A paradox inside Newtonian world

In summary: And then the system will start to move to the left.In summary, the center of mass does not move, even when masses are removed.
  • #491
The sum of all the forces, to every ball is finite, yes. Negative, but finite.
 
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  • #492
Tomaz Kristan said:
The sum of all the forces, to every ball is finite, yes. Negative, but finite.
And the sum of all the forces on all the balls is infinite. This has been proven twice now. Frankly, you're trolling at this point.
 
  • #493
> And the sum of all the forces on all the balls is infinite.

The sum of all forces on all balls doesn't count. You can tile a cube to have the same "effect" of the "infinite sum of all forces".

It is not I who trolls here, OMF.

What only matters is:

The sum of all the forces, to every ball is finite, yes. Negative, but finite.

Now, if that's not true, is the only question.
 
  • #494
Tomaz Kristan said:
The sum of all the forces, to every ball is finite, yes. Negative, but finite.
To every individual ball. Look this would go a lot faster if you bothered to do some calculations.
 
  • #495
Calculation

The right side force to mass point m is:

(G*m*m/2)/(d*d)+(G*m*m/4)/(d*d*1.1*1.1)+...+... = (0.992*G*m*m)/(d*d)

What else do you need?
 
  • #496
Tomaz Kristan said:
The right side force to mass point m is:

(G*m*m/2)/(d*d)+(G*m*m/4)/(d*d*1.1*1.1)+...+... = (0.992*G*m*m)/(d*d)

What else do you need?

What you have written there is what, this?:

[tex]\sum_{i=0}^{\infty} \frac{Gm^2}{2^{i+1} d^{2} \sum_{j=0}^{i} 10^{-j} }= \frac{0.922 Gm^2}{d^2}[/tex]

Im just turning your ...'s into sums.
 
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  • #497
Looks quite good to me.
 
  • #498
but its not right. Left side approaches zero.
 
  • #499
The left side is quite weak, but I don't care. At least not more than for the OMF's calculation somewhere above.

But the right side is correct and that's enough.
 
  • #500
how is it correct? i was just putting what you said into calculable terms. How did you get that number, please show the math.
 
  • #501
I repeat myself:

>> (G*m*m/2)/(d*d)+(G*m*m/4)/(d*d*1.1*1.1)+(G*m*m/8)/(d*d*1.11*1.11)+...+... = (0.992*G*m*m)/(d*d)

It's trivial to see that.
 
  • #502
Even

(G*m*m/2)/(d*d)+(G*m*m/4)/(d*d*1.1*1.1)+(G*m*m/8)/(d*d*1.11*1.11)+...+... < G*m*m/(d*d)

would be quite enough. The left side force is finite. Also always exceeds the right side force.

No more is needed, no fancy math can change this strange fact. :cool:
 
  • #503
Tomaz Kristan said:
Am I wrong or not? What's your say?

- Thomas

Thomaz. The mathematians, physicists and engineers have answered your question. They have answered it more than fully, in many different ways, in a 34 page thread. You choose not to listen. So what do you actually want??
 
  • #504
BillJx said:
Thomaz. The mathematians, physicists and engineers have answered your question.

Good! What was the answer?

Was it ... that a finite force is affecting every ball? All pointed to the left? At least at t=0?

:smile:
 
  • #505
Tomaz Kristan said:
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.
 
  • #506
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.
 
  • #507
Tomaz Kristan said:
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.

Tomaz Kristan said:
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?
 
  • #508
> 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.
 
  • #509
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.
 
  • #510
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?
 
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  • #511
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.
 
  • #512
First of all, the force to the mass center is NOT the sum of all forces. Not at all.

Do you know that?
 
  • #513
Tomaz Kristan said:
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]
 
  • #514
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.
 
  • #515
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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