This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Hanging over a pulley there is a rope, with a weight at one end.
At the other end hangs a monkey of equal weight. What happens if
the monkey starts to ascend the rope? Assume that the mass of the
rope and pulley are negligible, and the pulley is frictionless.
The monkey is pulling down on the rope hard enough to pull itself up. This
increases the tension in the rope just enough to cause the weight to rise at
the same rate as the monkey, since they are of equal mass.