Question

why is the work done on a system by a conservative force always negative when the potential energy of the system increases and vice versa. does it have anything to do with the assumption that potential energy of the system is zero at infinity?

Answer 1

potential energy has increased meaning work has been done by you AGAINST the potential gradient(from lower potential to higher potential)
usually the conservative force does work so as to move the body from higher potentail to lower potentail(doing +ve work generally)
but since work is done AGAINST theis rule the work done by conservative force is -ve

Answer 2

work u do against the conservative force.......that is the point being that work done by the conservative force is -ve
u cannot say aha i am doing more work than conservtive force
we are interested to know the work done in increasing potentail enrerrgy BY the conservative force(in terms of it)

Answer 3

thanks for ur answer,doubt is cleared now