To approach this problem, first let's note that the corbeled arch will be symmetric. Thus, we only need to find out how many bricks are needed to span half of the arch (0.50 m) and then double that number.
Let's denote the number of bricks required to span half of the arch as n. According to the principle of stability given, the length that the top brick can extend is 0.30 m (total length of the top brick) * (1/2 + 1/4 + 1/6 + ... + 1/(2n)), where n is the number of bricks for half of the arch. Notice that we are summing a series of fractions with denominators of even integers.
We want to find the minimum number of bricks such that their extensions can cover half of the arch (0.50 m), so:
0.50 <= 0.30 * (1/2 + 1/4 + 1/6 + ... + 1/(2n))
Divide both sides by 0.30:
5/3 <= 1/2 + 1/4 + 1/6 + ... + 1/(2n)
Now we can find the smallest n that satisfies this inequality by calculating the sum of fractions:
(1/2) = 0.5
(1/2) + (1/4) = 0.75
(1/2) + (1/4) + (1/6) = 0.92
(1/2) + (1/4) + (1/6) + (1/8) = 1.08
We find that n = 4 satisfies the inequality. So we need 4 bricks to span half of the arch. Since the arch is symmetric, we need another 4 bricks to span the other half. Additional bricks are required at the top and the base of each half-span, so we add 4 more bricks (2 for the top and 2 for the base).
Thus, a minimum of 4 + 4 + 4 = 12 bricks is needed to build the corbeled arch.
Four bricks are to be stacked at the edge of a table, each brick overhanging the one below it, so that the top brick extends as far as possible beyond the edge of the table.
*The construction in stable equilibrium, bricks must extend no more than (starting at the top) 1/2, 1/4, 1/6, 1/8 of their length beyond the one below.
A builder wants to build a corbeled arch, based on the principle of stability, what minimum number of bricks, each 0.30 m long, is needed if the arch is to span 1.0 m? Be sure to include in the total number of bricks one brick on top and one brick at the base of each half-span of the arch.
I can't figure out how to approach the above problem. I tried to set up an equation where the distance spanned is equal to the length of the brick divided by two times the number of bricks.
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