By weighted average method, the x-coordinates of the center of mass of the compound figure, the uniform thin L-shaped construction brace is [tex]\bar x = \frac{1.10\cdot m_{A}+2.10\cdot m_{B}}{m_{A}+m_{B}}[/tex] meters.
How to determine the coordinates of the center of mass of a compound figure
Let suppose that the entire construction has a uniform mass, then the coordinates of the center of mass can be determined by definition of weighted average:
[tex]\bar x = \frac{\sum \limits_{i = 1}^{n}x_{i}\cdot m_{i}}{\sum \limits_{i=1}^{n}m_{i}}[/tex] (1)
[tex]\bar y = \frac{\sum \limits_{i = 1}^{n}y_{i}\cdot m_{i}}{\sum \limits_{i=1}^{n}m_{i}}[/tex] (2)
If we know that a = 2.20 m and b = 1.63 m, then the x-coordinates of the center of mass of the compound figure is:
[tex]\bar x = \frac{1.10\cdot m_{A}+2.10\cdot m_{B}}{m_{A}+m_{B}}[/tex]
By weighted average method, the x-coordinates of the center of mass of the compound figure, the uniform thin L-shaped construction brace is [tex]\bar x = \frac{1.10\cdot m_{A}+2.10\cdot m_{B}}{m_{A}+m_{B}}[/tex] meters.
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