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 ∝ [tex]\frac{w\times h^{2} }{l}[/tex]
[tex]L=\frac{k\times w\times h^{2} }{l}[/tex]
where k = proportionality constant
If w = 3 inches, h = 5 inches, l = 120 inches and L = 2600 pounds
Then, [tex]2600=\frac{k\times 3\times 5^{2} }{120}[/tex]
[tex]2600=\frac{75k}{120}[/tex]
[tex]k=\frac{2600\times 120}{75}[/tex]
k = 4160
If w = 5 inches, h = 8 inches and l = 168 inches
[tex]L=\frac{4160\times 5\times 8^{2} }{168}[/tex]
L = 7923.81 pounds
