| Topic: |
Science > Physics |
| User: |
"MobyDikc" |
| Date: |
15 Feb 2006 03:54:12 PM |
| Object: |
Mathematical model of inertia |
Can someone provide a mathematical model of inertia?
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| User: "Sam Wormley" |
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| Title: Re: Mathematical model of inertia |
16 Feb 2006 12:21:19 PM |
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MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 01:42:15 PM |
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Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
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| User: "Sam Wormley" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 03:49:09 PM |
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MobyDikc wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
Conservation of Momentum
http://scienceworld.wolfram.com/physics/ConservationofMomentum.html
Conservation of Energy
http://scienceworld.wolfram.com/physics/ConservationofEnergy.html
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
18 Feb 2006 03:08:16 AM |
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"Sam Wormley" <swormley1@mchsi.com> wrote in message news:pxrJf.774589$x96.763395@attbi_s72...
MobyDikc wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
Conservation of Momentum
http://scienceworld.wolfram.com/physics/ConservationofMomentum.html
Conservation of Energy
http://scienceworld.wolfram.com/physics/ConservationofEnergy.html
Conservation of Momenergy
http://www.physics.drexel.edu/~vogeley/SpecialRel/lecture8.pdf
Dirk Vdm
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| User: "" |
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| Title: Re: Mathematical model of inertia |
18 Feb 2006 03:16:45 AM |
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Hugh Hefner's Unabashed *****-shunary:
Conservation of Mom's-Energy:
http://www.daffynishun.com/UltimateAuthority/LeadHumanityDownPenrosePath.pdf
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| User: "Eric Gisse" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 03:27:39 PM |
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MobyDikc wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
Conservation of momentum. The sum of the initial momenta is equal to
the sum of the resulting momenta.
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| User: "Hexenmeister" |
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| Title: Re: Mathematical model of inertia |
18 Feb 2006 12:52:16 PM |
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"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1140211659.564002.305800@z14g2000cwz.googlegroups.com...
[snip]
Androcles.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 03:40:14 PM |
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Eric Gisse wrote:
MobyDikc wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
Conservation of momentum. The sum of the initial momenta is equal to
the sum of the resulting momenta.
The kind of description of the state of the system I'm looking for
would be the new velocity and direction of the small ball after
colliding with the large ball, and the calculations that were used to
determine them.
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| User: "Greg Neill" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 03:46:11 PM |
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"MobyDikc" <mobydikc@gmail.com> wrote in message
news:1140212414.630060.51490@f14g2000cwb.googlegroups.com...
The kind of description of the state of the system I'm looking for
would be the new velocity and direction of the small ball after
colliding with the large ball, and the calculations that were used to
determine them.
Switch to a frame of reference in which the momenta are
equal and opposite (center of momentum frame), exchange
the momenta, then change back to the original frame.
Voila.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 04:18:42 PM |
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Greg Neill wrote:
"MobyDikc" <mobydikc@gmail.com> wrote in message
news:1140212414.630060.51490@f14g2000cwb.googlegroups.com...
The kind of description of the state of the system I'm looking for
would be the new velocity and direction of the small ball after
colliding with the large ball, and the calculations that were used to
determine them.
Switch to a frame of reference in which the momenta are
equal and opposite (center of momentum frame), exchange
the momenta, then change back to the original frame.
Voila.
Are you saying, you switch the momentum of the balls?
The momentum of the big ball is zero, since its velocity is zero too.
So when the 1KG ball hits the 200,000 KG ball, are you saying the big
ball goes into motion and the little ball stops completely?
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| User: "Eric Gisse" |
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| Title: Re: Mathematical model of inertia |
17 Feb 2006 05:29:04 PM |
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MobyDikc wrote:
Eric Gisse wrote:
MobyDikc wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Starting with F = ma, set F = 0
Newton's First Law
http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html
Newton's first law states that 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.
Ok. So, let's say I have a ball with a mass of 1kg. It is travelling in
a straight path at a steady rate of 5 meters per second.
It is travelling toward another ball which is 200,000KG and is
perfectly at rest.
Also, we're ignoring gravity for a second.
