| Topic: |
Science > Physics |
| User: |
"Don1" |
| Date: |
09 Sep 2005 07:16:34 AM |
| Object: |
The relativity of displacement |
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another. The
symbols l, s, and d are used by various texts, more or less
indiscrimatly to signify displacements of any kind, regardless of how
they are caused.
I've made an effort to diffentiate them with l for inertial
displacement; s for forced displacement, and d for their sum; so that l
+ s = d, and since motion is a unit of displacement per a unit of time
t: l/t + s/t = d/t.
The first law of physics describes inertial displacement - a distance
(l) - of a body moving relatively through empty space when there is
nothing interacting with it so that it can travel at a constant speed
in a straight line.
The second law of physics describes forced displacement - a distance
(s) - from where it would have been, gone, or stayed, if not for being
forced to change its velocity by a force of contact - friction etc. -
with other bodies; so that the resultant motion d/t is what actually
occurs.
Don
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| User: "PD" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 12:28:52 PM |
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Don1 wrote:
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another.
That is because they are not correct. Nor, apparently, do you know what
displacement means. I found this extract from Arons to be pertinent.
From Teaching Introductory Physics, by Arnold B. Arons, John Wiley &
Sons, 1998, pg. and onwards:
==========================
Many presentations start in by ignoring the fact that the words "force"
and "mass," which in everyday speech, are heavily loaded metaphors, are
being taken out of everyday context and given very sophisticated
technical meaning, completely unfamiliar to the learner.... Students
have, in general, not been made self-conscious about, or sensitive to,
such semantic shifts, and they continue to endow the terms with the
diffuse metaphorical meanings previously absorbed or encountered. It is
helpful to make students explicitly conscious of the fact that the
words remain the same but that the meanings are sharply revised.
... Learners' difficulties in encompassing the law of inertia and the
concept of force stem in large measure from the wealth of common sense
preconceptions and experiential "rules" that most of us assimilate to
our view of the behavior of massive bodies before we are introduced to
Newtonian physics. Some of these views are Aristotelian (e.g., the
necessity of continued application of a push to keep a body moving, it
being very difficult to abandon thinking of rest as a condition
fundamentally different from that of motion, or to accept the view
that, rather than asking what keeps a body moving, we should ask what
causes it to stop), but many of these common sense views are more
closely related to the medieval notions of impetus associated with
names such as Buridan and Oresme.
All investigations show these "naive" conceptions to be very deeply
entrenched and very tenaciously held, and it is important for teachers
to understand that student difficulties are not reflections of
"stupidity" or recalcitrance. The difficulties are rooted in seemingly
logical consequences of perceived order and experience and are
vigorously reinforced by insistent use (or actually misuse) of words
drawn from everyday speech (inertia, mass, force, momentum, energy,
power, resistance) before these words have been given precise
operational meaning in physics. Persistent misuse of the terms in
thinking to oneself and in communicating with others is a major
obstacle to breaking away from the naive preconceptions.
... Investigations of understanding of the law of inertia further show
that it is far from sufficient to inculcate the law verbally and
supplement it with a few demonstrations of the behavior of frictionless
pucks on a table or gliders on an air track. Many students will
memorize and repeat the first law quite correctly in words but, when
confronted with the necessity of making predictions and describing what
happens in actual physical situations, concretely accessible to them,
they revert repeatedly to the naive preconceptions and predictions....
===============================================================
PD
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 02:00:32 PM |
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PD wrote:
Don1 wrote:
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another.
SNIP<
Quite a spiel PD, but I fail to see the pertinence. Students should be
taught to think and question things for themselves; including the
relativity of displacements: Where bodies continually change their
positions due to their inertial (relative) motion, and forced (changes
in) inertial motion.
Don
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| User: "PD" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 02:16:16 PM |
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Don1 wrote:
PD wrote:
Don1 wrote:
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another.
SNIP<
Quite a spiel PD, but I fail to see the pertinence. Students should be
taught to think and question things for themselves; including the
relativity of displacements: Where bodies continually change their
positions due to their inertial (relative) motion, and forced (changes
in) inertial motion.
It's very pertinent. It cautions students to not try to conflate
common-use definitions for terms with the precise meanings that are
developed as used in physics. The only way to *not* adopt those
meanings and avoid running into contradictions and unsound results is
to carefully and systematically *redefine* those terms, being careful
to advise the audience that you're doing so.
