My Mechanics textbook claims that the sum of the work by internal forces is not generally zero.
translated to English the paragraph reads:
Notice about the work by internal forces: the work by the internal forces is in general not equal to zero although the sum of the internal forces is always equal to zero. Since the work also depends on the relative displacement of the two pointmasses in the material system, the work provided by these 2 internal forces will generally not be equal to zero.
Other sources claim that the work done by internal forces is always zero. Why does a car engine not do work if the wheels don't slip? (answer by Mark Eichenlaub)
Then I didn't do any work on the system at all since, by definition, only external forces can do work.
http://in.answers.yahoo.com/question/index?qid=20110131130859AAMLJLd
the net work done by internal forces is zero since they do not cause motion of the object.
To me it would seem that these sources contradict eachother. Do they? If so, which one is correct? If not, please explain why they don't contradict eachother.
Answer
Work is a subtle concept that can be approached in various ways. There are ambiguities that can be reduced somewhat through the careful use of language. Ultimately, however, these ambiguities can only be eliminated by specifying a theory of physics and stating the definition within that theory.
Suppose our theory is Newton's laws applied to frictionless gear trains. Then the forces are normal forces exerted by a gear tooth A on another gear tooth B. By Newton's third law, the forces are equal in magnitude and opposite in direction. Since these are normal forces, the displacements of A and B are equal. Work can be defined either as $dW=F\cdot dx$ or as the transfer of energy by a mechanical force; since these are normal forces, the two definitions are equivalent. By Newton's third law, A's work on B cancels B's work on A.
Suppose instead that our theory is Maxwell's theory applied to oppositely charged particles A and B moving in a vacuum. We release A and B at some distance from one another. Their subsequent motion is that they oscillate about their common center of mass, radiating electromagnetic waves (and periodically passing through each other). There is clearly no way we can define work so as to make A's work on B always cancel B's work on A. Energy is going out into the electromagnetic waves, and there is no way to count this energy into the definition of work, since it's nonmechanical.
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