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Mass of Ceramic on a Wire

  1. Jul 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A metal wire is given a ceramic coating to protect it against heat. The machine that applies the coating
    does not do so very uniformly.

    The wire is in the shape of the curve
    curve.PNG

    The density of the ceramic on the wire is
    two.PNG

    Use a line integral to calculate the mass of the ceramic on the wire.

    2. Relevant equations
    ∫ f(r,t,ρ) drdtdρ

    3. The attempt at a solution
    Here's my 'attempt at a solution':
    I tried to make a triple integral, but I dont quite know what to do next.
    0π0π0π
     
  2. jcsd
  3. Jul 15, 2016 #2

    SteamKing

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    Why? A triple integral won't help you solve this problem.

    First, think about how you would find the length of the metal wire (without the ceramic coating). How would you express that length as a line integral?

    http://tutorial.math.lamar.edu/Classes/CalcIII/VectorArcLength.aspx

    Once you figure out what a small element of the length of the wire is, then apply the density function of the ceramic coating. How would you calculate the total mass of the ceramic?
     
  4. Jul 18, 2016 #3

    haruspex

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    ... because you are not given a diameter for the wire nor the thickness of the coating, so you have no idea what the volume is.
    I would take it that the given density is grams/centimetre, not grams/ cubic metre, and that the curve has units of centimetres.

    By the way, you can simplify it by a simple substitution for t.
     
  5. Jul 18, 2016 #4
    Ok, so I tried to do it in a CAS. Here is what I got...not sure how right it is though.


     
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