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 4 inches wide, 6 inches high, and 192 inches long can hold a load of 3950 pounds. What load would a beam 3 inches wide 5 inches high, and 216 inches long of the same material support? Round your answer to the nearest integer if necessary.

Answer 1

data

First beam

w = 4 in

h = 6 in

l = 192 in

Second beam

w = 3 in

h = 5 in

l = 216 in

Formula

S = (w h^2) / l

Substitution

S = (4 * 6^2) / 216

Simplification

S = 144/216

Result

S = 2/3

Second beam

S = (3 *5^2)/216

Simplification

S = 75/216

Result

S = 25/72

Rule of three

2/3 ----------------------3950 pounds

25/72 ------------------ x

x = 2057 pounds

The second beam can hold 2057 pounds