Part A Locate the centroid of the wire bent in the shape shown. Take x = 270mm ,

Question

Part A Locate the centroid of the wire bent in the shape shown. Take x = 270mm , y = 540 mm, z = 360mm. (Figure 1) Express your answer to three significant figures and include the appropriate units. x = Value Units Part B Locate the centroid of the wire bent in the shape shown. z = 270 mm, y = 540 mm, z = 360 mm. Express your answer to three significant figures and include the appropriate units. y = Value Units Part C Part C Locate the centroid of the wire bent in the shape shown. x = 270 mm, y = 540 mm, z = 360 mm. Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Let us break the rod into three segments, length x = 270 mm is segment 1, y = 540 mm is segment 2 and z = 360 mm is segment 3. And then identify the centroid of each of the segment.

Now for segment 1 :

l1 = 270 mm, coordinate of centroid, x1 = 270/2 = 135 mm, y1 = 0, z1 = 0.

For segment 2 :

l2 = 540 mm, coordinate of centroid, x2 = 270 mm, y2 = 270mm, z2 = 0.

For segment 3 :

l3 = 360 mm, coordinate of centroid, x3 = 270 mm, y3 = 540 mm, z3 =-180 mm.

Then the coordinate of the centroid of the whole system is,

x = (l1*x1+l2*x2+l3*x3)/(l1+l2+l3) = (270135+540270+360270)(270+540+360) = 238.85 mm

y = (l1*y1+l2*y2+l3*y3)/(l1+l2+l3) = (2700+540270+360540)(270+540+360) = 290.77 mm

z = (l1*z1+l2*z2+l3*z3)/(l1+l2+l3) = (2700+5400?360180)(270+540+360) = -55.38 mm

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