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January 26, 2015

January 26, 2015

Posted by **Amy** on Wednesday, November 10, 2010 at 6:05pm.

Hemisphere - 5 m radius. at the bottom

Cylinder - radius 5 m and height 10m in the middle

Circular cone radius 5 m and height 4 m at the top

The top of the tank is 2 m below the ground surface and is connected to the surface by a spout. find the work required to empty the tank by pumping all of the water out of the tank up to the surface.

density of water = 1000 kg/m^3

Gravity = 10 m/s^2

I am doing to where I have three parts to this question. I find the work of all of them then add the work done of all 3 together.. However, I cannot figure out how to find the work done for the hemisphere OR the circular cone. Please help me solve this out I have no idea where to start!

- Calculus 2 -
**Damon**, Wednesday, November 10, 2010 at 7:00pmOK, Here is the hemisphere.

we have a hemisphere with base 16 feet below ground and bottom 21 feet below ground.

We need its volume and the distance of the cg below ground.

The volume is easy, half a sphere

(1/2) (4/3) pi r^3 = (2/3) pi 125 = 250 pi/3

the centroid of a sphere is 3/8 r from the base as derived here:

http://mathworld.wolfram.com/Hemisphere.html

Therefore the center of mass of the hemisphere is

21 +(3/8)5

below earth

therefore we must lift a weight of water of

rho g (250 pi/3) a distance of (21+15/8) meters

that is in Joules

use rho = 10^3 kg/m^3 and g = 10 m/s^2

- whoops base at 16 meters -
**Damon**, Wednesday, November 10, 2010 at 7:01pmrho g (250 pi/3) a distance of (16+15/8) meters

- Calculus 2 -
**Damon**, Wednesday, November 10, 2010 at 7:06pmNow do the cone the same way

base is at 6 meters

volume = (1/3) pi r^2(4)

cg is at [6 - (1/4)4] meters below ground

- Get this now? -
**Damon**, Wednesday, November 10, 2010 at 7:18pmCan you do the rest now?

- Calculus 2 -
**Amy**, Thursday, November 11, 2010 at 10:30amWhy would you do the distance of hemisphere from 0 to 16, when we are doing just the hemipsher alone then adding it to the rest after.. wouldnt distance by 5-dy

- Calculus 2 -
**Damon**, Thursday, November 11, 2010 at 6:52pmYou are lifting the water from the cg of the hemisphere all the way to the surface.

that is 16 meters to the top of the hemisphere plus another 15/8 to the cg

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