1. I am quoting a text from a web sight before my question.

"Let's assume we have a 5 kg box on the floor. Let's arbitrarily call its current potential energy zero, just to give us a reference point. If we do work to lift the box one meter off the floor, we need to overcome the force of gravity on the box (its weight) over a distance of one meter. Therefore, the work we do on the box can be obtained from:
Work=Fd =mgh=(5)(9.8)(1) =49J "

My Question here is, if you apply F=mg on the box the box will stay at rest then how it can be lifted 1 meter?
In the answer if you say that you have to apply a little more force (F1) to produce acceleration in the body then my counter question will be, This means we are not applying constant force on the body first we apply a little more force on the body to produce acceleration and then we reduce the force to mg, if this is the case then to calculate the work we first need to calculate the work done by F1 (the little more force to produce acceleration) lets call it W1 then we need to calculate the work done by the force mg lets call it W2 and the total work will be W=W1+W2. Am I right?  2.

3. No. Technically, you do have to apply more than mg but the extra force above mg you apply will accelerate it, giving it a little bit of kinetic energy. But then when you get to the top of your lift, you have to apply a little less than mg for an instant to let it decelerate. The net result is that you again have zero kinetic energy and the only thing to worry about in your calculation is the potential energy.  4. Ah, well you are confusing how Energy and Force relate. Energy that it takes is the force exerted over a certain path. A path integral so to speak. Imagine we'd be perfect lifting creatures. Then I could spend my lifetime moving the box up and down, just costing me energy, yet the box would still have the same potential energy that it has when I just lift it up. That is because we have spend energy on warmth, dissipation. You name it.
In reality you always do more work then you gain in potential energy, if only for thermodynamical usage. But if you'd calculate the force, even if it is bigger at the start, and you'd follow it's path the energy it would take to lift it up can be seen rather simple: imagine that you'd lift it up infinetly small. Then the difference is force can also be infinitely small. And the answer of the integration would simply be E=mgh. If you change the time it takes, you get a whole different way of calculating. This is called Analytical mechanics. And is used for more complex mechanical system.  energy, physics, work 