According to your model of inertia, what happens when the smaller ball
hits the larger ball? What is the state of the system after the
contact?
Conservation of momentum. The sum of the initial momenta is equal to
the sum of the resulting momenta.
The kind of description of the state of the system I'm looking for
would be the new velocity and direction of the small ball after
colliding with the large ball, and the calculations that were used to
determine them.
http://www.amazon.com/gp/product/0201073927/104-5192934-8134345?v=glance&n=283155
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| User: "Hexenmeister" |
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| Title: Re: Mathematical model of inertia |
18 Feb 2006 12:52:17 PM |
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"Eric Gisse" <jowr.pi@gmail.com> wrote in message
news:1140218944.823168.210570@f14g2000cwb.googlegroups.com...
[snip]
Androcles.
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| User: "Sam Wormley" |
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| Title: Re: Mathematical model of inertia |
15 Feb 2006 04:15:48 PM |
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MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
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| User: "" |
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| Title: Re: Mathematical model of inertia |
15 Feb 2006 06:09:00 PM |
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Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
That's a model of morons and calculus.
A model of inertia is dF=0.
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| User: "Sam Wormley" |
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| Title: Re: Mathematical model of inertia |
15 Feb 2006 09:56:56 PM |
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wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
That's a model of morons and calculus.
A model of inertia is dF=0.
I didn't say what the values were. If you wan to measure
inertial mass, you might want to observe values other
than zero.
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| User: "" |
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| Title: Re: Mathematical model of inertia |
15 Feb 2006 10:20:53 PM |
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Sam Wormley wrote:
zzbunker@netscape.net wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
That's a model of morons and calculus.
A model of inertia is dF=0.
I didn't say what the values were. If you wan to measure
inertial mass, you might want to observe values other
than zero.
I don't. Since the question was about inertia,
not tnertial mass. Since interial mass,
by defintion in Relativatonity,
M = C^2/E.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
16 Feb 2006 11:11:47 AM |
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Sam Wormley wrote:
zzbunker@netscape.net wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
That's a model of morons and calculus.
A model of inertia is dF=0.
I didn't say what the values were. If you wan to measure
inertial mass, you might want to observe values other
than zero.
So. Which is it?
Is the mathematical model for inertia "F=ma" or "dF=0"?
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| User: "" |
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| Title: Re: Mathematical model of inertia |
16 Feb 2006 12:32:01 PM |
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MobyDikc wrote:
Sam Wormley wrote:
zzbunker@netscape.net wrote:
Sam Wormley wrote:
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
The differential equation F = ma
That's a model of morons and calculus.
A model of inertia is dF=0.
I didn't say what the values were. If you wan to measure
inertial mass, you might want to observe values other
than zero.
So. Which is it?
Is the mathematical model for inertia "F=ma" or "dF=0"?
Pick up any Calculus text book and drop it on the floor,
Euclid's Axioms, .The General Theory of Relativity,
The Doppler Effect, and dF=0 immediatley follows.
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| User: "" |
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| Title: Re: Mathematical model of inertia |
15 Feb 2006 04:27:37 PM |
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Yeah. You see, you have all this mass distributed uniformly in the
Universe. Basically it tugs equally in all directions on a mass.
Thus, the mass tends to stay at rest if at rest and tends to move
uniformly in a straight line if it's already doing that. I think it
was some guy named Mach? who came up with that.
Inertia - it's not just for breakfast anymore!
- Don ("Say, ***** - hunt on someone else's land, not here, PLEASE!!!!!)
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| User: "Rock Brentwood" |
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| Title: Re: Mathematical model of inertia |
22 Feb 2006 07:31:00 PM |
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MobyDikc wrote:
Can someone provide a mathematical model of inertia?
In modern geometry, this law is captured by positing a connection on
the underlying spacetime continuum, and posing the geodesic law,
stating that inertial motion is that which takes place on a geodesic:
d^2 x^m/ds^2 + sum(Gamma^m_{np} dx^n/ds dx^p/ds) = K
dx^m/ds
where s is a parametrization of the trajectory (x0,x1,x2,x3) =
(x0(s),x1(s),x2(s),x3(s)).
