If the counterweight fell off and you had to hold the elevator for 5 hours how much work would you do?

Answer 1

If you are holding the weight of the elevator in a static position without moving it, you are doing no work at all! This may seem counter-intuitive, after all your muscles get tired after a while. But imagine replacing yourself with a strut of metal or wood to hold the weight, and then taking your hands away. It stays in the same place. But a passive piece of wood or metal is not capable of doing any work, unless it has kinetic energy, which it obviously doesn't as it is static. You could extend this analogy to the steel or wooden frame of a building-it is supporting the weight for as long as the building stands, but does no work. In the case where you are holding the weight, your muscles will indeed get tired after a while, but that is due to not being able to move, and the build up of lactic acid in the muscles. If you are still in doubt, imagine picking up a stone on the seashore, and then holding it. Certainly during the picking up you are doing work, because you are raising it against the gravitational force, but once you have it in a comfortable grip in your hand, doing work ceases. Of course if you start walking you are doing extra work because you are now a bit heavier than before, but that is because of the movement, each pace involves using some energy but standing still does not.