Consider a system consisting of two particles of a given mass, floating in space, aligned horizontally, constrained to remain at a fixed distance from each other by a massless thin rod (or string). If I apply a horizontal force on the first particle (meaning it is parallel to the vector joining the two particles), the second particle is forced to accelerate due to the constraint force between the two. In other words: If I draw a Free Body Diagram of the second particle, the only force acting on it is the constraint force, or the force caused by the pull of the rod or string, and since this second particle does accelerate in the same direction, then said force is doing work on it. How is this not a counterexample to the assumption in analytical mechanics that constraint forces do zero work? Or how I am misinterpreting such principle?
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