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Does tHis Make Sence?

  1. Nov 16, 2005 #1
    a cubical box has edges of length 40cm with an open top.

    Find the x, y, z coordinates of The Centre Of Mass

    *****

    in my head I cut the box along the x axis to get this

    (let m = the mass of one side of the box)

    [tex]COMx=\frac{1}{M}\times(m1x1 + m2x2)[/tex]

    [tex]COMx=\frac{1}{5M}(2.5M\times 40cm)+(2.5M\times 0cm)[/tex]
    [tex]COMx=20cm[/tex]

    [tex]COMy=(2a\times 40cm)+(3M\times 0)[/tex]
    [tex]COMy=16cm[/tex]

    [tex]COMz=\frac{1}{5M}(2.5M\times 40cm)+(2.5M\times 0cm)[/tex]
    [tex]COMz=20cm[/tex]

    Therefore [tex]COM=(20cm,16cm,20cm)[/tex]
     
    Last edited: Nov 16, 2005
  2. jcsd
  3. Nov 17, 2005 #2
    You could also decompose the problem : the sides are equivalent to a 4m mass on the axis of symmetry. Then the bottom makes lowering of the CM by : l/2/5=l/10.

    Which in your case l=40, hence the lowering from the center is 4cm, and because the center is at y=20, you get CM(y)=20-4=16cm which is the same result.
     
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