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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.

Hint: The mass of any segment of the plywood sheet is proportional to the area of that segment.

Answer :

Final answer:

The center of gravity is calculated by summing up the products of the area and their corresponding x or y distances for the remaining 3 quadrants and dividing by the total area of those 3 quadrants.

Explanation:

In this problem, you are asked to find the center of gravity of a plywood sheet with one quadrant removed. The mass of the sheet is proportional to its area, meaninig segments with larger area will have higher mass. The x-coordinate of the center of gravity can be calculated using the formula: X = (1/Area of total sheet) * Integral of (x * differential mass) over the total area of the plywood sheet. Similarly, the y-coordinate of the center of gravity is obtained by switching x with y in the previous formula. When one of the quadrants is absent, as in your plywood, you need to sum up the products of the area and their corresponding x or y distances for the remaining 3 quadrants and divide by the total area of those 3 quadrants.

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