I've read over 10 books about work and energy, and I just simply can't understand it.
First of all, they go ahead and randomly define that work is force times distance: $$W=F X \cos\theta$$ Okay, cool, this is just a definition.
Next, they go ahead and tell us that energy is the "ability to do work", then they tell us about the kinetic energy, potential energy and spring energy, all of them derived from the definition they have introduced to us ($F X$ or $\int F\,dx$). Then they tell us that the energy is conserved.
What I just don't simply understand, why is this 'ability to do work thingy' (which is energy) conserved?
They came up with a random definition and derived all the energy equations from it and then they tell us this quantity is conserved, why?
For example, why didn't they define work as $W=F X^2$ or $W=(F 2) X^3$ or anything like that, and then derive all the energy equations from there? Why is it $W=F X$? And did they come up with this conclusion from Newton's laws?