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Math Help - Work--please check my work for me

  1. #1
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    Work--please check my work for me

    Electrons repel each other with a force that is inversely proportional to the square of the distance between them, call the proportionality constant k. Suppose one electron is fixed at x=0. Find the work done to move a second electron along the x-axis from the point x=10 to x=1.

    So the F=k/x^2 and W=F*d, but what do I use for the distance? 10?

    Would it just be integral (from 10 to 1) of 10k/x^2 dx?

    Someone told me it would be integral (10 to 1) of k/x^2 dx without the 10, but what about the distance? This is what is confusing me.
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    Electrons repel each other with a force that is inversely proportional to the square of the distance between them, call the proportionality constant k. Suppose one electron is fixed at x=0. Find the work done to move a second electron along the x-axis from the point x=10 to x=1.

    So the F=k/x^2 and W=F*d, but what do I use for the distance? 10?

    Would it just be integral (from 10 to 1) of 10k/x^2 dx?

    Someone told me it would be integral (10 to 1) of k/x^2 dx without the 10, but what about the distance? This is what is confusing me.
    The distance is in your limits of integration. Remember that Work = Force  \times distance. If you think about it in terms of Reimann sums then You are multiplying the Nonconstant force by a tiny bit of distance dx and then adding up all of the contibutions to get the total amount of work done.
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  3. #3
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    Ok, so just integral(10 to 1) k/x^2 would do it?
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  4. #4
    Behold, the power of SARDINES!
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    Yep
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