For example, in the above, what you call "relativity of displacements"
and "inertial (relative) motion" do not have any obvious bearing on
similar-sounding terms as they are used in physics. That means either
you do not understand the terms as they are used in physics, or you are
using the same words but attach different meanings which you have not
advertised.
PD
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 02:51:29 PM |
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"PD" <TheDraperFamily@gmail.com> wrote ...
It's very pertinent. It cautions students to not try to conflate
common-use definitions for terms with the precise meanings that are
developed as used in physics.
Yes. But Aron's intent was to caution teachers.
The only way to *not* adopt those
meanings and avoid running into contradictions and unsound results is
to carefully and systematically *redefine* those terms, being careful
to advise the audience that you're doing so.
That is certainly the conventional wisdom. I have found, though, that it
doesn't work very well. And even when it does work, it's a very inefficient
process.
Much work has been done (a lot of it because of Aron's many contributions to
the field) in the development of curricular materials that lead students via
experience to see the difference between the common meanings and the
technical meanings of these terms. And more importantly, to see the NEED
for such differences.
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| User: "PD" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 03:14:10 PM |
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Herman Trivilino wrote:
"PD" <TheDraperFamily@gmail.com> wrote ...
It's very pertinent. It cautions students to not try to conflate
common-use definitions for terms with the precise meanings that are
developed as used in physics.
Yes. But Aron's intent was to caution teachers.
Agreed. It cautions teachers to warn students about that conflation.
The only way to *not* adopt those
meanings and avoid running into contradictions and unsound results is
to carefully and systematically *redefine* those terms, being careful
to advise the audience that you're doing so.
That is certainly the conventional wisdom. I have found, though, that it
doesn't work very well. And even when it does work, it's a very inefficient
process.
That's why it's not done very often. Every once in a while, though, it
is required, and there are masters at it. Einstein did it. Feynman did
it. But they also had mastery of the previous meanings of those words.
Much work has been done (a lot of it because of Aron's many contributions to
the field) in the development of curricular materials that lead students via
experience to see the difference between the common meanings and the
technical meanings of these terms. And more importantly, to see the NEED
for such differences.
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 04:07:11 PM |
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PD wrote:
Herman Trivilino wrote:
"PD" <TheDraperFamily@gmail.com> wrote ...
Snip<
That is certainly the conventional wisdom. I have found, though, that it
doesn't work very well. And even when it does work, it's a very inefficient
process.
That's why it's not done very often. Every once in a while, though, it
is required, and there are masters at it. Einstein did it. Feynman did
it. But they also had mastery of the previous meanings of those words.
Or thought they did.
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 08:41:08 AM |
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"Don1" <dcshead@charter.net> wrote ...
That's why it's not done very often. Every once in a while, though, it
is required, and there are masters at it. Einstein did it. Feynman did
it. But they also had mastery of the previous meanings of those words.
Or thought they did.
Well, no. They are both on record as claiming they were never very good at
teaching. The much-heralded Feynman Lectures on Physics, for example, is
the result of an early 1960's experiment in introductory physics instruction
at Cal Tech. Feynman said he wasn't sure that the experiment worked.
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 04:39:13 PM |
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PD wrote:
Herman Trivilino wrote:
"PD" <TheDraperFamily@gmail.com> wrote ...
Snip<
That is certainly the conventional wisdom. I have found, though, that it
doesn't work very well. And even when it does work, it's a very inefficient
process.
That's why it's not done very often. Every once in a while, though, it
is required, and there are masters at it. Einstein did it. Feynman did
it. But they also had mastery of the previous meanings of those words.
Or thought they did.
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 02:28:53 PM |
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PD wrote:
Don1 wrote:
PD wrote:
Don1 wrote:
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another.
SNIP<
Quite a spiel PD, but I fail to see the pertinence. Students should be
taught to think and question things for themselves; including the
relativity of displacements: Where bodies continually change their
positions due to their inertial (relative) motion, and forced (changes
in) inertial motion.
It's very pertinent. It cautions students to not try to conflate
common-use definitions for terms with the precise meanings that are
developed as used in physics. The only way to *not* adopt those
meanings and avoid running into contradictions and unsound results is
to carefully and systematically *redefine* those terms, being careful
to advise the audience that you're doing so.
