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Re: "Owner" of potential energy.



Dario Moreno wrote:

> PEs = kx^2/2 belongs to the mass when the other end of the spring is
> anchored to earth.
May be you intended to say that kx^w/2 "belongs"
to the spring ?

and Jim Green wrote:

In the case of the spring it is not clear in what is proposed -- Is it
contemplated that both the ball and the Earth be attached to the
spring? If so and it is a real spring, then the property of energy of the
spring will increase by the deltaPE of each atom of the spring

Yes, one end attached to earth (whose motion is neglected in both the
spring and gravitational cases) and one end to a mass.

However, I am thinking of an ideal (ie. massless) spring not a real one.

In that case, gravitational and elastic PE are analogous, are they
not? (To make the analogy better, arrange the little mass to be
surrounded by a number of planets on all sides, like the usual
electrical-spring model of atomic lattice sites in salts.) If (a big
"if" and conceptually a very lousy "if") I am going to attribute the
energy to a single object, surely it must go to the mass in both
cases?

There appears to be a paradox lurking here, but actually it's merely
a problem of simplifying assumptions:

If I compress an ideal spring between my hands, lock it in a
compressed position with a massless u-shaped bracket, and place the
contraption on my desk, is there any PE stored in it?

answer 1: Yes. By releasing the bracket I can use this device to do
mechanical work on a dart say.

answer 2: No. An ideal spring has zero mass. Any zero-mass object at
rest has zero energy. (Photons have the loophole of traveling at c.)

Push any simplification too far and you're bound to get nonsense. As
Jim says, you need real atoms in a spring to get the interatomic
electrical force which manifests itself as the elastic force.

This is why so far in my various postings about work and energy I
have ignored vibrational PE and KE. You run into problems with
"ideal" springs. For example, it's impossible to do pseudowork on a
spring because you have to press with equal and opposite forces from
the two ends.
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/