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Answer :
The beam that is 6 inches wide, 6 inches deep, and 12 feet long can support 4.5 pounds.
Given that the strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length. Let us assume that a constant, k, is used to relate the strength of the beam to the width, depth, and length.
That is, k × width × depth²/length = strength.
Part 1
Given that the beam is 6 inches wide, 8 inches deep, and 4 feet long, and can support a weight of 576 pounds, we can determine k as follows:
k × 6 × 8²/4 = 576k × 6 × 64/4 = 576192k = 576k = 576/192k = 3
Using k, we can determine the strength of the second beam that is 6 inches wide, 6 inches deep, and 12 feet long.That is k × width × depth²/length = strength
For the second beam, width = 6 inches, depth = 6 inches, length = 12 feet = 144 inches.
Therefore, strength = 3 × 6 × 6²/144 = 4.5 pounds
Part 2
Therefore, the beam that is 6 inches wide, 6 inches deep, and 12 feet long can support 4.5 pounds.
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