For example, in the above, what you call "relativity of displacements"
and "inertial (relative) motion" do not have any obvious bearing on
similar-sounding terms as they are used in physics. That means either
you do not understand the terms as they are used in physics, or you are
using the same words but attach different meanings which you have not
advertised.
PD
Horseradish, as if conflate has a special meaning in physics; or weight
isn't a particular force. G'me a break, or is that break a leg.
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 03:02:37 PM |
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"Don1" <dcshead@charter.net> wrote ...
For example, in the above, what you call "relativity of displacements"
and "inertial (relative) motion" do not have any obvious bearing on
similar-sounding terms as they are used in physics. That means either
you do not understand the terms as they are used in physics, or you are
using the same words but attach different meanings which you have not
advertised.
Horseradish, as if conflate has a special meaning in physics; or weight
isn't a particular force. G'me a break, or is that break a leg.
Take a look at a word like "accelerate". The common meaning is that used
when referring to, for example, the accelerator pedal in a car. Here, to
accelerate means to speed up.
In physics language, to accelerate means not only to speed up, but also to
slow down, and to change directions. In this context, not only is the
accelerator pedal a device used to make the car accelerate, so are the brake
pedal and the steering wheel!
You may not agree with that meaning, and certainly you are free to come up
with your own definitions and meanings. You seem to have a propensity for
doing just that. A commendable attribute.
However, your definitions and relationships lead to numerical results that
DON'T match what we observe in Nature. They may be more satisfying to you
on a philosophical basis, but they suck wind when it comes to being
physically meaningful.
You just don't get that. And, based on years of attempting to engage you in
a meaningful dialogue, I am forced to conclude that you probably never will.
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 04:37:52 PM |
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Herman Trivilino wrote:
Snip<
In physics language, to accelerate means not only to speed up, but also to
slow down, and to change directions. In this context, not only is the
accelerator pedal a device used to make the car accelerate, so are the brake
pedal and the steering wheel!
You may not agree with that meaning, and certainly you are free to come up
with your own definitions and meanings. You seem to have a propensity for
doing just that. A commendable attribute.
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Don
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 08:45:14 AM |
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"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 09:10:56 AM |
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Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Don
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 11:10:11 AM |
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"Don1" <dcshead@charter.net> wrote ...
Yes Herman, it's velocity does change by 32 ft/s each second;
Yes. It does. We can verify this by taking measurements.
but the_distance_ it falls is about 16 ft/second greater each second that
it
falls.
There is no way to verify this. We can measure the distance it falls during
each second. The results of the measurements do not match your claim of
"16 ft/s greater". In fact, it's not possible to measure a distance of 16
ft/s. We can measure a speed of 16 ft/s. We can measure a distance of 16
ft. But we can't measure a distance of 16 ft/s.
We can measure the distance it falls during each second. If it's falling
straight downward, the distance increases each second, but by an amount that
changes each second. One way an object can move to produce an increase in
distance each second of 16 ft is if it moves at a steady speed of 16 ft/s in
a straight line.
When we observe freely falling objects, they never move like this.
Your meanings DON'T match what we observe. They may satisfy you in some
philosophical sense, but they don't match what we observe. In other words,
they don't make good physics.
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 12:12:43 PM |
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Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
Yes Herman, it's velocity does change by 32 ft/s each second;
Yes. It does. We can verify this by taking measurements.
but the_distance_ it falls is about 16 ft/second greater each second that
it
falls.
There is no way to verify this. We can measure the distance it falls during
each second. The results of the measurements do not match your claim of
"16 ft/s greater". In fact, it's not possible to measure a distance of 16
ft/s. We can measure a speed of 16 ft/s. We can measure a distance of 16
ft. But we can't measure a distance of 16 ft/s.
We can measure the distance it falls during each second. If it's falling
straight downward, the distance increases each second, but by an amount that
changes each second. One way an object can move to produce an increase in
distance each second of 16 ft is if it moves at a steady speed of 16 ft/s in
a straight line.
When we observe freely falling objects, they never move like this.
Your meanings DON'T match what we observe. They may satisfy you in some
philosophical sense, but they don't match what we observe. In other words,
they don't make good physics.
