I just wanted to start a thread about the basic concepts of work and energy to clarify some things I have been wondering about. Firstly, work and kinetic energy are concepts independent of force fields; right? Am I right to think that the relationship of force and kinetic energy with respect to distance is analogous to the relationship of force and momentum with respect to time? Because if I apply a constant force for a certain time period I change my momentum from an initial momentum to a final one ([itex] F \Delta t = \Delta P [/itex]). Similarly; if I apply a constant force for a certain distance I change my kinetic energy ([itex] F \Delta x = \Delta E_k [/itex]). Work is like if I gave a name to the quantity [itex] F \Delta t = \Delta P [/itex], which as far I know has no name and is only know as change in momentum or F times distance. Is all of that too far off? Anyway.. potential energy only exists in the presence of a force field; correct? So in the absence of a force field, work done on a system will always equal the kinetic energy of that system. Like if there was no force fields in the universe there wouldn't even be a concept called potential energy. So is it that in the presence of a force field [itex] W=E_p + E_k [/itex]? I guess the only thing that is confusing me at this point is the fact that the expression for potential energy depends on what force field you're dealing with. Is that correct to assume or is there a general expression for potential energy? Is it the integral of force with respect to position? EDIT: Also, what would be the analogue to potential energy in my momentum analogy? Maybe some special case since force fields are not necessarily dependent on time?