Escape velocity for charged spheres with negative potential energy

[aftershock]

This is a conceptual question I've been thinking about dealing with conservation of energy.

For example, say you have two charged spheres, one positive and one negative. The positive one is glued in place while you kick the negative one away. How fast would you have to kick the negative one so that it won't come back?

I'm aware these types of problems are pretty simple. potential + kinetic = 0

What I don't understand is how the final energy of the system is zero. Where'd it go?

EDIT: Is it because the potential energy is negative, so the sum is zero initial energy also? That's a weird concept to me to be honest.

 

[tiny-tim]

hi aftershock!

I'm aware these types of problems are pretty simple. potential + kinetic = 0

What I don't understand is how the final energy of the system is zero. Where'd it go?

i don't know where you got that equation from …

the correct equation is KE + PE = constant, not zero …

in other words, KE_i + PE_i = KE_f + PE_f

if you define PE at ∞ to be zero, then PE at distance r is minus kqQ/r, so escape velocity (defined as the speed that you need to reach infinity at speed zero) is the speed corresponding to KE = kqQ/r

 

[aftershock]

hi aftershock!


i don't know where you got that equation from …

the correct equation is KE + PE = constant, not zero …

in other words, KE_i + PE_i = KE_f + PE_f

if you define PE at ∞ to be zero, then PE at distance r is minus kqQ/r, so escape velocity (defined as the speed that you need to reach infinity at speed zero) is the speed corresponding to KE = kqQ/r

Yeah I meant in this particular problem the constant is 0. If we define PE to be 0 at ∞ like you said.

Not that it is always equal zero, of course I know that's not true.

Thanks for the reply!