Question

. In the frame below, the mass per unit length for member BD is half of the mass per unit length for members AC and CE, which are equal. Locate the position (T, y) of the center of gravity. Member AC' has length 13 m and member CE has length 8m. Point B lies half way between points A and C and point D lies half way between C and E.

Could you please show me how to approach the incorporating mass into finding the center of gravity, so far I know how to find the center, but without the mass complication. Thanks

Answer 1

Let us take m = mass per unit length x = m_1 x_1 + m_2 x_2 + m_3 x_3/m_1 + m_2 + m_3 y = m_1 y_1 + m_2 y_2 + m_3 y_3/m_1 + m_2 + m_3 Centroid: - x = (13 times m) (0) + (8 times m) times 4 + (7.632 times m) times (2)/13 m + 8 m + 7.632 m x = 47.264 m/28.632 m = > x = 1.65 m y = (13 m) times (6.5) + (8 m) times 13 + (7.632 m) times (13 - 13/4)/28.632 m y = 262.912 m/28.632 m y = 9.182 m