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Re: "Owner" of potential energy.



> It is okay to say one object owns it entirely provided the other
> object is so massive that it doesn't change in KE. In that case, the
> dynamics of this massive object are of no real interest.
>
> So PEg = mgh belongs to the ball when the other object is the earth.
> PEs = kx^2/2 belongs to the mass when the other end of the spring is
> anchored to earth.

If the ball is raised to the height of h (in an inertial frame), then
negative conservative work has been done on the ball by the Earth. Hence
the ball now has its _property_ of energy increased by PE=~mgh. If during
the process the Earth is moved by the same mechanism (in an inertial
frame), negative conservative work is also done on the Earth by the
ball. The Earth now has its _property_ of energy increased by PE=~Mgh',
where h" ain't very big, but M is. Both h and h' have to be determined by
assuming that the CM of the system does not move -- in an inertial frame.

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 -- usually
~0.5kx^2 in total -- but the PE=~mgh and the PE =~Mgh' re still valid for
the ball and for the Earth.

Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen