Still not getting getting correct solution

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The discussion revolves around calculating the maximum force between two protons accelerated towards each other at 1650 km/s. The user references the conservation of energy principle, stating that initial kinetic energy (KE_i) equals final potential energy (U_f) when initial potential energy (U_i) is zero. They express confusion over the equations used, particularly the force equation derived from Coulomb's law and its relation to kinetic energy. Key questions include the meaning of KE_i and the force (F) in this context. Clarification on the derivation and application of these equations is sought to resolve the discrepancies in the solution.
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Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 1650 km/s,measured relative to the earth. find the maximum force that these protons will exert on each other.
KE_i + U_i = KE_f + U_f ;where U_i=0 and KE_f=0,so KE_i=U_f
if r= (q^2/(4*pi*epsilon_0))(1/KE_i) then F=(1/(4*pi*epsilon_0))(q^2/r^2) but the solution comes out as incorrect.
 
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Can you explain what this eqn is about - where does it come from?
What is the question ?
What is KE_i ?
What is F ?
 

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