yuki
  • yuki
There is a cylindrical barrel with radius 1 and height 4. It is half full of oil and the oil weights 50lb/ft^3. If we want to pump the oil from the bottom to the top of the barrel, how much work is done? I made the distance from the top of the barrel to a certain point of the barrel "x" so that the volume of the oil being pumped up is " pi(1)^2*x " and the weight would be 50 times this. The distance that this guy has to travel is "4-x". The limits of the integration I chose was from 2 to 4. I calculated the answer to be 400pi/3 but the actual answer is 300pi. Can someone help me ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
work = force times distance
amistre64
  • amistre64
let me see if I recall the formula..
amistre64
  • amistre64
distance moved is from 4-y for any given section; weight for any given volume is 50 times pir^2

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yuki
  • yuki
yep
amistre64
  • amistre64
since it is half full we integrate from 0 to 2
amistre64
  • amistre64
[S] 50pi r^2 (4-y) dy sound about right?
yuki
  • yuki
The answer was right, but one question.
amistre64
  • amistre64
yes?....
yuki
  • yuki
Is the volume of the cylindrical oil considered as 50(pi)r^2 dx ?
amistre64
  • amistre64
r in this case is a constant i beleive since the shape has straight sides
amistre64
  • amistre64
if it was conic; then radius would change with respect to x or y depending on its orientation
amistre64
  • amistre64
sin ce we are lifting in the vertical direction; the sums are added vertically up the y..or down the y :)
yuki
  • yuki
Let me try it again and see if I can do it on my own.
amistre64
  • amistre64
ok :) I think you can ;)
yuki
  • yuki
Great, it was a simple mistake I had there. I get it now. I really appreciate your help. I have to take a AP calculus diagnostic exam next week for a job interview and it will decide if I can marry my girl or not.

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