The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.
Based on the given conditions,
The safe load = L
A wooden beam of width = w
Height = h
Length = l
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∝ (w × h²)/l
L = (Equation-1)
Where k = proportionality constant
If w = 4 inches, h = 7 inches, l = 240 inches and L = 2540 pounds
Then,
We can substitute values in equation-1,
L =
2540 = (k*4*)/240
2540 = (k*4*49)/240
2540 = (k*196)/240
2540*240 = k*196
609600 = k*196
609600/196 = k
3110.20 = k
If w = 5 inches, h = 8 inches and l = 216 inches
L =
L = ( 3110.20 * 5 * )/216
L = ( 3110.20 * 5 *64 )/216
L = 995264/216
L = 4607.7 pounds
Therefore,
The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.
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