalent to the work we did.

    Now, let's say that we took two hammers and pounded both magnets
    until they lost their magnetism. Then, the potential energy between
    the two magnets will dissappear. Thus, the system has lost energy
    without any part of the system gaining energy. Thus, we have
    demonstrated that the Law of Conservation of Energy is wrong.

    Let me recap: First, we did work to move two repelling magnets
    together. Thus, we lost energy, while the magnets gained potential
    energy. We then destroyed the magnetism of the magnets, thus losing
    the potential energy. Thus, all-in-all, we lost energy.

    This idea, which works on magnetism, can also be applied to
    gravity.

    Consider two stationary gaseous planets, both made entirely of
    deutrium. Let's move them apart from each other. That is, let's do
    work on the planets, thus increasing the gravitational potential
    energy between the planets. The increase in gravitational potential
    energy will be equivalent to the amount work we did separating the
    planets.

    Now, let's say that the deutrium of both planets began to fuse by
    the following equation:

    deutrium atom + deutrium atom => helium atom + neutron + 3.27 MeV
    (from http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)

    (It is true that I didn't include the initial energy to start the
    fusion. However, the above equation is properly balanced, so we do
    not have to consider the initial energy required.)

    Now, it is obvious that mass is being converted into energy.
    Since the mass of both planets are decreasing, the gravitational
    potential energy between both planets will also decrease. Thus, the
    work we did moving the planets apart will diminish. Thus, we have
    again demonstrated the Law of Conservation of Energy is wrong.

    Let me recap: First, we did work be moving the two planets
    apart. Thus, we lost energy, while the planets gained gravitational
    potential energy. We then converted some of the mass of the planets
    into energy. Thus, in the process, we lost gravitational potential
    energy. Thus, all-in-all, we lost energy.

    -\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-
    -|-|-| (3) WORK -|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-
    -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-


    -------
    Once one has realized that energy is not conserved, the big
    question that arises is how did something so obvious allude us, and
    for so long. The answer to that has many reasons. One reason is that
    we did not define work intuitively. I will now attempt to rectify
    that.


    -------
    First, let's realize that force has two equations, or rather,
    that it can be observed in two different ways. First, there is
    "general force":

    f_g = pA

    where f_g is general force
    p is pressure
    A is area

    And then there is "effective force":

    f_e = ma

    where f_e is effective force
    m is mass
    a is acceleration

    Thus, effective force is general force which is allowed to "change
    motion". (By change motion, I mean that the force is allowed to
    increase/decrease velocity (unhindered by other forces).)


    -------
    Consider the following scenario: two classmates, Jack and Jill,
    both able to hold a one-kilogram brick. Naturally, holding that brick
    on Earth is approximately equivalent to maintaining a force of 10
    Newtons. Let's say that Jack held his brick for 20 seconds, and Jill
    held her brick for 2 seconds. Now, without using any scientific
    jargon, who did the most work? Jack obviously did more work than
    Jill. Thus, intuitively, work should equal force multiplied by time.


    -------
    Notice, that this means that work done on an object does not
    necessarily have to change motion. On the contrary, even if you
    placed a book on a table, work is being done; the table is maintaining
    a force, and likewise, the book is maintaining a force. The force of
    gravity between the two is causing stress at the atomic level. Work,
    in general, does not require a change in velocity. Thus, I call the
    following the equation for "general work":

    W_g = f_g*t

    where W_g is general work
    t is a period of time

    Now, there are two definitions of general work; one is a verb, the
    other is a noun. The verb general work is force multiplied by time.
    The noun general work is the *result* of general work (verb). In
    other words, the process of general work (verb) causes general work
    (noun) to be accomplished.

    Of course, as with force, there is also a "effective work". Effective
    work is general work which is allowed to change motion. So, take the
    term "f_g" and make it effective, that is, change it into "f_e". And
    thus:

    W_g = f_g*t
    W_e = f_e*t
    = ma*t

    where W_e is effective work

    And since in Newtonian physics

    v = a*t

    where v is velocity

    we can simplify the equation for effective work to the following:

    W_e = mv

    In Newtontonian physics, momuntum is equal to "mv".

    Now, there are also two definitions of effective work; one is a verb,
    the other is a noun. The verb effective work is general work which is
    allowed to change motion. The noun effective work is the *result* of
    general work (verb) which is allowed to change motion. In other
    words, the process of effective work (verb) causes effective work
    (noun) to be accomplished.

    Thus, effective work (verb) causes a change in momentum and effective
    work (noun) equals the change in momentum.


    -------
    I concede that I do not know how general work and effective work
    are changed when they are considered in Relativistic terms.


    -------
    I propose that the real unit for work (that is, general work,
    which is force multiplied by time) should be "P", for Prescott,
    Joule's middle name. Thus, one prescott equals one newton second. I
    relegate the old, traditional meaning for work to the term "productive
    work".


