Universal Physics Journal






Author: Ethan Skyler 



Purpose Article V is an investigation into the mutual force rule whereby each force, of an mutual pair of forces, is predicted to always act on a different object and therefore never do both of these mutual forces act upon the same object. For certain this popular rule places strict limits on our thoughts and therefore our understandings regarding the effect upon objects of the forces present during an event, especially an accelerational one. My goal in Article V is to determine if the mutual force rule is a valid rule. 



Article V "... the horse will be equally drawn back towards the stone; for the distended rope, by the same endeavor to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other." [1]


(2) During this stone dragging event, at
the point where the rope is attached to the horse, the horse is bearing on
the rope with a forwarddirected force that is equal in magnitude
and opposite in direction to the rearwarddirected mutual force that the
rope is bearing on the horse. The same exchange of mutual forces between objects occurs at the point where the rope
is attached to the stone. Here the rope is bearing on the stone with
a forwarddirected force that is equal and opposite to the
rearwarddirected mutual force that the stone is bearing on the
rope. At this point, when considering the forces present between two
contacting objects, the mutual force rule appears to be valid.


(3) Now consider that the mutual force from the horse that is causing the stone to slide along the ground is being transferred in a serial manner along the entire length of the rope to the stone. Just as we have located this forwarddirected force at the interface between the horse and the rope, and again at the interface between the rope and the stone, if we choose to study the rope along its entire length, we will notice, as did Newton, that the rope exhibits certain "distended" characteristics that indicate that opposing tension forces are hard at work along its strands. These characteristics are not exhibited when the tension forces in each direction are absent, allowing the rope to remain in a relaxed state. Yet, while under tension, at any point along the rope's length, the forwarddirected mutual force from the horse, being transferred back along the rope to the stone, is equally opposed by the rearwarddirected mutual force from the skidding stone, being transferred forward along the rope to the horse. Here the force from the horse and the mutual force from the stone are opposing each other when tested at any point along the same affected object, with that object being the "distended" rope.


(4) Has the mutual force rule
failed us so soon? It's prediction that mutual pairs of
forces always affect different objects definitely is not true when one
considers the forces present at any point along the "distended" rope's length that is
located between the rope's two end points. Here it is clear that the
mutual force rule only remains valid if one restricts the testing
of forces present during an event to the point of contact between two
objects. This means that in order to remain valid, the mutual force "rule" needs to be supplemented with a
second rule regarding where the mutual force rule applies and
where it does not apply and therefore, when it is valid, and when it is not valid. But
then of what real value is a "rule" that is wrong at least half of
the time?



(5) Before abandoning the mutual force rule as being a rule without merit, I want us to consider how this
rule is commonly applied during an accelerative event. Take a stone
of manageable size and using a 1/4" diameter masonry bit, drill a 1 inch deep hole
in the stone, insert
a plastic expansion plug, and screw a metal eyebolt firmly into the
stone. Test to see if the eyebolt is secure by inserting a long
screwdriver through the eye and pulling sideways on the shank of the screwdriver,
while pushing on the stone with a force equal to several times the weight of the stone. Be
prepared for the expansion plug to fail during this test. Next tie one
end of a light rope to the eyebolt and fashion a large loop in the other
end of the rope about 2 to 3 feet from the stone. Now swing the
stone in a circle about your person by pulling in a leading manner on the
loop in the rope. Once up to a comfortable speed, maintain a
constant rate of rotation for the stone. While whirling the stone in a circle, feel and think
about the mutual pairs of forces you and the stone are experiencing. Merely
reading of this event is not sufficient. It is much better to personally
perform this event to complete your experience and understanding of the
forces present, provided that you are in possession of all your limbs and
are generally in good health.


(6) A force is described in physics as a
"vector" quantity since it has both magnitude and
direction. If a force had only magnitude, it would be classified as
a "scalar" quantity such as temperature. While whirling
the stone, the mutual pairs of forces you are concerned with are the inwarddirected
forces and the outwarddirected forces. These are often referred to
as centripetal forces (center seeking) and centrifugal forces (center
fleeing). To eliminate confusion, I will use inwarddirected and
outwarddirected when referring to these forces. It is paramount
that you understand that these terms refer to nothing more than the
direction of the force. An inwarddirected force on the stone does
not mean that the stone will actually move closer to you during this
whirling event. Likewise, an outwarddirected force on the stone
does not mean that the stone will actually move farther away from
you. Inwarddirected and outwarddirected simply mean that the stone
is experiencing forces impressed in these two opposite directions relative to the
stone's axis of orbit about your person while the stone's radial
distance from this axis remains unchanged.


