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Re: ELASTIC POTENTIAL?



At 11:21 PM 10/29/01 -0500, Ludwik Kowalski wrote:
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?

1) Grad(potential) is always a force, a plain force. The fields describe a
force per unit something if-and-only-if they have a potential per unit
something. The spring is no different in this regard. Grad(potential) is
a force.

2) The gravitational field is a field. The electrical field is a
field. The spring is not a field, so we shouldn't be too surprised if it
doesn't behave exactly like a field.

You could make a field of springs. Example: a mattress contains a D=2
array of springs. To a fair approximation it provides a force per unit
area (per unit deflection).