Think of it like a pneumatic piston holding up a weight, except the piston is a bit leaky so you need to pump in air continuously to maintain the position. The chemical reactions in muscles need to occur continuously to keep the muscle pulling. (A similar analogy is, you need to keep applying an electric current to an electromagnet to sustain the magnetic field).
It’s because your muscles contract chemically and are held in place chemically, but the mechanical force from holding something is constantly breaking those chemical bonds. It takes energy to reset the muscle position and re-establish the chemical bonds. You’re never technically holding something perfectly still because what’s really happening is a constant release and contraction due to those bonds breaking and reforming.
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