I’m an applied math grad student and I wanted to check my conceptual understanding of what I thought was a basic mechanics problem. You have two blocks connected by a weightless, frictionless string passing through a tiny hole in a table. On the table, one block (mass m) rotates without friction about the hole, while the other (mass M) dangles below the hole. The dangling block is at rest. The original question was: How much work does it take to move the dangling block down a distance d (presumably to a new static equilibrium)? However, if my current understanding is correct, it would be impossible for it to reach a new equilibrium on its own, because the original equilibrium is unstable. As soon as you nudge the dangling block, it should accelerate over time. So the least you could do would be to hold up the block to maintain the equilibrium, but of course this would involve doing negative work to slow it down (the textbook's solution gives a positive answer, which is where the difficulty first started for me). Does this seem correct? I’m happy to share my reasoning, but I’m curious to have someone else take a crack at it.