- #1
doctordiddy
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Homework Statement
http://imgur.com/BWo3tLh
Using the fact that the weight of water is 62.5lb/ft3, find the work (in ft-lbs) required to pump the water out of the outlet when r =3ft. Make sure your answer is correct to within ten ft-lbs.
Homework Equations
The Attempt at a Solution
I figured that Work is just force*distance, and force in this case is 62.5*V, while distance is just 3-height of the water, which i set as y
I then get this equation for work
62.5V(3-y)
to find volume i wrote this as
∫62.5(pi)r^2(3-y) from y=-3 to y=0 bottom of hemisphere to top)which can be written as
62.5pi∫r^2(3-y)
I then tried to figure out a relationship between r and y, and i figured that because the hemisphere fit on the graph y=√(9-x^2) and then i plugged in r for x and rearranged it to give
r=√(9-y^2)
Then i put this back into the equation to finally get
62.5pi∫(9-y^2)(3-y) = 62.5pi∫27-9y-3y^2+y^3
After integrating i get 62.5pi(27y-9y^2/2-y^3+y^4/4)
Then plugging in the points from -3 to 0 i finally end up with
-62.5pi(-81-81/2+27+81/4) =~14579 ft lbs
this is incorrect though.
I feel like i may have used a wrong substitution for r, but i do not know how i can relate r and y. can anyone help?
Thanks