I understand that the energy equations are derived from f=ma. From what I understand, this was reformulated under lagrangian and hamlitonain mechanics. So force here is merely a consequence or at least equal to the energy changing with respect to position. So an apple falling from a tree does so only because its energy changed, with respect to distance. We don't have to consider forces at all, for forces are only mathematically tantamount to changes in energy. That is the appearance of "forces" are ascribed to energy changes. Maybe we can even say that its the changes in energy that causes the motion, instead. This is very different philosophically. But what is the more accurate picture? F=ma came first and then the reformulations came after. However, I'm sure if history scientific discovery was different, maybe everything we conceive would be energy based instead, without much conception of push pull forces.