Imagine an object moving in a straight line in space, perhaps shaped like a yo-yo (to make rotational effects negligible). Suddenly a constant force is exerted at right angles to the direction of motion, such that the object is now deflected into a circular path.
What is the energy required (or work done) to maintain the constant deflection of this circular path?
Start over, and imagine a second identical object moving in the opposite direction, but offset so that when a similar force is applied to it, it travels in the same circular path, but offset by 180 degrees. Clearly, the energy required to keep both objects moving in the path is twice that for just one of them. Now, start again, but this time have the two objects instead link up with a cable and snap fastener, as they go by each other. The cable tension causes both objects to travel in the same circular path as before.
Does the cable do the same work that was done before to keep the two objects in the circular path? If not (and besides, how can a cable do work?), then was the energy wasted before, to do what a simple cable can do without energy?