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Calculus 3 question- don't even know how to approach this problem

  1. Feb 24, 2010 #1
    Find the mass of one turn of wire in the form of a helix with a linear density e^(-z) in lbs/ft.

    Would I write as <e^(-z)*cost,e^(-z)*sint, t>? Maybe?
  2. jcsd
  3. May 20, 2011 #2
    The first thing to check for is units. The problem with your proposed solution is that the x and y components have units of weight, while the z component has units of length.

    What is given is the density (ratio weight per length), so to get weight just multiply the density by the length. The arclength of a curve is given as the integral of the modulus of the derivative of the curve. So just put the density inside the integral and solve.
  4. May 20, 2011 #3


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    First, you should note that the problem is not well posed. It makes a difference which turn of the wire since the density is not constant. You want to calculate

    [tex]\int_C \delta(x,y,z)\ ds[/tex]

    with appropriate units.
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