Though not well-known, this formulation is generic -- applicable not
just to a Lorentzian spacetime, such as would be considered in General
Relativity, but even a Galilean spacetime (a' la Newtonian Physics) in
the corresponding Galilean General Relatlvity ... potentially even an
Aristotlean spacetime has its own law of inertia, with its own
definition of connection, etc. I don't think anyone has yet ever
written down what an Aristotlean spacetime looks like in modern
geometric language.
For Lorentzian spacetimes, the connection that defines geodesics is the
Levi-Civita connection, which is defined as the unique torsion-free
connection that leaves the metric invariant. For a Galilean spacetime,
the definition is a little more subtle -- there it's a torsion-free
connection that leaves the contravariant metric invariant and the
"time" field invariant as well.
That means that in a coordinate chart (x0,x1,x2,x3) with the 0
coordinate parallel to the time field, the corresponding connection
coefficients Gamma^0_{mn} = 0. The coeffiicents Gamma^i_{00} give you
minus the gravitational force, which allows you to incorporate both
inertial and gravitational force under a common framework -- as
dictated by the Equivalence Principle. The coefficients Gamma^i_{0j}
are of interest, since they contain a contribution from a field B^i_j
which in many ways plays the analogue of a magnetic field. This is the
Newtonian version of what in General Relativity is known as
graveto-magnetism. It's not well-known, even in the advanced
literature, that there even is such a thing; most people who deal with
this think graveto-magnetism is a purely relativistic phenomenon. It's
not. It's also Newtonian.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
20 Feb 2006 09:05:56 AM |
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MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Let's try this.
Can someone provide the mathematical statement of "unless acted on by
an outside force an object in motion stays in motion and an object at
rest stays at rest."?
Next, can someone provide the work to use that math to answer the
following question.
There is a ball with a mass of 20kg moving toward a 5kg ball at 1 m/s.
At 0 seconds, the balls are 2 meters apart.
What is the state of the system at 3 seconds.
Show all the math involved to make that prediction.
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
20 Feb 2006 04:06:08 PM |
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"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140447956.172319.119380@g44g2000cwa.googlegroups.com...
MobyDikc wrote:
Can someone provide a mathematical model of inertia?
Let's try this.
Can someone provide the mathematical statement of "unless acted on by
an outside force an object in motion stays in motion and an object at
rest stays at rest."?
Next, can someone provide the work to use that math to answer the
following question.
There is a ball with a mass of 20kg moving toward a 5kg ball at 1 m/s.
At 0 seconds, the balls are 2 meters apart.
What is the state of the system at 3 seconds.
Show all the math involved to make that prediction.
Before collision:
World line of ball_1: x = v t
World line of ball_2: x = d
Total momentum: m1 v
Total energy: 1/2 m1 v^2
This setup satisfies the initial conditions that at t = 0
the distance between the balls is d.
Collision event:
{ x = v t
{ x = d
giving
( x, t ) = ( d, d/v )
After collision:
World line of ball_1: x - d = v1 (t-d/v)
World line of ball_2: x - d = v2 (t-d/v)
Total momentum: m1 v1 + m2 v2
Total energy: 1/2 m1 v1^2 + 1/2 m2 v2^2
Assuming total inelasticity of the collision,
conservation of momentum demands
m1 v = m1 v1 + m2 v2
and conservation of energy demands
1/2 m1 v^2 = 1/2 m1 v1^2 + 1/2 m2 v2^2
Solving for v1 and v2 gives
v1 = (m1-m2) / (m1+m2)
v2 = 2 m1 v / (m1+m2)
So we have the complete histories for both balls:
1) for t < d/v:
World line of ball_1: x = v t
World line of ball_2: x = d
2) for t >= d/v:
World line of ball_1: x = d + (m1-m2) / (m1+m2) (t-d/v)
World line of ball_2: x = d + 2 m1 v / (m1+m2) (t-d/v)
Your question
| > There is a ball with a mass of 20kg moving toward a 5kg ball at 1 m/s.
| > At 0 seconds, the balls are 2 meters apart.
| > What is the state of the system at 3 seconds.
is translated into
m1 = 20, m2 = 4, v = 1, d = 2, T = 3
You can make the calculations.
