Finding Particle Velocities in Center of Mass Calculation

[Littlepig]

hi there.

I'm having some problems with Center Mass calculations... I have a CM moving at x-axis with Vx, and it as a mass of M.

Now, assume CM is made of n particles, but i only know their masses(all equal m), not their speed. My problem is how do i find their velocities? By Energy and momentum conservation,

$$MV=m\sum^{n}_{i=1}v_{i}$$
and
$$MV^{2}=m\sum^{n}_{i=1}v^{2}_{i}$$
substituting V in second; as M=m*n(Mass of mass center is the sum of the masses of all particles) and simplifying
$$(\sum^{n}_{i=1}V_{i})^2/n=\sum^{n}_{i=1}v^{2}_{i}$$

And I'm stuck here. Even if i begin to assume something, like a random velocity of one particle, i can't get a algorithm that have physical meaning for solving this equation in order to $$v_{i}$$ for every i

Can any1 tell me if there's a solution, or at least a clue about it?

Thanks in advance,
Littlepig

 

[Doc Al]

I'm having some problems with Center Mass calculations... I have a CM moving at x-axis with Vx, and it as a mass of M.

You mean: You have a system with total mass M whose CM has a velocity = Vx.

Now, assume CM is made of n particles, but i only know their masses(all equal m), not their speed. My problem is how do i find their velocities?

Not enough information.

By Energy and momentum conservation,

$$MV=m\sum^{n}_{i=1}v_{i}$$

This is correct (by definition of CM).

and
$$MV^{2}=m\sum^{n}_{i=1}v^{2}_{i}$$

This is not correct.

Simple example: Imagine a gas of particles in a jar. Total momentum = 0, velocity of CM = 0, yet total KE of the particles does not equal zero.

 

[Littlepig]

Yeah, you are right..xD i must then reformulate my problem...xD

Tk U very much