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Work: Emptying a 2x1x1 box of water.

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data

    How much work is required to empty a 2x1x1 ft box of water? Assume density of water is 62.5 lb/ft3.

    2. Relevant equations

    [tex]\int_a^b A(x)xdx[/tex]
    [tex]A(x)=lw=2[/tex]

    3. The attempt at a solution

    [tex]62.5\int_0^1 2xdx=125\left[ \frac{x^2}{2} \right]_0^1=62.5[/tex]

    Did I get it right?
     
  2. jcsd
  3. Jun 19, 2011 #2
    looks good to me. Although if I were to give advice, I would say don't try to memorize those kinds of formulas. Instead, try to remember a method for setting these types of problems up. Usually this involves some form of considering a small "slice" of water of width [itex]\Delta x [/itex] and finding the small amount of work [itex] \Delta W [/itex] and then summing up over the entire volume of the water.
    this method might seem tedious for simple problems, but it might give you a better understanding of what is really going on here.
     
  4. Jun 19, 2011 #3
    Yeah, I know exactly what you mean. The whole point of covering work is to solidify the concept of the integral being an infinite sum of infinitesimals. I didn't show or explain my derivation, but I didn't memorise the formula, as it appears.

    I was just wondering, because this was a question on a test and I was beginning to believe I missed it. I'll see for sure tomorrow (Monday).
     
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