Kinetic energy and speed of system of charges (electric potential)

[jpdelavin]

Homework Statement

A square of side s has a point charge at each corner. They all have the same charge +q, but different masses, m1, m2, m3, and m4, respectively. Initially, all of the charges are held at rest until they are released. Of course, they would repel each other and move away from each other until they are very very far. What is their final velocities at infinity (i.e. a long long time after they are released)?

Homework Equations

U_i=kq₁q₂/r
KE=(1/2)mv²

The Attempt at a Solution

I know that the initial electric potential energy of the system is:

U=(kq²/s)(4+sqrt(2))

To conserve energy, I know that this should also be the total kinetic energy of the system at infinity.

Now, I don't know how to divide the kinetic energy among the charges. If I do this, I can get the final velocity using KE=(1/2)mv².

Am I correct? Can you give any hints on how to divide the kinetic energy? Should I just divide it equally?

 

[tms]

Can you think of any physical principles that might dictate how the energy is distributed? What else might be conserved, for instance?

 

[jpdelavin]

momentum, perhaps? but that still would just leave me with two equations right, and i have four unknowns?

 

[Poley]

Try treating three of the charges as one single charge distribution. The energy of the fourth charge DUE to the distribution of the other three should be constant.

 

[tms]

momentum, perhaps? but that still would just leave me with two equations right, and i have four unknowns?

You are working in 2 dimensions, don't forget. Also think about symmetries.

It will also help if you set up your coordinates so that the charges are on the axes.

 

[jpdelavin]

@Poley: Is this what you mean?

For particle 4 for example:
.5*m4*v4^2=q*(kq/a+kq/a+kq/(a*sqrt(2))