anyone good with calc 2 work problem? A cylinder tank with radius 1 m and height 2 m is full of water. How much work is needed to pump half of the amount of water out of the tank? (density of water is 1000kg/m^3)

Question

triciaal · Answer

work?  Is this all of the question?

we know the original volume and the new volume 

E = m c^2 ?

anonymous · Answer

I have W = ∫9800π (2-y)dy

anonymous · Answer

@triciaal yes, that is the full question. And I have no idea what you just said.

empty · Answer

Can you explain how you got your integral @sourwing ? That looks about right though, since as you pump water out the height you'll have to pump increases so you have to do more work on the remaining water than you did to begin with right?

anonymous · Answer

@Empty yes, that's right. The work exerted on the second half is greater than that of the first half. I'm only stuck on the limit of integration though

triciaal · Answer

now that you have all of the question it makes sense

empty · Answer

The limits of integration might go from 2 to 1 to represent the fact that you're pumping water from the top to halfway down since these are the values of y in which you are pumping an infinitesimal disk of water from with height dy.

empty · Answer

I say "might" because I haven't actually derived this myself yet

anonymous · Answer

the diagram is like this|dw:1434954369546:dw|