Consider the following mass distribution where the x- and y-coordinates are give

Question

Consider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.4 kg at (0.0, 3.7) m, and 4.0 kg at (2.8, 0.0) m. Where should a fourth object of 8.1 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? x = m y = m
Consider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.4 kg at (0.0, 3.7) m, and 4.0 kg at (2.8, 0.0) m. Where should a fourth object of 8.1 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? x = m y = m
Consider the following mass distribution where the x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.4 kg at (0.0, 3.7) m, and 4.0 kg at (2.8, 0.0) m. Where should a fourth object of 8.1 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? x = m y = m

Explanation / Answer

Let the coordinates of required point be x and y

considering sum of moments about x:

5 x 0 + 3.4 x 0 + 4 x 2.8 + 8.1 x = 0

0 + 0 + 11.2 + 8.1 x = 0

x = -11.2/8.1 = -1.38 m

considering sum of moments about y:

5 x 0 + 3.4 x 3.7 + 4 x 0 + 8.1 x y = 0

y = -1.55 m

Hence, 8.1 should be placed at (-1.38,-1.55) m

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