There *is* an input of energy. When you lift a weight (a.k.a. heavy iron thing) against gravity you must spend energy to do so. That energy doesn’t just flutter off into the void, it is stored in the object as potential energy. When you let go of the object, it falls to the ground, transforming that potential energy into kinetic energy. The energy is transformed again when the magnetically conductive object travels through a magnetic field, inducing an electric current in the object. Because the current has no where to go, it is again transformed into heat that radiates from the object. But wait… where does all of this current and heat come from!? It comes from the kinetic energy, the object’s motion as it’s falling! So the object is losing kinetic energy as it falls through the magnetic field and thus slowing down in the presence of that field.
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