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After a certain number of repetitions usually the muscle being stressed starts aching, the pain grows until it becomes unbearable then one can still continue pushing the muscle to higher extremes but after a while it does not matter how hard one pushes and how good one became at ignoring the pain, because the muscle will simply stop moving.

but

After a few seconds of rest, usually even 5 or 10 seconds are enough, the muscle is ready for more repetitions.

And this repeats until one is bored to death or can no longer tollerate the pain.

What mechanism makes it so that your muscle stop working and ignore your signals to to keep pushing but they work again after a few seconds?

Is it a mechanical block in the structure of muscle fibers or is it the brain trying to stop you from working out?

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  • "Failure" probably has as many different definitions as there are different ways to reach what one would call "failure". For example, exercise form can often deteriorate as one becomes more fatigued -- but whether that's even a muscular failure or nervous system failure is still debated in many places.
    – ManRow
    May 18 '20 at 14:52
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This article discusses how muscles fatigue. This occur through mechanisms inside the central nervous system (central fatigue) or inside the muscle (peripheral fatigue).

From the article: "Very broadly, peripheral fatigue seems to occur partly due to an accumulation of ions that reduce the release of calcium ions (extracellular potassium) or impair the sensitivity of the actin-myosin myofilaments to calcium ions (reactive oxygen species), partly due to the production of metabolic byproducts that interfere with actin-myosin crossbridge function (phosphate ions and adenosine diphosphate), and partly due to a reduction in the availability of substrate in the various energy pathways."

All muscle cells have 3 substrates stored locally that can be used as energy:

  • ATP (Adenosine TriPhosphate): can be used immediately but only last 3 seconds
  • Creatine phosphate: this is first broken down to ATP so it is slightly slower than ATP. Last for about 8-10 seconds.
  • Glycogen: can also be used to produce ATP but this process is slower. Last about 90 seconds. Oxygen is not needed to produce ATP.

These 3 are "the substrate in the various energy pathways" from the quote above.

During the break the cells in the muscle have time to refuel these substrates from the bloodstream and to remove the metabolic byproducts from the cell.

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