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Calculus and Beyond Homework Help
Empty Tank: Work Calculation w/ Origin at Apex of Cone
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[QUOTE="songoku, post: 6858181, member: 171861"] [B]Homework Statement:[/B] A tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. It is filled with water to a height of 8 m. Find the work required to empty the tank by pumping all of the water to the top of the tank. (The density of water is 1000 kg/m^3) [B]Relevant Equations:[/B] W = ##\int F dx## I take the origin to be at the apex of the cone. Using the similarity of the triangle, where ##r## is radius of water and ##y## is height of water from the apex of cone: $$\frac{r}{y}=\frac{4}{10}$$ $$r=\frac{2}{5}y$$ The mass of water = ##\rho .V## = ##\rho . \pi r^2~\Delta y## = ##\rho . \pi \frac{4}{25}y^2~\Delta y## The weight of water = ##\rho . \pi \frac{4}{25}y^2~\Delta y. g## The distance needed to move the water to the top of the tank = 10 - y The work needed: $$W=\int_{2}^{10} \rho . \pi \frac{4}{25}y^2. g (10-y) ~dy$$ But I got wrong answer and the teacher said my origin was wrong. I still don't understand why I can't take origin to be at the apex. Thanks [/QUOTE]
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Empty Tank: Work Calculation w/ Origin at Apex of Cone
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