# A paradox inside Newtonian world

by Tomaz Kristan
P: 406
 Quote by Tomaz Kristan 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.
 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.
P: 406
 Quote by Tomaz Kristan 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 by Tomaz Kristan 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?
 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.
 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.
 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?
 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.
 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?
P: 406
 Quote by Tomaz Kristan First of all, the force to the mass center is NOT the sum of all forces. Not at all. Do you know that?

$$M\mathbf{R} = \sum_i m_i \mathbf{r}_i$$
$$M\dot{\mathbf{R}} = \sum_i m_i \dot{\mathbf{r}_i}$$
$$M\ddot{\mathbf{R}} = \sum_i m_i \ddot{\mathbf{r}_i}$$
 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.
 Mentor P: 28,792 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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