| Topic: |
Science > Physics |
| User: |
"Don1" |
| Date: |
22 Apr 2006 04:01:00 PM |
| Object: |
Why choose 1 as the standard? |
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
Don
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| User: "Herman Trivilino" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 10:44:46 AM |
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"Don1" <dcshead@charter.net> wrote ...
Besides; While Galileo prooved that all objects free fall with the same
acceleration,
Actually, he proved that they didn't. Check it out for yourself. He
measured the discrepancy between the times of fall, found it to be small,
and speculated that it would reduce to zero under ideal conditions. So far,
his speculation has turned out to be valid, within the limits of
experimental error.
why would anybody choose to use another harder to
remember figure than one (1) as the standard?
Galileo propesed this as a standard. It never gained acceptance because
others were using different standards. In the modern era, such a definition
wouldn't be precise enough to be used as a standard, anyway.
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| User: "T Wake" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 04:05:25 PM |
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"Don1" <dcshead@charter.net> wrote in message
news:1145739660.795533.23050@g10g2000cwb.googlegroups.com...
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
Don
You have too much spare time on your hands.
--
For Google Groups users this may be important
http://blinkynet.net/comp/uip5.html
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| User: "Hexenmeister" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 06:28:14 AM |
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"Don1" <dcshead@charter.net> wrote in message =
news:1145739660.795533.23050@g10g2000cwb.googlegroups.com...
| Besides; While Galileo prooved=20
"Proved", *****-head.
Get a fuckin' spell checker even you can't punctuate.
Androcles
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| User: "" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 05:37:00 PM |
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Don1 wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
1 what?
Don
(...Starblade Riven Darksquall...)
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| User: "Don1" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 07:58:24 PM |
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wrote:
Don1 wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
1 what?
Just plain One: All the units cancel.
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| User: "Herman Trivilino" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 10:48:22 AM |
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"Don1" <dcshead@charter.net> wrote ...
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
1 what?
Just plain One: All the units cancel.
No. Galileo proposed a name for the unit. You can check this out for
yourself by reading what he wrote. Virtually all of his written works have
been translated, and many of them can be found in any decent library.
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| User: "Stephen Montgomery-Smith" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 08:19:07 PM |
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Don1 wrote:
Starbles@Earthlink.net wrote:
Don1 wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
1 what?
Just plain One: All the units cancel.
That's pretty nifty. It simplifies things a lot. For example,
What is the distance between Kansas City and St Louis? Answer: One.
How long does it take concorde to go from New York to London? Answer: One.
How much sugar should be used in a typical cake recipe? Answer: One.
What is the strength of the earth's magnetic field? Answer: One. (In
particular, it doesn't depend where you are on the earth.)
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| User: "The Ghost In The Machine" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 02:00:22 PM |
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On Sat, 22 Apr 2006 17:58:24 -0700, Don1 wrote:
Starbles@Earthlink.net wrote:
Don1 wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
1 what?
Just plain One: All the units cancel.
In order to answer this even close to properly one has to first ask what a
"unit" in this context is.
Acceleration is typically taught as the change in velocity. Velocity is
typically taught as the change in position. (QM changes this a bit but
never mind.) So one might teach that a rock, ball, or particle is at
position 0 at time 0, position 2 at time 1, position 4 at time 2, etc. in
a certain experiment.
But what is that position measured in? Ah...there's a standardized meter
stick over there. So we might call the positions
x t
0 m 0 s
2 m 1 s
4 m 2 s
6 m 3 s
8 m 4 s
10 m 5 s
Since it's clear x/t in this hypothetical experiment is constant, we can
divide the two and come up with the value 2. 2 what? Well, there's also
the units to consider; one actually gets (8m)/(4s). Were m and s
variables of some sort one can simply factor things (8/4) * (m/s),
or 2 m/s.
It turns out this works very well.
Now suppose we conduct a slightly different experiment (Galileo rolled
balls down a marked ramp; we might contemplate something similar here),
and get the following results.
x t
0 m 0 s
0.25 m 1 s
1.00 m 2 s
2.25 m 3 s
4.00 m 4 s
6.25 m 5 s
Clearly, v is no longer constant; it's dependent on t. If one naively
divides, one gets:
x t x/t
0 m 0 s ?
0.25 m 1 s 0.25 m/s
1.00 m 2 s 0.50 m/s
2.25 m 3 s 0.75 m/s
4.00 m 4 s 1.00 m/s
6.25 m 5 s 1.25 m/s
This turns out to be incorrect by a factor of 2, if one wants
instantaneous velocity. Since this is a hypothetical experiment, one can
do elementary curve-fitting and come up with the formula
x = 0.25 * t^2
with no error. (In a real experiment one has to work around various
issues using least-squares.)
