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>> 2) You can change the sum of KE and PE of a system by doing work
>> with a conservative force
....
Example 1: ...
*) Define "the system" to be a charged particle, initially at rest, but
free to move.
*) Apply an electric field, initially zero, then nonzero, then zero again.
*) The particle picks up a nonzero kinetic energy. BTW it also
picks up nonzero momentum. Energy and momentum were transferred
across the boundary of "the system".
*) Potential is the same before and after, so the *sum* of KE and PE
is changed, not just KE at the expense of PE.