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I am working on filling out tag wikis and descriptions, but I am running into problems where I am not able to articulate differences. I have the vague sense that we use and differently, but what is this difference?

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I would be pedantic and give you the physics definitions but that's not helpful. However, with that in mind, you can use strength to generate power but not power to generate strength. Therefore, I would go with:

  • Strength as in power generated by muscles.
  • Power is the amount of energy transferred or converted per unit time from such sources as strength, speed, and leverage.

As an example, if i wanted to improve my Aikido, I would get more speed in movement (power) over building muscles (strength)…

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    Yep, strength is the amount of work muscles can do, power is the amount of work they are doing. – slugster Apr 15 '19 at 13:00
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Strength is the ability to do work over time, usually a consistent slow application. Generally we should be using this when talking about weight training, or the ability to force your opponent into a position they are trying to resist. There is no real speed component, it is pure strength vs strength or strength vs weight.

So for a basic definition, I would go with

Strength: A consistent, slow application of force over a period of time against a resisting object.

Power is the fast application of the above, which gives you the equation of Power = Speed x Strength. This is where it gets a little blurry, since you can't have a ton of power without a concomitant increase in strength and/or speed.

Power: The explosive force exhibited by a coordinated exertion of both strength and speed in a technique.

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