Electric Potential Energy - Final Velocity

[Glendon Koss]

Homework Statement

Four protons (each with mass 1.7

10-27 kg and charge 1.6

10-19 C) are initially held at the corners of a square that is 7.1

10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the final speed of each proton is small compared to the speed of light.)

Homework Equations

U_electric = (1/4πϵo)(q₁q₂/r)

The Attempt at a Solution

E_f = E_i
K₁ + K₂ + K₃ + K₄ = U_1,2 + U_2,3 + U_3,4 + U_4,1 + U_1,3 + U_2,4

U_1,2 = U_2,3 = U_3,4 = U_4,1
and
U_1,3 = U_2,4

U_1,2 = (1/4πϵo)(1.6E-19)2/7.1E-9 = 3.245E-20 J
U_1,3 = (1/4πϵo)(1.6E-19)2/√2(7.1E-9) = 1.933E-24 J

U_1,2 + U_2,3 + U_3,4 + U_4,1 + U_1,3 + U_2,4 = 4(3.245E-20) + 2(1.933E-24) = 1.298E-19 J

K₁ + K₂ + K₃ + K₄ = 1.298E-19 J

I'm not sure where to go from here. How do I get the final speed of each proton?

 

[kuruman]

Is there any reason why one particular proton will have more kinetic energy than the others?

 

[TSny]

U_1,2 = (1/4πϵo)(1.6E-19)2/7.1E-9 = 3.245E-20 J
U_1,3 = (1/4πϵo)(1.6E-19)2/√2(7.1E-9) = 1.933E-24 J

Check the second calculation