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yuki
 5 years ago
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 "4x". 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 ?
yuki
 5 years ago
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 "4x". 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 ?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0work = force times distance

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0let me see if I recall the formula..

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0distance moved is from 4y for any given section; weight for any given volume is 50 times pir^2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0since it is half full we integrate from 0 to 2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[S] 50pi r^2 (4y) dy sound about right?

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0The answer was right, but one question.

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0Is the volume of the cylindrical oil considered as 50(pi)r^2 dx ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0r in this case is a constant i beleive since the shape has straight sides

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if it was conic; then radius would change with respect to x or y depending on its orientation

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sin ce we are lifting in the vertical direction; the sums are added vertically up the y..or down the y :)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0Let me try it again and see if I can do it on my own.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok :) I think you can ;)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0Great, 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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