water in a cylinder if height 10 ft and radius 4 ft is to be pumped out? find the work required if:
1) the tank is full of water and the water is to pumped over the top of the tank.
2) the tank is full of water and the water must be pumped to the height 5ft above the top of the tank
3)the depth of the water in the tank is 8 ft and the water must be pumped over the top of the tank
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nath, you need to know that the work W=FS=GS=mgh here.
the main issue im having with this problem is part and 3
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i need help with the set up of these two problems
you see, in part 2, the water at the upmost has to go up for 5ft, the water at the bottom has to go up 15ft. then you can use calculus here.
so what the second part the distance varies from part 3 but what is the limits of integration
the area of the bottom of the tank is S=πr^2=16π ft^2; H(h) is the height H that the water at h above the bottom of the tank has to go up. in part 2, H(h)=15-h. ∫(0, 10)H(h)dx = ∫(0, 10)(15-h)dx =∫(0, 10)(15h-h^2/2)dx = 100 m^2. W=DgS*∫(0, 10)H(h)dx/h=1000*9.8*16π*100/10≈4.924*10^6J.
i'm sorry, i made a mistake. S=16π ft^2= 4.667m^2.