Physics, 15.01.2020 06:31 neymar6895
Abucket weighing 2 kg and a rope of negligible mass is used todraw water from a well that is 40.8 meters deep. just before thebucket starts being raised from the bottom of the well, the bucket isfilled with 6 kg of water. unfortunately, there is a hole in the bucketand water leaks out at the rate of 0.12 kg per second. the bucketis pulled up at a constant rate of 0.8 meters per second.(a)how much water is in the bucket when the bucket reaches thetop of the well? (b)find the work done pulling the bucket to the top of the well.(assume that the acceleration of gravity is 9.8 meters per secondper second.)
Answers: 2
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seconds?
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of water in the bucket will have leaked out by the time the bucket reaches the top of the well. There will be no water in the bucket by the time the bucket reaches the top of the well. 
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at a constant rate.For the last 1 second, the mass of the bucket will stay constant at 
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of the bucket about time 
as a piecewise function:
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is constant. Thus the power 
that pulls the bucket upward at time 
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and 
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piece-by-piece:![\displaystyle \begin{aligned}W &= v\cdot g\cdot \int_{t_0}^{t_1}{m(t)\cdot dt}\\ &=0.8\times 9.8 \left [\int_{0}^{50}(8-0.12\;t)\cdot dt + \int_{50}^{51}2\cdot dt\right]\\ &=0.8\times 9.8 \left [\left(8\;t - \frac{0.12}{2}\;t^{2}\right)\bigg|^{50}_{0} + (2\;t)\bigg|^{51}_{50}\right] \\&=0.8\times 9.8 \left [\left(8\times 50-\frac{0.12}{2}\times 50^{2}\right)+ (51\times 2 - 50\times 2)\right]\\&=\rm 1975.68\;J \end{aligned}](/tpl/images/0455/7730/78d18.png)
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Abucket weighing 2 kg and a rope of negligible mass is used todraw water from a well that is 40.8 me...
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