I am really confused about this. The potential energy acquired by an object is equal to $mgh$, if we are on any planet, where $g$ is the planet's gravitational acceleration, which directly comes from the definition of work, that is $W = F.s$. But, suppose I am holding a book, and I lift it with a force greater than its weight $mg$, will it acquire more potential energy than before, just because $F$hand $>F$bookweight ?
In addition to this, I want to ask this. Suppose I am standing in space, near a planet, where there in no air resistance, no external disturbance, just me and the planet. An suppose I am standing on the planet, and there is a book on the ground, and there is a gravitational field between us, which is attracting me and the planet. Now, if I pick up the book and take it to a certain height more than its weight on the planet, will it have acquired more potential energy? (Remember there is no drag, no resistance nothing)