Dirk Vdm
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
20 Feb 2006 05:29:58 PM |
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"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote in message
news:k3rKf.269669$So7.7702599@phobos.telenet-ops.be...
[snip]
Assuming total inelasticity of the collision,
Third typo, sigh.
We assume total elasticity ;-)
Dirk Vdm
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 10:42:28 AM |
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Dirk Van de moortel wrote:
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote in message
news:k3rKf.269669$So7.7702599@phobos.telenet-ops.be...
[snip]
Assuming total inelasticity of the collision,
Third typo, sigh.
We assume total elasticity ;-)
Dirk, also, you responded to my question, which was originally stated
as "Can someone provide a mathematical model of inertia?"
If your answer is in mathematics, why so many typos?
You may think that a bit unfair of a quesiton, but look at my solution
to the problem:
http://groups.google.com/group/sci.physics/msg/313a0b32546fd53d?hl=en&
It is a single algorithm, not a mixture of equations and instructions
in English like yours.
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 11:29:51 AM |
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"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140540148.744526.14700@o13g2000cwo.googlegroups.com...
Dirk Van de moortel wrote:
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote in message
news:k3rKf.269669$So7.7702599@phobos.telenet-ops.be...
[snip]
Assuming total inelasticity of the collision,
Third typo, sigh.
We assume total elasticity ;-)
Dirk, also, you responded to my question, which was originally stated
as "Can someone provide a mathematical model of inertia?"
If your answer is in mathematics, why so many typos?
You may think that a bit unfair of a quesiton, but look at my solution
to the problem:
http://groups.google.com/group/sci.physics/msg/313a0b32546fd53d?hl=en&
Have you counted the number of typos you made before
you got it right?
Dirk Vdm
It is a single algorithm, not a mixture of equations and instructions
in English like yours.
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 11:42:13 AM |
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Dirk Van de moortel,
Have you counted the number of typos you made before
you got it right?
Less than yours.
Do you deny that your solution is a mixture of equations and English
instructions?
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 12:04:23 PM |
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"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140543733.193135.276170@z14g2000cwz.googlegroups.com...
Dirk Van de moortel,
Have you counted the number of typos you made before
you got it right?
Less than yours.
Congratulations.
Do you deny that your solution is a mixture of equations and English
instructions?
Watch that orifice, Helland.
Dirk Vdm
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 12:12:45 PM |
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Dirk Van de moortel wrote:
"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140543733.193135.276170@z14g2000cwz.googlegroups.com...
Dirk Van de moortel,
Have you counted the number of typos you made before
you got it right?
Less than yours.
Congratulations.
Do you deny that your solution is a mixture of equations and English
instructions?
Watch that orifice, Helland.
I asked for a mathematical answer.
We both answered it.
I proposed an alogorithm.
You proposed a mixture of equations, English instructions, and
visualizing pictures in your brain.
Folks, Dirk denies this. He won't let himself admit, and he doesn't
want to discuss it. He sets the message up so that I can't even respond
where he posts his message.
That's denial. That's a man's natural hostile reaction to confronting
their beliefs.
Pathetic.
I'd think you were a bad person if it weren't so typical.
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| User: "Dirk Van de moortel" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 12:20:55 PM |
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"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140545565.403123.13750@g44g2000cwa.googlegroups.com...
Dirk Van de moortel wrote:
"MobyDikc" <mobydikc@gmail.com> wrote in message news:1140543733.193135.276170@z14g2000cwz.googlegroups.com...
Dirk Van de moortel,
Have you counted the number of typos you made before
you got it right?
Less than yours.
Congratulations.
Do you deny that your solution is a mixture of equations and English
instructions?
Watch that orifice, Helland.
I asked for a mathematical answer.
We both answered it.
I proposed an alogorithm.
A whopping 13 words before the first typo.
Congratulations.
Dirk Vdm
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| User: "MobyDikc" |
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| Title: Re: Mathematical model of inertia |
21 Feb 2006 02:46:12 PM |
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Dirk Van de moortel wrote:
A whopping 13 words before the first typo.
Congratulations.
Dirk is trying to address my questions by way of typos.
Congrats. You've hit a new level.
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