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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 "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 ?

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  1. amistre64
    • 5 years ago
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    work = force times distance

  2. amistre64
    • 5 years ago
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    let me see if I recall the formula..

  3. amistre64
    • 5 years ago
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    distance moved is from 4-y for any given section; weight for any given volume is 50 times pir^2

  4. Yuki
    • 5 years ago
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    yep

  5. amistre64
    • 5 years ago
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    since it is half full we integrate from 0 to 2

  6. amistre64
    • 5 years ago
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    [S] 50pi r^2 (4-y) dy sound about right?

  7. Yuki
    • 5 years ago
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    The answer was right, but one question.

  8. amistre64
    • 5 years ago
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    yes?....

  9. Yuki
    • 5 years ago
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    Is the volume of the cylindrical oil considered as 50(pi)r^2 dx ?

  10. amistre64
    • 5 years ago
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    r in this case is a constant i beleive since the shape has straight sides

  11. amistre64
    • 5 years ago
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    if it was conic; then radius would change with respect to x or y depending on its orientation

  12. amistre64
    • 5 years ago
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    sin ce we are lifting in the vertical direction; the sums are added vertically up the y..or down the y :)

  13. Yuki
    • 5 years ago
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    Let me try it again and see if I can do it on my own.

  14. amistre64
    • 5 years ago
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    ok :) I think you can ;)

  15. Yuki
    • 5 years ago
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    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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