*Answer:* Let be the mass of the bucket and the depth of
the well. The gravitational force acting on the bucket is of magnitude and
is directed vertically downwards. Hence, (where upward is defined to be positive).
The net upward displacement of the bucket is . Hence, the work performed by the
gravitational force is the product of the (constant) force and the displacement of the
bucket along the line of action of that force:

Note that is negative, which implies that the gravitational field surrounding the bucket gains energy as the bucket is lifted. In order to lift the bucket at a constant rate, the man must exert a force on the bucket which balances (and very slightly exceeds) the force due to gravity. Hence, . It follows that the work done by the man is

Note that the work is positive, which implies that the man expends energy whilst lifting the bucket. Of course, since , the energy expended by the man equals the energy gained by the gravitational field.