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Linear Mass Density Problem

  1. Mar 2, 2005 #1
    I'm having a hard time with this.
    A long thin rod lies along the x-axis. One end is at x=2.00 m and the other at x=3.00 m. Its linear mass density λ = 0.300 x2+ 0.500, in kg/m. Calculate mass of the rod.

    Can anybody help?
  2. jcsd
  3. Mar 2, 2005 #2
    I take it you mean [itex]\lambda = .300x^2 + .500[/itex]?

    Note that

    [tex]m = \int_{x_1}^{x_2}\lambda(x) dx[/tex].

  4. Mar 2, 2005 #3
    But then how would I find the center of mass?
  5. Mar 2, 2005 #4
    The center of mass is just the weighted average of the density. You really should be able to look these formulas up on your own, or memorize them.

    [tex]x_{CM}= \frac{1}{m}\int_{x_1}^{x_2} x \lambda(x) dx[/tex]

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