Problem 9.48 The location of the center of mass of the partially eaten, 12-inch

Question

Problem 9.48

The location of the center of mass of the partially eaten, 12-inch diameter pizza shown in the figure (Figure 1) is Xcm = - 1.5 in
and Ycm = -1.5 in .

Part A

Assuming each quadrant of the pizza to be the same, find the center of mass of the uneaten pizza above the x axis (that is, the portion of the pizza in the second quadrant). Find the x-coordinate.

Express your answer using two significant figures.

  in  

Part B

Find the y-coordinate.

Express your answer using two significant figures.

  in  

Part B

Find the y-coordinate.

Express your answer using two significant figures.

Explanation / Answer

given
x - coordinate of the center of mass is Xcm = -1.5in
y - coordinate of the center of mass is Ycm = -1.5in
let x2 , x3 & x4 bethe x - cordinates of remaining 3 parts of the pizza &let y2 , y3 & y4 bethe y-cordinates.
then by symmetry x2 = x3
= x4 ----(1)
& y2 = -y3
= -y4 -------(2)

Xcm = mx2 + mx3+ mx4/m+m+m
= m(x2 + x3 + x4)/3m
= m(x2 + x2 + x2) /3m
= x2/3
or x2 = 3Xcm
= 3(-1.5in)
xcm = - 4.5 in

Ycm = my2 + my3 +my4/m+m+m
= m(y2 - y2 -y2)/3m
= -y2/3
or y2 = -3Ycm
=-3(-1.5in)
ycm = 4.5 in

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