Galileo measured free fall, and concluded that bodies fall at a rate of
g/2 = 16'/sec^.
Don
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| User: "Herman Trivilino" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 08:46:04 PM |
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"Don1" <dcshead@charter.net> wrote ...
Your meanings DON'T match what we observe. They may satisfy you in some
philosophical sense, but they don't match what we observe. In other
words,
they don't make good physics.
Galileo measured free fall, and concluded that bodies fall at a rate of
g/2 = 16'/sec^.
Your recollections of what you've read that Galeleo did don't match what we
observe, either.
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| User: "The Ghost In The Machine" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 05:00:04 PM |
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In sci.math, Don1
<dcshead@charter.net>
wrote
on 10 Sep 2005 10:12:43 -0700
<1126372363.450213.316850@z14g2000cwz.googlegroups.com>:
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
Yes Herman, it's velocity does change by 32 ft/s each second;
Yes. It does. We can verify this by taking measurements.
but the_distance_ it falls is about 16 ft/second greater each second that
it
falls.
There is no way to verify this. We can measure the distance it
falls during each second. The results of the measurements do
not match your claim of "16 ft/s greater". In fact, it's not
possible to measure a distance of 16 ft/s. We can measure a
speed of 16 ft/s. We can measure a distance of 16 ft. But we
can't measure a distance of 16 ft/s.
We can measure the distance it falls during each second. If
it's falling straight downward, the distance increases each
second, but by an amount that changes each second. One way an
object can move to produce an increase in distance each second
of 16 ft is if it moves at a steady speed of 16 ft/s in a straight
line.
When we observe freely falling objects, they never move like this.
Your meanings DON'T match what we observe. They may satisfy
you in some philosophical sense, but they don't match what we
observe. In other words, they don't make good physics.
Galileo measured free fall, and concluded that bodies fall at a rate of
g/2 = 16'/sec^.
No, they *accelerate* at the rate 32 ft/s^2. The fall is actually
approximated by the formula x = -1/2 g t^2, though it depends on
one's signs.
In any event I am given to understand Galileo measured many things,
and used ramps with marks to slow the acceleration sufficiently to
allow more accurate timing, and to estimate the distance of the ball
as it rolled down the ramp, while observing some sort of timing
device. (One possibility: a slow-drip water clock. I'd have to look
to see whether he had access to a grandfather clock or other such.)
Don
--
#191,
It's still legal to go .sigless.
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| User: "tj Frazir" |
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| Title: Re: The relativity of displacement |
11 Sep 2005 08:20:12 AM |
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F is the distance from the center of mass to th center of gravity inside
each atom.
The energy slope affects the orbital path of all the parts of the atom
..
F is identical to the distance the atoms center of mass has moved from
the center of gravity.
Or F is identical to the distance the center of gravity is from the
center of mass.
Wile dark energy is energy under presure at c as photons from outside
our visible universe pass evry point with no wavelength at c.
Mass takes up more space in motion per time unit.
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
MASS is equal the energy it displaces.
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| User: "Richard Henry" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 11:52:56 PM |
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"Don1" <dcshead@charter.net> wrote in message
news:1126361456.597860.70370@g47g2000cwa.googlegroups.com...
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of
free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The
point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Consider an object released to fall freely in a gravitational field of
32ft/s/s.
What distance has it fallen, and what is its velocity, after 1 second? 16
feet, 32 feet/s
What distance has it fallen, and what is its velocity, after 2 seconds? 64
feet, 64 feet/s
What distance has it fallen, and what is its velocity, after 3 seconds? 144
feet, 96 feet/s
What distance has it fallen, and what is its velocity, after 4 seconds? 256
feet, 128 feet/s
Where does "16' per second, per second" fit into that?
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
11 Sep 2005 07:32:39 AM |
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Richard Henry wrote:
"Don1" <dcshead@charter.net> wrote in message
news:1126361456.597860.70370@g47g2000cwa.googlegroups.com...
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of
free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The
point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Consider an object released to fall freely in a gravitational field of
32ft/s/s.
What distance has it fallen, and what is its velocity, after 1 second? 16
feet, 32 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)1
sec^2 = 16'.
What distance has it fallen, and what is its velocity, after 2 seconds? 64
feet, 64 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)2
sec^2 = 64'.
