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 3 inches wide, 5 inches high, and 120 inches long can hold a load of 2600 pounds. What load would a beam 5 inches wide, 8 inches high, and 168 inches long, of the same material, support?

Answer 1

Answer:

Load that the beam can support = 7923.81 pounds

Step-by-step explanation:

The safe load L, of the beam varies directly as the product of the width and the square of the height.

L∝ (w × h²)

And varies inversely as the length of the wooden beam.

L ∝ $\frac{w\times h^{2} }{l}$

$L=\frac{k\times w\times h^{2} }{l}$

where k = proportionality constant

If w = 3 inches, h = 5 inches, l = 120 inches and L = 2600 pounds

Then, $2600=\frac{k\times 3\times 5^{2} }{120}$

$2600=\frac{75k}{120}$

$k=\frac{2600\times 120}{75}$

k = 4160

If w = 5 inches, h = 8 inches and l = 168 inches

$L=\frac{4160\times 5\times 8^{2} }{168}$

L = 7923.81 pounds