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Re: [Phys-L] point particles puzzle

On Monday, June 30, 2014 2:26 PM, Carl Mungan <mungan@usna.edu> wrote:

"That conclusion doesn't follow because F is an individual force, not the
sum of all forces. (The sum of forces can be used to compute pseudowork but
not real work.)
>The person pulling does positive work on the spring. The spring does equal
and opposite negative work on the person. As a result the person loses
chemical energy and the spring gains elastic potential energy. If one
subdivides the spring into portions (rather than considering the whole
spring at once as I just did) then one end moves farther than the other end
and so the equal and opposite forces at their two ends do not do equal and
opposite work, and each portion of the spring thus gains a portion of the
elastic PE."

This is a good point and well formulated.
There is a more simple example illustrating the same aspect.
Consider an electron-positron pair. Its members are regarded as point-particles and, in classical treatment, we may not bother about indeterminacy principle. Move them farther apart by imposing two individual external forces applied each to its respective particle and varying so as to keep the speed of each particle constant.  Net work on each particle is zero, but the net work done by external forces alone is not. This is only an apparent inconsistency because we must also look at the internal forces, whose combined work is non-zero either. So we cannot treat this kind of problem without considering the interaction field. This immediately shows that the potential energy of the pair increases at the cost of non-zero work done by the external forces.
The net energy of the whole system (pair+the source of external forces) may remain constant, which can be linked to the net zero work done by all participating forces.

Moses Fayngold,
NJIT

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