Three equal masses lie at the corners of an equilateral triangle of side l. find the center of mass.

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Physics

Gary

1 January, 02:50

Three equal masses lie at the corners of an equilateral triangle of side l. find the center of mass.

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Slade Freeman · Answer 1

If two of the masses are at (0, 0) and (L, 0), by symmetry the x-coordinate of the third mass must be L/2, and then by the Pythagorean theorem its y-coordinate must be L (âš3) / 2. Thus the position of the third mass is (L/2, L (âš3) / 2). Let each mass be m and C be the position of its center of mass. Then C = (1 / (3m)) (m (0, 0) + m (L, 0) + m (L/2, L (âš3) / 2)). = (1/3) (3L/2, L (âš3) / 2). = (L/2, L (âš3) / 6). That is, X_c = L/2 and Y_c = L (âš3) / 6.