Calculating the Speed of Charged Spheres Moving Away from Each Other

[Canadian]

Homework Statement

Four 1.0 g spheres are released simultaneously and allowed to move away from each other. What is the speed of each sphere when they are very far apart?

The Attempt at a Solution

Here's what I got initial potential energy is equal to final kinetic energy.

0.9866 m/s but according to the computer program that's not right. Where'd I go wrong.

Thanks

 

[Sojourner01]

I think your logic is sound but the working is a little iffy. Each sphere sits in the potential of the other three - that's a definite sum of potential energy for each. Moving then to a potential of zero has a definite energy conversion. The only important factors are the initial and final positions.

Consider first one of the spheres. It sits in a potential Kq^2/r from two of the other spheres, and Kq^2/sqrt(2)*r from the third. These sum to give its potential energy. Through symmetry, each of the other spheres is identical.

You appear to have too many terms in that potential energy summation.

 

[Canadian]

Ok thanks, I think I see where I was going wrong I only need to consider the forces acting on one sphere alone since the rest will be identical in their speed.

Is this better? The computer program still doesn't like the answer I got.

 

[Canadian]

Bump . .

Should I be dividing by 4 somewhere since there are 4 charges??

 

[Sojourner01]

I'm honestly not sure. I had assumed that since the spheres were moving from a potential to no potential, the energy transfer was definite.

I think you'll have to go back to the definition of energy in a potential - integrate the instantaneous force on each sphere with respect to distance. I'm too tired and crap at maths to do this myself. Good luck.