[Physics] Why does positive work done by internal conservative forces $\implies$ decrease of potential energy

Question

Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U_{initial}-U_{final}$$

A positive work done by a force translates into a negative variation of potential energy. That sounds ok, given the interpretation of $U$ stated above. If a force does some work, then the "potentiality" of doing more must decrease.

But the equation says also that any time the force does a negative work, the potential energy increases. Why does this happen, in the light of such interpretation of $U$?

Answer 1

If a force does negative work, it is in fact trying to work against another force, doing positive work.

When you lift up a book from the floor, gravity does negative work on the book, while you do positive work. And the books rises higher up, so $U$ increases.

• Negative work just means "receiving" instead of "giving" away energy. Which basicly is the same as saying that something else is doing work on it.

There is not more to it than that.