The objects in the figure below are constructed of uniform wire bent into the sh

Question

The objects in the figure below are constructed of uniform wire bent into the shapes shown (Figure 1) . Each piece has a length of 0.47 . 1.Find the x- and y- coordinates of the center of mass of the object A . The angle shown is 59 . Assume the origin to be at the bottom left point. 2.Find the x- and y-coordinates of the center of mass of the object B . Assume the origin to be at the bottom left point. 3.Find the x- and y-coordinates of the center of mass of the object C . Assume the origin to be at the bottom left point. 4.Find the x- and y-coordinates of the center of mass of the object D . Assume the origin to be at the bottom left point.

Explanation / Answer

I'll do b. It is symmetrical, so the x dimension is known as (1/2) L I assume the sticks have a finite width, not given. But I think it is needed. Also assuming the sticks overlap at the corners, otherwise you get into bevels and gets very complicated. for the y dimension, assume the width of each stick is d and length is L (0.46 is too complicated to carry) Break it down to 3 rectangles, each of dimensions of d x L. Starting with y = 0 at the bottom. The formula is sum of moments (area x distance from reference) divided by sum of areas. C = [ dL(d/2) + 2dL(L/2) ] / [ dL + 2dL ] C = ( d²L/2 + dL²) /(3dL) = (1/3) (d/2 + L) if you assume d is very small, this reduces to L/3 you can use similar methods for the others.

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