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2) I don't see how static friction can be a force FIELD
so therefore the question of whether it is derived
from a potential is unaskable. I don't see how the
work can be a function of path (or the opposite) if
there are no paths (because things are static).
4) To enlarge the discussion, consider Coriolis
forces. They are a function of velocity, not a
function of position. They are manifestly not
the gradient of any potential. But they contribute
zero work to the particle, regardless of path, so
their work is path-independent. I consider them
conservative for this reason.