Question on Electrical Potential Energy

[tigerguy]

Two particles each have a mass of 5.8E-3 kg. One has a charge of +5.0E-6 C, and the other has a charge of -5.0E-6 C. They are initially held at rest at a distance of 0.70 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value?
--
I've been trying a few steps to solve this question. I realize that I need to take a conservation of energy approach, where the Electrical Potential Energy initial = EPE final + KE final.

I'm not sure, however, if I am missing any potential energies, and how to calculate the EPE. How would I mathematically differentiate between initial and final?

Maybe someone can lead me in the right direction with how to calculate the EPE and confirm if my thinking up to this point is correct.

 

[Office_Shredder]

Remembering that electric potential energy = -kq1q2/r (how do you get those cool white boxes with the math terms in them?), you can easily calculate the potential energy at the full and half distance between them. Keep in mind that the EPE is negative... if they're infinitly far away, it's equal to zero, and gets smaller (more negative) as they approach.

Then each of them should have an equal kinetic energy

 

[tigerguy]

So you are saying basically that kq1q2/r initial = 1/2mv^2 + kq1q2/r final, where the r initial is 0.70 and the r final is 0.35? And then solve for the v?

Thanks for your help so far

 

[Office_Shredder]

tigerguy, the only problem is the 1/2mv^2. There are two objects moving with equal speed, so you need to keep their kinetic energies separate (although they can be added together)

 

[tigerguy]

When you say keep their kinetic energies separate, do you mean that I need two terms that represent kinetic energy (where they would add to mv^2, as their masses are the same)?

 

[Office_Shredder]

Exactly, because they are both moving.

If you had two bowling balls, and 10J of kinetic energy to give them (forgive me for being ambiguous about how the energy is transferred), and you wanted to make them both move at the same speed, how would you calculate the speed? You wouldn't use 1/2mv^2 = 10

It's the same concept here

 

[tigerguy]

I'm getting mv^2 equaling a negative answer, which is obviously wrong. I'm confused as to where I've gone wrong:

-kq1q2/r = -kq1q2/r + mv^2

 

[Doc Al]

You haven't specified the values of r; realize that $r_1 = r_2/2$.