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Answer :
A beam of the same material that is 2 inches wide and 1 inch thick can support 80 pounds.
We can solve this problem using the concept of variation. Here's how:
1. Express the relationship:
Since the strength of the beam varies jointly with its width (w) and the square of its thickness (t^2), we can express this relationship as follows:
Strength (S) ∝ w * t²
2. Find the constant of proportionality:
We know that a beam 7 inches wide and 3 inches thick supports 2520 pounds. Plugging these values into the equation, we can find the constant of proportionality (k):
2520 ∝ 7 * 3²
2520 ∝ 63k
k ≈ 40 (rounded to the nearest whole number)
3. Calculate the strength of the second beam:
Now, we can calculate the strength of the second beam with a width of 2 inches and a thickness of 1 inch:
Strength (S2) = k * w2 * t2²
S2 = 40 * 2² * 1²
S2 ≈ 80 pounds
Therefore, the second beam, which is smaller in size, can support approximately 80 pounds.
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