I was reading about energy, and I got to know that energy is the ability to do work. Then I read about work, and I found that almost everywhere, resources say that when an object applies force to move another object through a distance, it is said to do work, and the Math is that $W = Fs$(Even the tag on this site which says work). So my first question is:
Can work be described in another way instead of saying this? This is not making a complete intuitive sense to me. And, why is it defined like this? What is the reason behind defining something called work? Is there any derivation to it?
And I am also not able to understand negative work. Lets recount the example of friction, which opposes the motion of an object, so we say that the work done is negative. But, if I go by the definition, then I think that friction is not making the object move through a certain distance, it is trying to stop it.
So what role does work play here?
And I saw many physics problems which looked extremely difficult to solve, but with this concept of conservation of energy, they were looking very simple. But still, I am not able to understand the reason behind the formulation.
Is this formulation more of an empirical result, or is it something else that I am missing?
I am not opposing this, just asking logic behind things. I hope readers are not annoyed with this :)