What distance has it fallen, and what is its velocity, after 3 seconds? 144
feet, 96 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)3
sec^2 = 144'.
What distance has it fallen, and what is its velocity, after 4 seconds? 256
feet, 128 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)4
sec^2 = 256'.
Where does "16' per second, per second" fit into that?
16' per second, per second, is (32'/sec^2)/2 = 16'/sec^2; which is
=g/2.
The velocity of course, simply increases 32'/sec^2 each second.
Don
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| User: "Richard Henry" |
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| Title: Re: The relativity of displacement |
12 Sep 2005 08:51:11 PM |
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"Don1" <dcshead@charter.net> wrote in message
news:1126441959.008417.23830@f14g2000cwb.googlegroups.com...
The velocity of course, simply increases 32'/sec^2 each second.
No, it doesn't.
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| User: "Steve Ralph" |
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| Title: Re: The relativity of displacement |
11 Sep 2005 07:38:50 AM |
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"Don1" <dcshead@charter.net> wrote in message
news:1126441959.008417.23830@f14g2000cwb.googlegroups.com...
Richard Henry wrote:
"Don1" <dcshead@charter.net> wrote in message
news:1126361456.597860.70370@g47g2000cwa.googlegroups.com...
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also
think
of _rates_ of acceleration, and rates of free fall: They express
the
value of longivity of acceleration and free fall. Like the rate of
free
fall found by Galileo; where g/2 = (about) 16' per second, per
second.
Whether you agree or disagree with the meanings is not the point.
The
point
is that your meanings don't produce results that match what's
observed.
For example, when we take measurements of an object in free fall we
find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s
each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Consider an object released to fall freely in a gravitational field of
32ft/s/s.
What distance has it fallen, and what is its velocity, after 1 second?
16
feet, 32 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)1
sec^2 = 16'.
What distance has it fallen, and what is its velocity, after 2 seconds?
64
feet, 64 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)2
sec^2 = 64'.
What distance has it fallen, and what is its velocity, after 3 seconds?
144
feet, 96 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)3
sec^2 = 144'.
What distance has it fallen, and what is its velocity, after 4 seconds?
256
feet, 128 feet/s
The distance fallen is: s=(g/2)t^2 = (16'/sec^2)t^2 = (16'/sec^2)4
sec^2 = 256'.
Where does "16' per second, per second" fit into that?
16' per second, per second, is (32'/sec^2)/2 = 16'/sec^2; which is
=g/2.
The velocity of course, simply increases 32'/sec^2 each second.
32 feet per second per second each second.
You're a genius, I really don't know how you do it.
sr
Don
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| User: "Sam Wormley" |
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| Title: Re: The relativity of displacement |
10 Sep 2005 09:15:27 AM |
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Don1 wrote:
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Don
Shead 16 ft/s is velocity, not distance!
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| User: "PD" |
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| Title: Re: The relativity of displacement |
12 Sep 2005 08:25:14 AM |
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Don1 wrote:
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Well, let's look at that for a second.
In second 1, starting from rest, an object will fall 16 ft.
In second 2, it will fall another 48 ft, which is 32 ft further than it
fell in the previous second.
In second 3, it will fall another 80 ft, which is 32 ft further than it
fell in the previous second.
In second 4, it will fall another 112 ft, which is 32 ft further than
it fell in the previous second.
PD
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| User: "Don1" |
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| Title: Re: The relativity of displacement |
13 Sep 2005 05:31:54 AM |
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PD wrote:
Don1 wrote:
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Well, let's look at that for a second.
In second 1, starting from rest, an object will fall 16 ft.
In second 2, it will fall another 48 ft, which is 32 ft further than it
fell in the previous second.
In second 3, it will fall another 80 ft, which is 32 ft further than it
fell in the previous second.
In second 4, it will fall another 112 ft, which is 32 ft further than
it fell in the previous second.
PD
Let's look at it for _four_ seconds PD.
In second 1, starting from rest, an object will fall 16 ft. Which is
16' x 1 sec^2.
In second 2, it will fall 64 ft, which is 16' x 2 sec^2 ft further
than it fell in the previous second.
In second 3, it will fall 144', which is 16x3 sec^2 further than it
fell in the previous second.