    -------
    Now, work defined as it is today (productive work) is wrong
    intuitively, but nonetheless, it is a *VERY* *USEFUL* "measuring
    tool". It calculates "useful" work, where usefulness is defined as
    causing an object (I use that term very loosely) to be displaced in a
    certain direction. Power calculates the rate at which this "useful"
    work is happening.


    ---------
    Now let me clarify the vocabulary I have used here:

    * "change motion": Allowing a force to increase/decrease velocity
    (unhindered by other forces)

    * "General work" (or just "work") (calculated in prescotts):
    In Newtonian physics "=f*t"

    * "Effective work" (calculated in prescotts):
    In Newtonian physics "=mv"

    * "Productive work" (calculated in joules):
    In Newtonian physics "=f*s" where "s" is displacement

    * "Useful/Useless work": Any work can be considered useful or useless
    depending on the situation.

    You may be asking, "Why allow general work to be called "work"
    for short, instead of allowing that short form to indicate "effective
    work" or "productive work"?" I kept it that way because "general
    work" is a more general term compared with the other two terms. It's
    kind of like how a comedian put it, "Why is it 'corn on the cob' and
    'corn'? Instead, it should be 'corn' and 'corn off the cob'." Of
    course, one could use the short-form "work" to indicate either
    "general work", "effective work" or "productive work" by its use in
    context.
    ---------

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    Now, I am going to apply work using prescotts on an electrical
    circuit.

    ***************************
    Let's find the average drift velocity:
    -------------------------
    A is the cross-section of the wire (m²)
    n is "free" electrons per unit volume (electrons/m³)
    e is the magnitude of charge of an electron
    (1.602 * 10^(-19) C/electron)
    v is the average drift velocity of the electrons (m/s)
    I is the current in the wire (C/s)
    dq is an infinitesimal amount of charge (C)
    dt is an infinitesimal amount of time (s)
    dN is an infinitesimal number of electrons (electrons)
    -------------------------
    (1) dq = e*dN

    dN = nAv*dt
    (2) dt = dN/(nAv)

    (1)/(2) dq/dt = e*dN/(dN/nAv)
    I = enAv
    v = I/(enA)

    ***************************
    Let's find force:
    -------------------------
    W_j is the Work in Joules (N*m)
    f is the force (N)
    s is the distance (m)
    V is the voltage (N*m/C)
    -------------------------
    W_j = F*s
    dW_j = F*v*dt
    dW_j/dt = F*v
    V*I = F*v

    V*I
    F = -----
    v

    = VenA

    -------------------------
    P is pressure (Pa)
    -------------------------
    F
    V = ---
    enA

    P
    = --
    en

    So we can say that "voltage is the electromagnetic-pressure (created
    by an EMF source) per density of charge."

    Notice that the pressure supplied by an EMF has nothing to do with the
    length of the circuit. A battery hooked to a 1-meter circuit of 1cm²
    wire uses the same pressure to start a current as a similar battery
    hooked to a 10000-meter circuit of similar wire!

    ***************************
    -------------------------
    W_i is the Initial Work (in Prescotts) (N*s)
    (the work done to start the electrical circuit)
    t is a duration of time (s)
    m_e is the mass of an electron (9.109 * 10^(-31) kg/electron)
    -------------------------
    W_i = F*t
    = VenA*t

    Notice that in this case "W_i" does not equal "m_e*v". This is
    because over the period of time "t", which is greater than the average
    change in time between electron collisions, the acceleration of the
    electron is hindered when the electron loses its energy during a
    collision.


    ***************************
    -------------------------
    U is Initial Work (in Prescotts) per Coulomb (N*s/C)
    Q is an amount of charge (C)
    p is the resistivity of the wire (ohm*m)
    l is the length of the wire (m)
    -------------------------
    U = W_i/Q
    = F/I
    = (VenA)/(V/R)
    = enAR
    = enA*(p*l/A)
    = enpl

    Thus, we can say that "U" is a constant for any given circuit. So,
    given any circuit, a constant amount of work is done to move a coulomb
    along the circuit.


    ***************************
    -------------------------
    µ is Initial Work (in Prescotts) per Coulomb*meter (N*s/(C*m))
    -------------------------
    µ = dU/dl
    = enp

    So, the rate at which work is done per unit distance depends on the
    material.

    ***************************
    -------------------------
    t_c is the change in time between electron collisions (s)
    -------------------------

    Each electron gains "m_e*v" of energy before it makes a collision and
    losses it's energy. The collision will take place in "t_c" seconds.
    "U" is the amount of work to move a coulomb "l" meters along the wire.
    And, in "l" meters, there will be "l/(v*t_c)" number of collisions.
    So,

    l m_e*v
    ----- * ----- = U
    v*t_c e

    l*m_e
    ------- = enpl
    t_c*e

    m_e
    t_c = ----
    e²np


    which is correct.

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    by Raheman Velji
    November 7, 2004

    you can also view this (and updated versions) at...
    ....http://www.angelfire.com/un/rv
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