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Thread: Find mass by linear density?

  1. #1
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    Find mass by linear density? ......SOLVED........

    A thin wire is bent into the shape of a semicircle x^2+y^2=4 x>0

    If the linear density is 3, find the mass of the wire.

    Anyone have a clue how to tackle this problem?

    Thanks for your help

    Possible answers -
    18pi
    6pi^2
    3pi
    6pi
    2pi
    Last edited by Alpina540; Jul 13th 2010 at 12:45 PM.
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  2. #2
    A Plied Mathematician
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    If the linear density $\displaystyle \lambda$ is constant, then you can just use the formula $\displaystyle M=\lambda L$, where $\displaystyle M$ is the mass, and $\displaystyle L$ is the length of the wire. Where would you go from there?
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  3. #3
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    Well it looks like now I need to find the length of the curve of wire.
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  4. #4
    A Plied Mathematician
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    Correct. And how could you find the length of a semicircle?
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  5. #5
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    So I just graphed it and cheated a bit and just ruffed out the length of the curve by the Pythagorean theorem and I got the curve to be ~ 6 so 3*6= 18

    So the answer is 6pi?

    Thanks again Adrian!
    Last edited by Alpina540; Jul 13th 2010 at 12:44 PM.
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  6. #6
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    You can get the exact answer (which is not $\displaystyle 18\pi$, by the way). What's the length of a wire that's in the shape of a circle?
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  7. #7
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    ok ok you win, lol (duh about the 18pi! thats what happens when 20 vector calc problems are running through your head.)

    (180/360)*((2(pi)*2)=6.28

    6.28*3=18.84
    6*pi=18.84

    Thanks for your help, I really appreciate it!

    -Anson
    Last edited by Alpina540; Jul 13th 2010 at 12:44 PM.
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  8. #8
    A Plied Mathematician
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    You're very welcome.
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  9. #9
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    By the way, "pie" is what you eat. "pi" is the standard transliteration of $\displaystyle \pi$.
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  10. #10
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    lol........ I knew that I just didn't think about it as I never write pi out in words.
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