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Homework Help: Linear Density & Center of Mass

  1. Nov 23, 2004 #1
    Would anyone be able to give me a hint for this question? Do I take the integral? I have possible answers but I am unsure.

    A rod of length 30.0 cm has a linear density given by:

    D = 50.0g/m + 20.0xg/m^2

    where x is the distance from one end measured in meters. a. What is the mass of the rod. b. how far from the x=0 end is the center of mass?
  2. jcsd
  3. Nov 23, 2004 #2


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    Yes, you have to do the integration from 0 to 0.3 m.

    Linear density (m') is mass/(unit length), so mass M = [tex]\int{m'(x)}\,dx[/tex].
    Last edited: Nov 23, 2004
  4. Nov 23, 2004 #3


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    You'll just integrate to find the mass:

    [tex]M = \int_0^L D(x') dx'[/tex]

    and the center of mass is given by

    [tex]x_{CM} = \frac {1}{M} \int_0^{L} x' D(x') dx'[/tex]
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