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A paradox inside Newtonian world

by Tomaz Kristan
Tags: inside, newtonian, paradox, world
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ObsessiveMathsFreak
#505
Feb27-07, 09:06 AM
P: 406
Quote Quote by Tomaz Kristan View Post
Was it ... that a finite force is affecting every ball? All pointed to the left? At least at t=0?
We knew that from the very beginning. Your paradox concerns the force on the center of mass. Could you give your proof that this force is also finite.
Tomaz Kristan
#506
Feb27-07, 11:42 AM
P: 218
I don't care for the mass center. I care only for the mass particles.

I am glad that you agree with me about those.

> Could you give your proof that this force is also finite.

I could, after this is settled with the majority here. That all balls are forced to the left hand side.
ObsessiveMathsFreak
#507
Feb27-07, 04:31 PM
P: 406
Quote Quote by Tomaz Kristan View Post
I don't care for the mass center. I care only for the mass particles.
Your paradox revolved around the fact that the center of mass of a closed system was supposedly moving. If your not going to aruge that anymore then there's not much else to discuss.

Quote Quote by Tomaz Kristan View Post
I could, after this is settled with the majority here. That all balls are forced to the left hand side.
Well I'm settled on the finite force on every individual ball part. Care to move on to the center of mass bit?
Tomaz Kristan
#508
Feb28-07, 03:19 AM
P: 218
> Well I'm settled on the finite force on every individual ball part.

Fine. Everybody else also?

> Your paradox revolved around the fact that the center of mass of a closed system was supposedly moving.

It can also revolves around the strange fact you admit. Only left pointed forces at t=0. A matter of choice.
nealh149
#509
Feb28-07, 07:27 PM
P: 112
This is absolutely ridiculous. OMP has provided a considerable amount of mathematic proof that this mathematic problem is unsolvable, results a divergency. Yet, Tomaz, you still continue to provide an equation that is set up, but not your process for solving it. OMP, thus far, has constructed the only VALID argument between the two of you. And you are still unable to provide full and complete calculation of the force on the center of mass, which is where the core of this seeminly fake paradox lies.
Tomaz Kristan
#510
Mar1-07, 06:19 AM
P: 218
What is your point?

That it is all OK, if all the net forces, to every ball, are finite and left pointing, as long as the force to the mass center is divergent?

Is that your point?
nealh149
#511
Mar1-07, 08:10 PM
P: 112
Yes because the force on the center of mass will be equal to the sum of the forces on all particles in the system. Thus the forces add to be infinite. This is a problem.
Tomaz Kristan
#512
Mar2-07, 02:00 AM
P: 218
First of all, the force to the mass center is NOT the sum of all forces. Not at all.

Do you know that?
ObsessiveMathsFreak
#513
Mar2-07, 09:27 AM
P: 406
Quote Quote by Tomaz Kristan View Post
First of all, the force to the mass center is NOT the sum of all forces. Not at all.

Do you know that?
It hadn't occurred to us.

[tex]M\mathbf{R} = \sum_i m_i \mathbf{r}_i[/tex]
[tex]M\dot{\mathbf{R}} = \sum_i m_i \dot{\mathbf{r}_i}[/tex]
[tex]M\ddot{\mathbf{R}} = \sum_i m_i \ddot{\mathbf{r}_i}[/tex]
Tomaz Kristan
#514
Mar2-07, 12:00 PM
P: 218
Do you know, that this is not the case?

You and I could be forced to accelerate in the opposite directions, yet the center of the mass of the you&me system, would not move at all. Let alone to be accelerated.

Just one example.
ZapperZ
#515
Mar2-07, 12:31 PM
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P: 29,239
This thread has gone long enough, and I believe that nothing has been achieved. This topic is now closed, and no new ones should be opened related to it.

Zz.


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