Seven homogeneous bricks, each having a length L , are arranged as depicted in the figure. Every brick is shifted by L/10 relative to the one in contact with it. Determine the x -coordinate of the centre of mass of this system with respect to the indicated origin.

Step-by-step solution

Let the mass of each brick be m . The origin O is at the left edge of the bottom-most brick. The x -coordinate of the centre of mass of the first (bottom) brick is: x₁ = L 2 From the figure, the next three bricks are successively shifted to the right by L 10 . Their centres of mass are: x₂ = L 2 + L 10 x₃ = L 2 + 2L 10 x₄ = L 2 + 3L 10 The top three bricks are successively shifted to the left by L 10 . Their centres of mass are: x₅ = x₄ - L 10 = L 2 + 2L 10 x₆ = x₅ - L 10 = L 2 + L 10 x₇ = x₆ - L 10 = L 2 The x -co