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 Photo collection by Th.Schiöler Applied mathematics concerning water-lifting 2: Powerfunction of a man |
| Powerfunction of a man |
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| Question: Is it possible to find the optimum power for a man hauling a bucket up from a well. In this problem, we have to supplement our physical laws with one taken from the physiology. It is impossible to lift a very heavy bucket. An empty one could be pulled up at a speed of about 1.3 m/s. A very heavy bucket has a speed of zero and the empty bucket a speed of 1.3 m/s. Somewhere between these two points we have the value which gives the optimum power. Nomenclature
At the top, we have a curve based on experiments. This is the vertical force verso the hauling speed. This curve was first introduced by Euler. The next curve is derived from the first. It is the product of the force and the speed.
 From this function, (a parabola) we can see that the maximum power is reached if the bucket is hauled at a speed of 0.55 m/s. The power is here 76 watt.  Next chapter: The test tube |