5. +-12 points My Notes Ask Your Teacher Find the x- and y-coordinates of the ce

Question

5. +-12 points My Notes Ask Your Teacher Find the x- and y-coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed as shown in the figure below. The dimensions of the cutout area = 4.30 ft and b = 2.50 ft. HINTS: Think of the board as being made of two rectangular pieces, very similar to what we did in lab. It is useful to redraw your board with the dimensions in your version of this problem, as the figure is "generic" and may not be a very good representation of the dimensions you were given. Find the x,y location of the centers of gravity of these two rectangles. Figure out how much mass each of the rectangles has. The mass will be proportional to the area of the rectangle. If you like, take the mass density of the plywood to be 1.0 kg/m2 for each square meter of board. With this information, predict approximately where the center of gravity of the board should be. Then use these masses (and their I prediction y(ft) r(ft) ft ft

Explanation / Answer

Let the center of gravity = (x1, y1)
If we put the removed portion in its place, then center of gravity of removed portion = (x2, y2),
center of gravity of whole sheet = (x, y),

A2 = a*b =4.3*2.5 = 10.75 ft2

A1 = 8*4 - 10.75= 21.25 ft2
x2 = 8 - 4.3/2 = 5.85 ft
y2 = 4 - 2.5/2 =2.75 ft
x = 8/2 = 4 ft
y = 4/2 = 2 ft

x = (A1x1 + A2 x2)/(A1+A2)

4 = (21.25* x1 + 10.75 * 5.85)/32

128=21.25x1+62.89

x1=3.06 ft

y = (A1 y1 + A2y2)/(A1+A2)

2 = (21.25 * y1 + 10.75 * 2.75)/32

64=21.25y1+29.56

y1=1.62 m

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