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Excellent question, to answer this, you must understand that the bucket and stick are not an isolated system, and hence will continually lose heat to the environment (if it is greater in temperature than the environment).

You are correct in saying the stirring the bucket of water will generate heat. The heat is minimal, and if the bucket and stick were somehow in a perfectly isolated system, you would eventually stir to its boiling point.

However, since they are not an isolated system, the water will gain temperature until the temperature is greater than that of the environment, at which point the water will begin losing energy/heat into the environment.

It is the rate of heat loss to the environment and rate of heat gain from the stirring that determine the final equilibrium temperature, since stirring generates heat at a very slow rate, once the water reaches the environmental temperature, the heat loss will approximately equal the heat gain.

Therefore, unless you being to stir extremely fast (may be possible with a machine) and the rate of heat gain is large enough to bring the temperature of the water to boiling point despite the constant heat loss tot he environment, you will never stir a bucket of water into boiling.

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Q: If friction generates heat why can't i stir a bucket of water to boiling point?
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