CAUTION (7) Perform this experiment at your own risk. Do not attempt it without wearing protective gear such as shoes, long pants, a longsleeved coat, gloves and a wellpadded motorcycle riding helmet. Do not perform this whirling event over a hard surface, such as concrete. Instead, always perform it over a soft surface such as a level grass lawn. You will experience a dizzy feeling during and after the event that could cause you to lose your balance and fall to the ground. If you think falling to the ground might cause you harm then do not perform this experiment. Instead, ask someone else to perform it while you observe. Then discuss with them the forces experienced. It is important that you ensure that observers of this event maintain a safe distance from the event should the rope be released or the stone pull loose while at speed. A distance of 60 feet should provide a good margin for safety while viewing this event.


(8) In order to accelerate the stone in an
orbital manner about your person, you will need to lead the stone with
your hand in the direction of orbit. This speeds up the stone by
providing a forwarddirected component of the inwarddirected mutual
acceleration/Action force
you are applying to the stone. Once up to speed, you will find that
only a small degree of "leading" will be required to cancel air
friction and thereby maintain the stone's speed and rate of rotation
around the circle. When you decide it is time to bring this whirling
event to an end, you will need to purposefully slow the stone's speed by
trailing it with your hand. This slows the stone's speed around the
circle by providing a backwarddirected component of the inwarddirected
force you are applying to the stone.


(9) When you have set up the whirling stone
experiment and taken all the precautions, begin whirling the stone about
your person by pulling on the rope in a leading manner. Once up to a
comfortable orbital speed, notice how you have to lean back in order to
keep from tipping forward in the direction of the stone. Also notice
that the faster the stone orbits the circle, the harder you must pull on the
stone. The inwarddirected acceleration/Action force you are
applying to the rope is predicted by Newton's absolute force formula, Force = mass * velocity ^2 /
radius. Assuming you maintain the stone at a constant radius from
the axis of orbit by lengthening your arm at the higher velocity, if you double the
stone's orbital velocity, the inwarddirected action force you must apply
to the stone will increase by the square of the stone's velocity to a
magnitude four times its former value! If you could possibly double
the stone's velocity a second time it is unlikely you could continue
providing the required inwarddirected acceleration/Action force which is now sixteen times its initial
magnitude!


(10) As you whirl the stone about your
person, is it not clear to you that your inwarddirected mutual force is
opposed by the stone's outwarddirected mutual force? The faster
you rotate, the harder you have to pull inward on your end of the rope,
the harder the stone pulls outward on its end of the rope.
Understand that this outwarddirected force from the stone is
directly proportional to the magnitude of the acceleration that the stone
is experiencing. Double the stone's orbital velocity about the
circle's axis
and the stone's rate of acceleration will increase by four times. As its
rate of acceleration increases by four times, so does its outwarddirected
acceleration/Reaction force increase by four times. This direct link
between the stone's acceleration rate and its acceleration/Reaction force
is undeniable evidence that the reaction force reflected back from the
stone is an
acceleration/Reaction force just as I predict.


(11) We do not need to look with complex thoughts to the distant stars in search of an explanation to the cause of the a/R force. We only need to look at the stone's rate of acceleration as the indicator of the magnitude of the action force that is causing the stone's acceleration, according to the formula Force = mass * acceleration, and finally to the Universal Law of Mutual Forces which tells us that the inwarddirected pull of the rope on the stone's eyebolt is exactly equal to the outwarddirected pull of the stone's eyebolt on the rope.


(12) Now you may think, at this point in our investigation, that the
mutual forces present between the rope and the eyebolt are proof that the
mutual force "rule" is indeed a valid rule. Furthermore, since these
mutual forces are acting and reacting on the different objects of the rope &
the stone's eyebolt, you may think that mutual pairs of forces always act on
different objects. Nothing could be further from the truth.
Understand that this opinion remains valid only if one never looks for
mutual forces at any other place than at the mutual point of contact between
any two objects. To purposefully limit one's analysis of mutual action
and reaction forces by only investigating the presence of mutual external
forces at mutual points of contact between objects is to purposefully limit
one's understanding of the important role mutual action and reaction forces
play in all manner of Universal events.


(13) For example, during this accelerative event, supporters of the
mutual force rule first compare the equality of the
inwarddirected acceleration/Action force the rope is applying to the
stone's eyebolt, to the outwarddirected acceleration/Reaction force the
stone's eyebolt is applying to the rope. They then use the mutual force rule to support their decision that this pair of action and
reaction forces are affecting different objects. Using this decision
as a basis, they then decide that there is but one inwarddirected force
acting on the stone, being the action force from the rope, with no force
being present that is acting or reacting in the outwarddirection on the
stone. It is in this manner that supporters of the mutual force rule use this rule in support of the "net force" theory
regarding the manner in which they think an acceleration/Action force can cause acceleration
for
matter.


