You got me there your right about the F=mg not being the same as F=ma, but I read about it F=mg is still correct tho if used right. My psychics teacher told me that you don't need to specify F(g)=mg like that because you'll get the same answer etc. Maybe it's different teaching system here in Sweden XDNot really. A is acceleration, you find it usuallly by doing speed/time. g is 9.8 and it's the acceleration of earth's gravitational pull.
That's why I specified F(g) as in gravitational force and not just "force". Or w as in weight, which is basically the same thing.