## College Physics (4th Edition)

The center of gravity is at the point $(0.417~s, 0.583~s)$
In general the center of gravity is: $x_{cog} = \frac{\sum (w_i~x_i)}{\sum w_i}$, where $w_i$ is the weight of each object, and $x_i$ is the position of each object. We can divide the plate into three equal square pieces with sides of $0.5~s$. We can find the center of gravity for each piece. We can find the coordinates of the center of gravity of the bottom left piece: $(0.25~s, 0.25~s)$ We can find the coordinates of the center of gravity of the top left piece: $(0.25~s, 0.75~s)$ We can find the coordinates of the center of gravity of the top right piece: $(0.75~s, 0.75~s)$ Let $W$ be the weight of each piece. We can find the x-coordinate of the plate's center of gravity: $x_{cog} = \frac{W~(0.25~s)+W(0.25~s)+W~(0.75~s)}{W+W+W}$ $x_{cog} = 0.417~s$ We can find the y-coordinate of the plate's center of gravity: $y_{cog} = \frac{W~(0.25~s)+W(0.75~s)+W~(0.75~s)}{W+W+W}$ $y_{cog} = 0.583~s$ The center of gravity is at the point $(0.417~s, 0.583~s)$