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The ripping process eats up a lot of energy in the breaking of bonds and a bit in the final acceleration of the two halves of the rope.
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In other words, work is being done on the rope, even though the work formula wont agree. The kinetic energy being applied by the two guys pulling the rope are ripping apart the bonds holding it together. Right?
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The thing you're not getting is that you don't "apply kinetic energy" to anything. You exert forces. The force may be countered by friction or an opposing force.
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But that was my point; if you're fighting gravity, or magnetism, then isn't energy "disappearing", since gravity and magnetism doesn't weaken( i.e. they have infinite power )?
And also, why wouldn't 'exerting forces' be exactly the same as applying kinetic energy? It's no less 'applying k. energy' just because it's not moving; that just means another force is applying a bigger amount of kinetic energy than you are, and in a different direction. Or in the case of an atmosphere, where you're not just pushing the object, but the air particles covering the direction you're pushing it in as well.