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Find the mass and density of a beam

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data
    I have a steel cantilever beam of length 5m, width 0.5m, and thickness 0.1m. The beam has uniform density.

    2. Relevant equations
    M &= \iint_D\rho(x, y)dxdy\\
    \rho &= M/\ell

    3. The attempt at a solution
    If I don't know the mass or density, how can I find either one when each is defined with the other?
  2. jcsd
  3. Oct 15, 2014 #2


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    The density is given to be constant, so just call it ##\rho##. You have to decide what the units are, depending on whether it is a linear or volume density. Given your formulas above, maybe it's a linear density. In any case, since it is constant, you don't need an integral to calculate the mass.
  4. Oct 15, 2014 #3
    How do I find the mass then? Will it just be called ##M = 5\rho## or can I get an explicit value for ##\rho##?
  5. Oct 16, 2014 #4


    Staff: Mentor

    With the given information all you can do is write expressions that represent mass and density. If the density is volume density (##\rho## in units of kg/m3), then the mass would be ##V\rho##.
  6. Oct 16, 2014 #5


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    Perhaps you're meant to look up the density of steel.
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