- #1
Littlepig
- 99
- 0
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,
[tex]MV=m\sum^{n}_{i=1}v_{i}[/tex]
and
[tex]MV^{2}=m\sum^{n}_{i=1}v^{2}_{i}[/tex]
substituting V in second; as M=m*n(Mass of mass center is the sum of the masses of all particles) and simplifying
[tex](\sum^{n}_{i=1}V_{i})^2/n=\sum^{n}_{i=1}v^{2}_{i}[/tex]
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 [tex]v_{i}[/tex] for every i
Can any1 tell me if there's a solution, or at least a clue about it?
Thanks in advance,
Littlepig
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,
[tex]MV=m\sum^{n}_{i=1}v_{i}[/tex]
and
[tex]MV^{2}=m\sum^{n}_{i=1}v^{2}_{i}[/tex]
substituting V in second; as M=m*n(Mass of mass center is the sum of the masses of all particles) and simplifying
[tex](\sum^{n}_{i=1}V_{i})^2/n=\sum^{n}_{i=1}v^{2}_{i}[/tex]
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 [tex]v_{i}[/tex] for every i
Can any1 tell me if there's a solution, or at least a clue about it?
Thanks in advance,
Littlepig