Rotating vs non-rotating mass.
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If the mass of the weight is m, and it is lifted to a height h, the weight lifter delivers energy (work) m*g*h to the weight. If the weight lifter drops the weight then that is the work delivered. In the case that the weight lifter drops the weight, the weight falls, trading potential energy for kinetic energy. Just before the weight makes contact with the floor the weight has kinetic energy 0.5*m*v^2 where v=sqrt(2*g*h). When the weight hits the floor (BAM!) the floor decelerates the weight, so the weight is now back at the zero energy. The floor does work m*g*h on the weight, leaving the weight at rest. So, the weight lifter, lifting the weight delivers m*g*h to the weight. If the weight lifter then brings the weight to rest then the weight lifter has done same work the floor did in the dropping case. So, a weight lifter raising and lowering the weight delivers 2*m*g*h to the weight. If any work is done, the efficiency can't be zero.
The fact that energy is temporarily stored in the weight has nothing to do with it, just like the fact that energy is temporarily stored in rotating mass has nothing to do with the mechanical power required to propel a bike.
For the weight lifter, the energy in the sound from dropping the weight or the heat in his muscles from lowering down the weight is the energy wasted in a process which has zero percent efficiency.
Indeed, we have every reason to believe that muscle efficiency is extremely sensitive to small mass differences, or even no mass differences at all. For example, holding your arm out horizontally obviously uses a lot more energy than letting it sit at your side, regardless of the fact that there is absolutely no mass difference whatsoever.
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