(14) Here you can see how the mutual force rule provides support for the "net force"
theory of acceleration. But in practice, is this flow of logic
correct? We already know that supporters of the mutual force rule
only look at these mutual forces as being present at the mutual point of
contact between the rope and the stone's eyebolt. Since they see
these mutual forces as affecting different objects, this curious bit of
logic tells them that the inwarddirected mutual acceleration/Action force being transferred
by the rope on out to affect the stone somehow passes by the outwarddirected
mutual acceleration/Reaction force being transferred by the stone on in to affect the rope.
Accepting that the rope's mutual force has passed by the stone's mutual force at their mutual point of contact with each other, supporters of the
mutual force rule think it is logically justifiable to accept
that from this mutual point of contact outward, the inwarddirected force from the rope is free to affect the stone's matter without having to
interface with any remaining portion of the stone's outwarddirected force.
To think in this manner is to ignore the fact that no force
can ever exist without directly interfacing against an equal force (Newton's
LAW III).


(15) The "... always affect different
objects." portion of the mutual force rule is causing these
supporters to mistakenly think that once the a/A force of your pull on
the rope has passed
outward beyond the mutual point of contact between the rope and the
stone's eyebolt, this inwarddirected a/A force somehow becomes
unopposed as it causes inwarddirected acceleration for the stone.
Not only is this "unopposed" assumption false, it is counter to Newton's LAW III and the Universal Law of Mutual
Forces whereby there can exist no "unopposed forces". There is a basic misunderstanding of forces at
work here.


(16) The truth is that your inwarddirected acceleration/Action force cannot "get past" the stone's outwarddirected
acceleration/Reaction force at the mutual point of contact between the rope and the
stone's eyebolt to act in the assumed unopposed manner of a "net
force" upon the stone's matter from that point on. No, just as
at every point inward along the entire length of the rope where your
inwarddirected force is equally opposed by the stone's (and the
rope's) outwarddirected force, at every point outward beyond the
juncture between the rope and the stone's eyebolt, the remaining portion of
your inwarddirected mutual force continues to find equal support in the
remaining portions of the stone's outwarddirected mutual force.
In Article IV we have come to know this outwarddirected
mutual force as the stone's absolute
acceleration/Reaction force, or a/R force, that varies in direct proportion to the
absolute acceleration being experienced by the stone, or portions
thereof.


(17) To demonstrate how equal and opposite mutual forces are present deep within the whirling stone, suppose we divide the stone in two with the inner half remaining attached to the rope and the outer half attached to the inner half via a short closedcoil tension spring. Now, as you whirl this divided stone around in a circular orbit, neglecting the spring's matter, all should agree that as much as the stone's inner half pulls with an inwarddirected acceleration/Action force against the outer half, causing inwarddirected acceleration for this outer half, the outer half pulls with an outwarddirected acceleration/Reaction force of equal magnitude against the stone's inner half. Proof of the presence of both of these opposing forces is indicated by the "distended" tension spring. Thus all should agree that you have proved there to exist an outwarddirected force being applied to the stone's inner half by the stone's outer half. Understand that this outwarddirected force is present regardless of whether the stone is divided in two or left whole. Dividing the stone in two simply makes it easier to detect the presence of the mutual action and reaction forces that are equally present deep within the undivided stone.


Conclusion (18) Realize now that you have just proved that there is indeed an outwarddirected force bearing on the stone's inner half. This fact alone stands as proof that mutual forces, equal in magnitude and opposite in direction, are mutually present deep within the whirling, undivided stone making the "mutual force rule" every bit as invalid as the "net force" theory of acceleration. (19) The truth of the forces present in this
whirling event becomes clear when you understand that the stone's (and
rope's) acceleration/Reaction forces provide equal and opposite support for your
acceleration/Action force at any point you choose to
investigate along any of the objects in the series. Instead of looking
in a faulty manner with the thought that the acceleration/Action force somehow gets past
the acceleration/Reaction force to effect on its own an object that lies outward and beyond
the point of inspection, one needs to look at this whirling event with the
understanding that no matter where one chooses to inspect for the presence
of forces along the series of whirling objects,
the forces one finds will always be mutual pairs of forces that are equal in
magnitude and opposite in direction. This is always what will be
found, in perfect agreement with Newton's LAW III and the Universal Law of
Mutual Forces. Ethan Skyler
References




Author's Commentary 



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