In second 4, it will fall 256', which is 16x 4 sec^2 further than it
fell in the previous second.
This is inaccordance with my claim; that the _distance_ it falls is
about 16 ft/second greater (per) each second that it continues to fall.
Don
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| User: "" |
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| Title: Re: The relativity of displacement |
13 Sep 2005 06:28:49 AM |
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Don1 wrote:
Let's look at it for _four_ seconds PD.
In second 1, starting from rest, an object will fall 16 ft. Which is
16' x 1 sec^2.
Correct...
In second 2, it will fall 64 ft, which is 16' x 2 sec^2 ft further
than it fell in the previous second.
Not correct... In TWO seconds, starting from rest, it will fall 64
feet. Since it fell 16 fet in the first second (see previous
calculation), it must have fallen 48 feet IN the seond second
In second 3, it will fall 144', which is 16x3 sec^2 further than it
fell in the previous second.
Wrong again... In THREE seconds, starting from rest, it will fall 144
feet. Since it fell 64 feet in the first two seconds (see previous
calculation), it must have fallen 80 feet IN the third second.
In second 4, it will fall 256', which is 16x 4 sec^2 further than it
fell in the previous second.
Wrong again... In FOUR.... Same process...
This is inaccordance with my claim; that the _distance_ it falls is
about 16 ft/second greater (per) each second that it continues to fall.
True, and that means your claim is wrong... And distance is not
measured in feet/second.
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| User: "PD" |
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| Title: Re: The relativity of displacement |
13 Sep 2005 08:18:16 AM |
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Don1 wrote:
PD wrote:
Don1 wrote:
Herman Trivilino wrote:
"Don1" <dcshead@charter.net> wrote ...
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.
Whether you agree or disagree with the meanings is not the point. The point
is that your meanings don't produce results that match what's observed.
For example, when we take measurements of an object in free fall we find
that it's velocity changes by 32 ft/s each second. NOT by 16 ft/s each
second!
Yes Herman, it's velocity does change by 32 ft/s each second; but the
_distance_ it falls is about 16 ft/second greater each second that it
falls.
Well, let's look at that for a second.
In second 1, starting from rest, an object will fall 16 ft.
In second 2, it will fall another 48 ft, which is 32 ft further than it
fell in the previous second.
In second 3, it will fall another 80 ft, which is 32 ft further than it
fell in the previous second.
In second 4, it will fall another 112 ft, which is 32 ft further than
it fell in the previous second.
PD
Let's look at it for _four_ seconds PD.
In second 1, starting from rest, an object will fall 16 ft. Which is
16' x 1 sec^2.
In second 2, it will fall 64 ft, which is 16' x 2 sec^2 ft further
than it fell in the previous second.
In second 3, it will fall 144', which is 16x3 sec^2 further than it
fell in the previous second.
In second 4, it will fall 256', which is 16x 4 sec^2 further than it
fell in the previous second.
This is inaccordance with my claim; that the _distance_ it falls is
about 16 ft/second greater (per) each second that it continues to fall.
Don
Once again you let algebra trip you up, trying to read meaning into the
expressions rather than looking at the numbers. Here are some tips:
1. An algebraic expression is a way of generating a set of connected
numbers consistently. In this case, what you should be trying to make
with the algebraic expression is a table of numbers, one column with s
and another column with t. This is a *general* rule for algebra: if you
aren't *completely* comfortable with algebra, then use the expression
to generate a table of numbers and look at that instead.
2. With the units you're using, the units for distance s should be in
ft (not ft/s, not ft/s^2) and the units for time t should be seconds.
If you see *anything else*, it's an indicator that you've done
something wrong.
3. The physics behavior is revealed in the table of s vs. t, because
that's what you'd measure with a stopwatch and a ruler. Those will be
numbers that you can visualize, draw on paper to scale, with clear
meaning.
4. As has been pointed out to you, if you put in 4 s for t, this is how
far it has gone in four seconds; that is, in the four seconds since
starting at t=0. It does *not* mean how far it goes in the fourth
second. To get that, you will have to look at your table of numbers and
do some subtractions.
PD
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| User: "Bob Cain" |
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| Title: Re: The relativity of displacement |
12 Sep 2005 02:05:07 PM |
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Don1 wrote:
Quite a spiel PD, but I fail to see the pertinence.
