If this bucket contains a liquid with density 800 kg/m^3 to a height of 4 meters, find the work required to pump liquid out of this bucket (over the top edge). Use 9.8 m/s^2 for gravity.
How do I setup the integral to solve this problem?
Calculus Work Problem: Create a bucket by rotating around the y axis the curve y = 3ln(x-2) from y = 0 to y = 6
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calculus
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0Hint: work is the force multiplied by the distance (in the integrand). – 2017-01-29
1 Answers
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$ \Delta V = \pi x^2 \Delta y$ $ y=3*\ln(x-2) -> y/3=\ln(x-2) -> e^(y/3)=(x-2)->x=e^(y/3)+2$ $ \Delta F = ma = \rho \Delta V 9.8 = 800*9.8*\pi (e^(y/3) + 2)^2 \Delta y$ $$ \Delta W = \Delta F * Distance = \Delta F (6-y)$$ $$ W=800*9.8*\pi \int^{4}_0 (e^(y/3) + 2)^2 (6-y) dy =$$
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1https://math.meta.stackexchange.com/q/5020/306553 mathjax reference to help us type maths on this site. – 2017-09-06