, ▁so ▁the ▁weight ▁force ▁of ▁the ▁ball ▁m g ▁is ▁constant . ▁Force ▁× ▁disp lacement ▁gives ▁the ▁work ▁done , ▁which ▁is ▁equal ▁to ▁the ▁gravit ational ▁potential ▁energy , ▁thus ▁ ▁The ▁more ▁formal ▁definition ▁is ▁that ▁potential ▁energy ▁is ▁the ▁energy ▁difference ▁between ▁the ▁energy ▁of ▁an ▁object ▁in ▁a ▁given ▁position ▁and ▁its ▁energy ▁at ▁a ▁reference ▁position . ▁ ▁Work ▁and ▁potential ▁energy ▁Pot ential ▁energy ▁is ▁closely ▁linked ▁with ▁forces . ▁If ▁the ▁work ▁done ▁by ▁a ▁force ▁on ▁a ▁body ▁that ▁moves ▁from ▁A ▁to ▁B ▁does ▁not ▁depend ▁on ▁the ▁path ▁between ▁these ▁points ▁( if ▁the ▁work ▁is ▁done ▁by ▁a ▁conserv ative ▁force ), ▁then ▁the ▁work ▁of ▁this ▁force ▁measured ▁from ▁A ▁assign s ▁a ▁scalar ▁value ▁to ▁every ▁other ▁point ▁in ▁space ▁and ▁defines ▁a ▁scalar ▁potential ▁field . ▁In ▁this ▁case , ▁the ▁force ▁can ▁be ▁defined ▁as ▁the ▁negative ▁of ▁the ▁vector ▁gradient ▁of ▁the ▁potential ▁field . ▁ ▁If ▁the ▁work ▁for ▁an ▁applied ▁force ▁is ▁independent ▁of ▁the ▁path , ▁then ▁the ▁work ▁done ▁by ▁the ▁force ▁is ▁evaluated ▁at ▁the ▁start ▁and ▁end ▁of ▁the ▁traject ory ▁of ▁the ▁point ▁of ▁application . ▁ ▁This ▁means ▁that ▁there ▁is ▁a ▁function ▁U ( x ), ▁called ▁a ▁" pot ential ," ▁that ▁can ▁be ▁evaluated ▁at ▁the ▁two ▁points ▁x A ▁and ▁x B ▁to ▁obtain ▁the ▁work ▁over ▁any ▁traject ory ▁between ▁these ▁two ▁points . ▁ ▁It ▁is ▁tradition ▁to ▁define ▁this ▁function