Speed of two charged particles repelling each other

[fight_club_alum]

Homework Statement

28. Particle A (mass = m, charge = Q) and B (mass = m, charge = 5 Q) are released from rest

with the distance between them equal to 1.0 m. If Q = 12 μC, what is the kinetic energy of

particle B at the instant when the particles are 3.0 m apart?

a . 8.6 J

b. 3.8 J

c. 6.0 J

d. 2.2 J

e. 4.3 J

Homework Equations

(delta (u) = delta ke

The Attempt at a Solution

(k*(Q*10^-6)*(5Q*10^-6))/1) - (k*(Q*10^-6)*(5Q*10^-6))/3) = 4.3152
4.3152 = u1 + u2 <-- I want u2 alone since the initial kinetic energy is zero
5u1 = u2
4.3152 = u1 + 5u1
4.3152 = 6u1
u1 = 0.7192
(5*0.7192) = 3.596 ~ 3.6 <-- not the right answer, it should be d

Any help, please?

 

[haruspex]

5u1 = u2

Why?

 

[fight_club_alum]

I think because particle two will have a bigger share of the total potential; I am not sure

 

[PeroK]

I think because particle two will have a bigger share of the total potential; I am not sure

What about Newton's second and third laws?

 

[haruspex]

I think because particle two will have a bigger share of the total potential; I am not sure

Maybe, but why in that ratio? Use conservation laws.

 

[fight_club_alum]

What about Newton's second and third laws?

Can you please just tell me how to correctly understand this problem because if I could understand it on my own I wouldn't have posted it in the first place?
Thank you

 

[PeroK]

Can you please just tell me how to correctly understand this problem because if I could understand it on my own I wouldn't have posted it in the first place?
Thank you

$F = ma$

Is the force on each particle the same? Is the mass the same? What about acceleration? What about KE?

 

[fight_club_alum]

$F = ma$

Is the force on each particle the same? Is the mass the same? What about acceleration? What about KE?

Yes the forces should be the same
They both have the same mass
So They both should have the same acceleration and the same KE
I think I see the issue by now, so the total u should be divided by two
Thank you so much