Question

The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 2 inches wide, 7 inches high, and 192 inches long can hold a load of 2480 pounds.

What load would a beam 4 inches wide, 6 inches high, and 120 inches long, of the same material, support?
(Round off your answer to the nearest integer.)

Answer 1

5830.54 pounds

Explanation:

load varies directly as the product of width and square of height and inversely as the length

load = kwh²/ L where w = width in inches, h = height also in inches, L = length in inches and k is constant

2480 = (k × 2 × 7²) / 192

2480 × 192 = k × 2 × 49

k = 476160 / 98 = 4858.78

load that 4 ince wide, 6 inches high, and 120 inches long of the same material support = kwh² / L = 4858.78 × 4 × 6² / 120 = 699664.32 / 120 = 5830.54 pounds