A man climbs up from ground to first floor using a ladder/stair. Assume that his kinetic energy does not change appreciably. Predict the sign of work done by ladder (if any).
I think the answer should be 'positive' because the negative work done by gravity has to be countered and hence some external agent must do positive work on us.
But, there's a second thought. Since at each instant normal reaction is perpendicular to direction of motion (in case of stairs) (motion being lifting of leg) therefore the work done must be zero. But then a question arises – who countered gravity?
I'm confused between the two. Both sound promising but not perfect.
Best Answer
The ladder (or the stairs) don't do any work at all. The reason for the same is that the ladder (or stairs) applies the force on our feet only when our feet are right in contact with the ladder (or the stairs). Thus, the point of application of force doesn't move at all while the force is being applied. Thus, net work done by the ladder (or the stairs) is zero because there is no displacement of the point of application of the force. As soon as the displacement occurs, the force ceases to be applied instantaneously.
Now, coming to the question of "who then did the work?". It is your body who did the work through its muscular forces using the (bio)chemical energy. In the case of an escalator or an elevator lifting you up, the point of application of force moves in the direction of the force (upward) and thus, the work done required to counter the work done by gravity is done by the elevator (or the escalator). Of course, this energy comes from the electricity used to run the elevator (or the escalator) and essentially, the electricity does the work instead of your body - giving you some rest and comfort!