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March 30, 2017

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The density of a 5.0-m long rod can be described by the linear density function λ(x) = 145 g/m + 14.2x g/m2. One end of the rod is positioned at x = 0 and the other at x = 5 m.
a) Determine the total mass of the rod.
b) Determine the center-of-mass coordinate.

  • Physics - Center of Mass - ,

    m=∫ρ•dx =∫(145+14.2x) •dx =
    = ∫145•dx+∫14.2•x•dx =
    =145•x + 14.2x²/2=
    =145•5 + 14.2•25/2 =902.5 g.

    Calculate the integral
    ∫ρ•x•dx =
    =∫(145+14.2x) •x •dx =
    = ∫145•x•dx+∫14.2•x²•dx =
    =145•x²/2 + 14.2x³/3=
    =145•25/2 + 14.2•125/3=2404.2 kg.

    x(c/m/) =∫ρ•x•dx/∫ρ•dx =2404.2/902.5=2.66 m.

    C.M. (2.66 m; 0)

  • Question - ,

    Question: Shouldn't the 2404.2 be in grams and not Kg?

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