If one knows elementary calculus the instantaneous velocity can be
construed as dx/dt, which turns out to be
v = dx/dt = 0.50 * m/s/s * t
(since v is in m/s and t contains s, things sort of have to cancel out)
and the acceleration is the instantaneous change in velocity, or
a = dv/dt = d^2x/dt^2 = 0.50 m/s/s
If one has sufficiently sophisticated equipment, one might get, during a
freefall measurement here on Earth:
x t
0 m 0.0 s
0.049025 m 0.1 s
0.196100 m 0.2 s
0.441225 m 0.3 s
0.784400 m 0.4 s
1.225625 m 0.5 s
1.764900 m 0.6 s
This shows an acceleration, as it turns out, of 9.805 m/s/s.
We now switch to a standard yardstick, marked off with 36 inches and
various fractions thereof, and redo the experiment. We might get in this
case
x t
0 in 0.0 s
1.930118 in 0.1 s
7.720472 in 0.2 s
17.370163 in 0.3 s
30.881890 in 0.4 s
48.252953 in 0.5 s
were a yardstick more precise than 1/32". :-) The acceleration in this
case is approximately 386.02326 in/s/s, although most will divide by 12
(since 1 ft = 12 in, 1 = 12 in/ft) and get 32.168635 ft/s/s as an
approximate value for 'g'.
It is possible to simply define a unit "1 g-length" (we'll call it "1 gl"
for short). This unit would have the property that a hypothetical
drop experiment would show:
x t
0 gl 0 s
0.5 gl 1 s
2.0 gl 2 s
4.5 gl 3 s
8.0 gl 4 s
and therefore the acceleration in this case is 1 g-length per second per
second. However, there are a few problems with this particular length
unit; for starters, it varies by about 0.5% across the globe of the world
as defined (the Earth is rotating and not perfectly spherical). Also, no
one's ever really wanted to define length in this fashion; the ancients
might have used marks on a rock or their own bodies (1 cubit = length from
fingertip to elbow, for example; 1 inch is probably derived from the width
of one's thumb). More modern methods include 1 millionth of a
quarter-circle of the world, a certain number of wavelengths of Kr-86
light (it turns out to be fractional), and the modern definition of
1/299792458th of the distance light travels in 1 second.
In short, a g-length has never been considered for the purposes of
standardization.
Neither, as it turns out, has a "nil". This is the distance light travels
in a nanosecond; one can extend this concept into kilonils (mil is
taken!), meganils, and giganils -- or simply lsecs. It turns out a nil is
exactly 29.9792458 cm or 0.299792458 m by definition, and might replace a
foot in general parlance sometime in the very far future, if there are any
feet left (and humans having them).
The drop experiment using nils might yield something like:
x t
0 nil 0.0 s
0.163530 nil 0.1 s
0.654119 nil 0.2 s
1.471768 nil 0.3 s
2.616477 nil 0.4 s
4.088245 nil 0.5 s
and one gets an acceleration of 32.70596 nils/s/s. Unlike g-length, a nil
is the same length everywhere in the Universe, at least according to
current theory. (A meter is too but one might have to explain to the
inhabitants why we picked two "magic numbers"; at least with a nil we'd
only have to explain one, namely 9192631770 Cs-133 oscillations/second.
Of course one might define an osc-length, which would be 3.26122557 cm in
length and truly universal -- unless the aliens use Hg ion clocks instead.
We can't win, I guess... :-) )
But a meter will do, for everyone outside of the US. :-) (Even within the
US the meter is commonplace for such things as repair tools.)
Followups to sci.physics.
--
#191,
It's still legal to go .sigless.
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| User: "Paul Cardinale" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 10:40:08 PM |
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So it comes out that you don't even know what units are.
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| User: "Herman Trivilino" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 10:49:06 AM |
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"Paul Cardinale" <pcardinale@volcanomail.com> wrote ...
So it comes out that you don't even know what units are.
It came out long ago.
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| User: "Eric Gisse" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 12:08:37 AM |
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Don1 wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
Don
What the hell are you babbling about now?
Why do you keep posting your drivel to sci.math?
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| User: "Gregory L. Hansen" |
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| Title: Re: Why choose 1 as the standard? |
23 Apr 2006 08:20:22 AM |
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In article <1145739660.795533.23050@g10g2000cwb.googlegroups.com>,
Don1 <dcshead@charter.net> wrote:
Besides; While Galileo prooved that all objects free fall with the same
acceleration, why would anybody choose to use another harder to
remember figure than one (1) as the standard?
Don
Because most of their measuring needs didn't involve measuring the
distance versus time of dropped objects.
--
"The preferred method of entering a building is to use a tank main gun
round, direct fire artillery round, or TOW, Dragon, or Hellfire missile to
clear the first room." -- THE RANGER HANDBOOK U.S. Army, 1992
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| User: "Joel" |
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| Title: Re: Why choose 1 as the standard? |
22 Apr 2006 11:49:58 PM |
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Sounds like you want "God's units", the set for which c, =B5, e,
the charge on an electron, &c. are all unity.
--Joel
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