Question

Using Center of Gravity Identical blocks of unit length are stacked on top of each other at the edge of a table. The center of gravity of the top block must lie over the block below it, the center of gravity of the top two blocks must lie over the block below them, and so on (see figure).

(a) When there are three blocks, show that it is possible to stack them so that the left edge of the top block extends 11/12 unit beyond the edge of the table.

(b) Is it possible to stack the blocks so that the right edge of the top block extends beyond the edge of the table?

(c) How far beyond the table can the blocks be stacked?

Answer 1

Therefore overhang = 1/2 + 1/4 = 3/4 For three bricks x_3 times 3m = x_1 times m If x_1 = 1/2, x_3 = 1/6 therefore Total overhang = 1/2 + 1/4 + 1/6 = 11/12 Similarly for 4 bricks x_4 times 4m = x_4 times m: x_4 = 1/8 therefore Total overhang = 1/2 + 1/4 + 1/6 + 1/8 = 2s/24 = 11/24 In lewis case the left edge overhang is more than one brick The pile of these bricks will fall when center of gravity exceeds beyond table edge For 4 bricks C.G m times L_1/2 + m times L_1 + m times 3L_1/2 + m_x_0/4m = m (1/2 + 1 + 3/2)/4m = 1 + 2 + 3/2/4 = 6/8 = 3/4 \r\n For 5 bricks m times 0 + m times 1/2 + m times 1 + m times 3/2 + m times 2/5m = m (1/2 + 1 + 3/2 + 2)/5 = 1 + 2