Aleaky 12-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weights 0.75 kg/m. initially the bucket contains 40 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15 m level. how much work is done
Answers: 3
at a height of 0 meters above the ground.At a height of 15 meters, the mass of the water would be 
.
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of water leaks out of the bucket everytime its height increases by 
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would be 
. Write that as a function of height:
.
of rope is still in the air while the bucket is at a height of 
.
.
.
.
.![\begin{aligned}W &= \int \limits_{0}^{15} (620.483 - 33.5175\; h) \, dh \cr &= \left[620.483\; h - \frac{1}{2}\times 33.5175\; h^2\right]^{15}_{0} \cr &= \left(620.483 \times 15 - \frac{1}{2} \times 33.5175 \times 15^2\right) - 0 \cr &\approx 5.5\times 10^{3}\; \rm J \cr &= 5.5\;\rm kJ \end{aligned}](/tpl/images/0434/1821/2fc10.png)
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