What developments led to the definition of Work as dot product of Force and Displacement vectors?
I did some searching but couldn't find a satisfying answer. Acc to what I have read the initial concept of work was associated with measuring work by horses. How did it get associated with energy. Another common answer I got was that "work indicates a transfer of a quantity that happens to be conserved in closed systems just like momentum". I see what that means but how can anyone ,possibly, come up with a formula as W=F.S from that (or anything else?) .
Also, did conservation of mv^2 in elastic collisions led to development of work formula and modern concept of energy.