Zero-Work Motion of a Suspended Slinky

We discuss the gravitational and the elastic potential energy of a Slinky suspended in a U-shape due to its own weight. If one symmetrically moves both ends of the Slinky along a particular parabola, or if one moves one end along a particular circle by fixing the other end, the total potential energy of the Slinky can be constant. External forces exchange these potential energies with each other without doing any net work. We present theoretical discussions and experiments suitable for physics classes in universities.