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Here's another analogy about the equipotential/g situation
that might help intuition.  Imagine you're walking across
a landscape of rolling hills, always keeping the same
altitude above sea level.  In this case you're walking
along a line of equal gravitational potential -- these are
called contour lines on a topographical map.  As you're
walking, or perhaps pushing a soccer ball, you will notice
a force to the side that depends on the steepness of the
hill where you happen to be.  This is the 2-dimensional
analog to the strength of gravity, and is represented on the
topo map by how close together the contour lines are.
You can certainly walk from a place where this force is
very weak (the hill is very shallow) to a place where it
is strong (the hill is steep) without gaining or losing
altitude, and therefore without gaining or losing any
potential energy.
        -- Bill

   

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