A paradox inside Newtonian world

ObsessiveMathsFreak

To every individual ball. Look this would go a lot faster if you bothered to do some calculations.

Tomaz Kristan

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?

K.J.Healey

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.

Tomaz Kristan

Looks quite good to me.

K.J.Healey

but its not right. Left side approaches zero.

Tomaz Kristan

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.

K.J.Healey

how is it correct? i was just putting what you said into calculable terms. How did you get that number, please show the math.

Tomaz Kristan

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.

Tomaz Kristan

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.

BillJx

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??

Tomaz Kristan

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?

ObsessiveMathsFreak

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

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

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.

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

> 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

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

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?