Basic equation of work is given by Fs. When work is done, the energy is stored either in form of potential or kinetic. My question arises when we look at a case of applying mg of force upwards on a box of mass m. If the box was initially stationary, with application of that force, the net force will be 0 thus the box will remain stationary with no change in potential energy. But if the box initially had some velocity, with application of mg upwards, the net force will be 0 again but this time the box will be constantly moving up. If the box constantly moves up, it will be gaining potential energy as well. It requires same amount of energy to generate mg upwards but in the first case, no energy is stored while in the second, some energy is being stored. So whats going on in this case? Thanks

Basic equation of work is given by $F\cdot s$. When work is done, the energy is stored either in form of potential or kinetic. My question arises when we look at a case of applying $m g$ of force upwards on a box of mass $m$. If the box was initially stationary, with application of that force, the net force will be 0 thus the box will remain stationary with no change in potential energy. But if the box initially had some velocity, with application of $m g$ upwards, the net force will be 0 again but this time the box will be constantly moving up. If the box constantly moves up, it will be gaining potential energy as well. It requires same amount of energy to generate $mg$ upwards but in the first case, no energy is stored while in the second, some energy is being stored. So whats going on in this case? Thanks