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anonymous

  • 5 years ago

a rectangular water tank has a length 20 ft, width 10 ft , and depth 15 ft . if the tank is full , how much work does it take to pump all the water out (using calculus)

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  1. anonymous
    • 5 years ago
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    so this is another combination of mathematical calculus and the physical energy problem.

  2. anonymous
    • 5 years ago
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    this one is much easier than the previous one, don't you think so? because there's no dripping water here~! :)

  3. anonymous
    • 5 years ago
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    but im still confused

  4. anonymous
    • 5 years ago
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    this is what i got 62.4(density of water)(200,the volume) integral 15-h limit 15 to zero

  5. anonymous
    • 5 years ago
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    the measurement is ft , not meter.

  6. anonymous
    • 5 years ago
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    i know that why u use 62.4 as the density

  7. anonymous
    • 5 years ago
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    youd better change to ISU, more convenient to calculate, as 1 g/cm^3 the density of the water/

  8. anonymous
    • 5 years ago
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    im sorry i had to go to bed, its midnight here

  9. anonymous
    • 5 years ago
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    oh okay thank you for ur help

  10. anonymous
    • 5 years ago
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    anwar di u think u can help me

  11. anonymous
    • 5 years ago
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    Is the water leaving the tank from the top or the bottom? I'll assume it's leaving from the bottom. W = F * d; draw the tank with the dimensions. Find the density of an infinitely thin "slab" of water. Its volume is going to be 20*10*dy = 200dy. The force is going to be the volume times the density, so 200dy * 62.4 = 12480dy. The distance that this slab is going to have to travel to leave the tank is y, so the work done in moving that slab is 12480ydy. Sum all the work done by all the slabs with... \[\int\limits_{0}^{15}12480ydy\] I got 1404000 foot-pounds of work.

  12. anonymous
    • 5 years ago
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    thank u for coming to the rescue , but the answer is 220,500 ft lb

  13. anonymous
    • 5 years ago
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    Integrate 12480ydy from 0 to 15 is what I meant to say...

  14. anonymous
    • 5 years ago
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    is the distance 15-y

  15. anonymous
    • 5 years ago
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    The distance would be 15 - y if the water was leaving from the top... I don't think that wouldn't get the amount of work to be 220500, though...

  16. anonymous
    • 5 years ago
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    it just says how much work would it take to pump the water, it doesn"t say top and bottom

  17. anonymous
    • 5 years ago
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    Well, for water to be pumped out of a tank it needs to be pumped out from somewhere. The water needs to move to a part of the tank to be pumped out.

  18. anonymous
    • 5 years ago
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    here what I have, I am not sure about it though.. haven't done physics in a while: we have the following formula: \[W=\int\limits_{v_i}^{v_f}pdv\] where p is pressure of water (can be found known depth and temperature of water), vi and vf are the initial and final volume respectively (both known)

  19. anonymous
    • 5 years ago
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    knowing depth..*

  20. anonymous
    • 5 years ago
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    so it doesn't matter if we use y or 15-y to represent the distance

  21. anonymous
    • 5 years ago
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    well we have the initial volume=20*10*15, final volume=0.. we will get a negative result for the work.

  22. anonymous
    • 5 years ago
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    if we use 15-y?

  23. anonymous
    • 5 years ago
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    hey im a little confused. can someone please explain to me how the distance become 15-y

  24. anonymous
    • 5 years ago
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    I have no idea why my answer is incorrect. If you draw the height of the tank and pick an arbitary point along the height, the distance between the top of the tank and that point is 15 - y.

  25. anonymous
    • 5 years ago
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    and when is it just y

  26. anonymous
    • 5 years ago
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    Distance betwen the arbitary point and the bottom of the tank.

  27. anonymous
    • 5 years ago
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    but in the triangle is the top is just y, and the bottom is 15-y

  28. anonymous
    • 5 years ago
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    Triangle?

  29. anonymous
    • 5 years ago
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    this is another question , when u slice a triangle and want to use similar triangles the top portion is y and the bottom half is 15-y ,( this just an example)

  30. anonymous
    • 5 years ago
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    Yes, I suppose you could think of it that way if you positioned the tank such that the x-axis was the top of the tank and 15 feet below that is the bottom of the tank.

  31. anonymous
    • 5 years ago
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    k ty

  32. anonymous
    • 5 years ago
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    hey i have a question can i ask

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