Final answer:
When two protons are released from rest at a closer distance, they will accelerate towards each other due to the electrostatic force of attraction. As they move closer, their potential energy decreases while their kinetic energy increases. When they reach their original separation, their kinetic energy will be at its maximum value and their potential energy will be zero.
Step-by-step explanation:
When two protons are released from rest at a closer distance, they will experience an electrostatic force of attraction due to their like charges. This force will cause them to accelerate towards each other. The energy of the system will be conserved, meaning that the total energy of the protons will remain constant. As they move closer, their potential energy decreases while their kinetic energy increases. When they reach their original separation, their kinetic energy will be at its maximum value and their potential energy will be zero.
The protons will have gained kinetic energy equal to the potential energy they started with. Since they share the total available energy, each proton will have gained half of this energy. Their final velocity can be calculated using the equation for kinetic energy:
KE = 1/2mv^2
We can set the initial potential energy equal to the final kinetic energy:
PE_initial = KE_final
1/2k(Q1)(Q2)/r_initial = 1/2mv^2
Where k is the electrostatic constant, Q1 and Q2 are the charges of the protons, r_initial is the initial separation between them, and m is the mass of each proton. By rearranging this equation, we can solve for the final velocity:
v = sqrt(k(Q1)(Q2)/m * (1/r_initial - 1/r_final))
Substituting the given values, we can calculate the final velocity when the protons reach their original separation.