Answer :
Final answer:
The center of gravity for the plywood sheet with the upper right quadrant removed falls at (5/3) feet along the x-axis and (7/3) feet along the y-axis.
Explanation:
The problem revolves around finding the center of gravity of a 4 ft x 8 ft uniform sheet of plywood with the upper right quadrant removed. The plywood can be treated as four equal quadrants with each quadrant having an equal proportion of the total mass. After the top right quadrant is removed, the total relevant mass is 75% of the original total.
The centre of mass of the plywood originally, assuming uniform density, is simply the geometrical center at x = 4/2=2 ft, y = 8/2=4 ft. Each of these three remaining quadrants will have their respective centers of mass at (1,1), (1,3), and (3,3), taking the bottom-left corner as the (0,0) coordinate.
The X-coordinate of the center of mass is given by: (1 x Mass of quadrant + 1 x Mass of quadrant + 3 x Mass of quadrant) / Total Mass, which translates into (1 + 1 + 3)(Mass of quadrant) / (3 x Mass of quadrant) = 5/3 ft, similarly, the Y-coordinate follows the same logic equal to (1 + 3 + 3) / 3 = 7/3 ft.
Learn more about Center of Gravity here:
https://brainly.com/question/20662235
#SPJ2
