We say that the force per unit mass (or per unit charge) is
given by the gradient of potential, P. In the case of gravity
(approximately uniform field, y<<R, m<<M) we have
PE=m*g*y, with respect to some reference level. Thus
P=PE/m=g*y and gradP=g, force per unit mass.
Where are the corresponding concepts in elasticity? We
have PE=0.5*k*x^2. What is P? (potential energy per
unit of what?)
Suppose I declare that P=0.5*k*x^2. Then gradP=k*x.
But this is just plain force, not force per unit of
something. What am I missing?
Ludwik Kowalski