Thus perfectly illustrating his point.
Students should be
taught to think and question things for themselves; including the
relativity of displacements: Where bodies continually change their
positions due to their inertial (relative) motion, and forced (changes
in) inertial motion.
On second thought, you must know of what you speak in order
to constantly construct such doubletalking and effective
trolls. This man is an artist. A con artist.
You could probably make money with this talent, Don. I
suggest the audiophile market or perhaps "alternative"
medicine. A fortune awaits you.
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
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| User: "Sam Wormley" |
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| Title: Re: The relativity of displacement |
09 Sep 2005 08:24:55 AM |
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Don1 wrote:
There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement....
Velocity
http://scienceworld.wolfram.com/physics/Velocity.html
Don1 wrote:
The motion that we see (d/t) consists of two kinds: Inertial (relative)
motion (vi) according to Newton's First Law, and Forced displaced
motion (s/t) according to his second law:
You are still utterly confused Shead...
Inertia
http://scienceworld.wolfram.com/physics/Inertia.html
The resistance to change in state of motion which all matter exhibits.
It's a concept, Shead, not a number with units, not a ratio.
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Also called the "law of inertia," Newton's first law states that a
body at rest remains at rest and a body in motion continues to move
at a constant velocity unless acted upon by an external force.
Newton's Second Law is about "inertial mass"
http://scienceworld.wolfram.com/physics/NewtonsSecondLaw.html
A force F acting on a body gives it an acceleration a which is in
the direction of the force and has magnitude inversely proportional
to the mass m of the body: F = ma
Inertia is an intrinsic property of mass. Most of what follows is
quoted from http://www.physlink.com/ae305.cfm
Gravitational Mass F = GmM/r^2
Inertial Mass F = ma
Acceleration a = dv/dt
1) Inertial mass. This is mainly defined by Newton's law,
the all-too-famous F = ma, which states that when a force
F is applied to an object, it will accelerate
proportionally, and that constant of proportion is the
mass of that object. In very concrete terms, to determine
the inertial mass, you apply a force of F Newtons to an
object, measure the acceleration in m/s^2, and F/a will
give you the inertial mass m in kilograms.
2) Gravitational mass. This is defined by the force of
gravitation, which states that there is a gravitational
force between any pair of objects, which is given by
F = G m1 m2/r^2
where G is the universal gravitational constant, m1 and m2
are the masses of the two objects, and r is the distance
between them. This, in effect defines the gravitational
mass of an object.
As it turns out, these two masses are equal to each other
as far as we can measure. Also, the equivalence of these
two masses is why all objects fall at the same rate on
earth.
The only difference that we can find between inertial and
gravitational mass that we can find is the method.
Gravitational mass is measured by comparing the force of
gravity of an unknown mass to the force of gravity of a
known mass. This is typically done with some sort of
balance scale. The beauty of this method is that no matter
where, or what planet, you are, the masses will always
balance out because the gravitational acceleration on each
object will be the same. This does break down near
supermassive objects such as black holes and neutron stars
due to the high gradient of the gravitational field around
such objects.
Inertial mass is found by applying a known force to an
unknown mass, measuring the acceleration, and applying
Newton's Second Law, m = F/a. This gives as accurate a
value for mass as the accuracy of your measurements. When
the astronauts need to be weighed in outer space, they
actually find their inertial mass in a special chair.
The interesting thing is that, physically, no difference
has been found between gravitational and inertial mass.
Many experiments have been performed to check the values
and the experiments always agree to within the margin of
error for the experiment. Einstein used the fact that
gravitational and inertial mass were equal to begin his
Theory of General Relativity in which he postulated that
gravitational mass was the same as inertial mass and that
the acceleration of gravity is a result of a "valley" or
slope in the space-time continuum that masses "fell down"
much as pennies spiral around a hole in the common
donation toy at your favorite chain store.
Useful references for Shead
http://scienceworld.wolfram.com/physics/Inertia.html
http://scienceworld.wolfram.com/physics/MomentofInertia.html
http://scienceworld.wolfram.com/physics/Mass.html
http://scienceworld.wolfram.com/physics/Momentum.html
http://scienceworld.wolfram.com/physics/NewtonsLaws.html
http://scienceworld.wolfram.com/physics/Weight.html
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