Two protons are at rest, 0.750nm apart. Consider the two situations: I) One prot

Question

Two protons are at rest, 0.750nm apart. Consider the two situations:
I) One proton is held fixed in position while the other is released, subject only to the electric forced exerted by the other proton.

II) both protons are released, subject only to the electric force between them.

How does the kinetic energy of proton in situation I, when it is infinitely far from the other compare to kinetic energy of protons in situation II, when they are infinitely far from each other? how do their speeds compare when they are infinitely far apart?

Explanation / Answer

The initial potential energy is the same in both cases, and the final potential energy is zero in both cases. This means that:

In situation 1, all of the initial potential energy becomes KE for the proton that moves.

In situation 2, due to symmetry, both protons share equally in the energy... so each of their final KE is half of the total energy.

Conclusion:

The KE of the proton in Sit 1 is twice the KE of a proton in Sit 2.

Since KE is prop to speed squared...

speed of proton in Sit 1 = sq root 2 * speed of a proton in Sit 2

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