A question I found in a book recently concerned two worms climbing up one side of a wall and back down the other side, such that the worms were each half across the wall (I.e. the lengths on either side of the wall were equal for each worm). To calculate the amount of work done against gravity, it is suggested that this can be done by using the change in height of the worm's centre of gravity, in the equation W = mgh.
My question is: does this imply that negative work can be done against gravity?
My initial instinct would be yes, since the worm starts with a height of the centre of gravity of 0m, which is raised (implying +ve work against gravity) and then lowered again (implying -ve work against gravity).
The second question is: how come the snail doesn't do total work of: the work done to raise half of its mass by the height of the wall + the work done to raise half of its mass to mean height of the trailing half above the wall?
More generally, if I (70kg) climb a ladder of height 1m and then climb back down again, have I done 70g N work against gravity? Or have I done 0N work?