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Math Help - Physics problem

  1. #1
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    please check my work....

    Question: A 100-ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building
    Solution:
    work = force* displacement

    work = 15 lb/ft *100 ft

    work = 1500 lb
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  2. #2
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    No, because the part of the chain nearer the top doesn't have to be pulled so far. Also, your answer, being work, has to be in units of foot-pounds.

    A link of the chain at distance x from the top and length dx weighs 15 dx pounds and is lifted x feet, so contributes 15x dx lb.ft to the work. Integrate to get \int_0^{100} 15 x \; {\mathrm d}x as total work.
    Last edited by rgep; December 28th 2005 at 10:48 PM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bobby77
    Question: A 100-ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building
    Solution:
    work = force* displacement

    work = 15 lb/ft *100 ft

    work = 1500 lb
    Work also equals the change in energy. The mass of the chain is 1500 lb,
    its initial centre of mass is at -50 ft (where we take the roof of the building
    as our height reference point).

    Now these are ridiculous units so lets convert them to the appropriate SI
    units:

    Mass 1500 lb \equiv 680.4 kg.
    Length 50 ft \equiv 15.24 m.

    Now the change in potential energy when the chain is at the top of the
    building is m.g.(h_{final}-h_{initial})\  \mbox{joules}, where:
    g \approx 9.81 \ \mbox{m.s^{-2}},
    h_{initial} is the initial height of the centre of mass and
    h_{final} is the final height of the centre of mass.

    So work done:

    WD\approx 680.4\times 9.81 \times 15.24\ \mbox{joules}\approx 101,722.8\ \mbox{joules},

    or if you must about 75,000 \ \mbox{ft-pounds} or 73,576,000 \ \mbox{poundals}

    Of course if you are happier with customary units you can repeat the
    calculation using them

    RonL
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