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 240 inches long can hold a load of 960 pounds. What load would a beam 6 inches wide, 9 inches high, and 192 inches long, of the same material, support? (Round off your answer to the nearest integer.)

a. 240 pounds
b. 480 pounds
c. 720 pounds
d. 960 pounds

Answer 1

The load a wooden beam can support depends on its width, height, and length. By using the given equation and substituting the known values, the load for a beam with different dimensions can be found. In this case, a beam 6 inches wide, 9 inches high, and 192 inches long can support a load of approximately 320 pounds.

Step-by-step explanation:

To find the load a beam can support, we need to use the given equation: L = k(w * h^2) / l, where L is the load, w is the width, h is the height, and l is the length. From the given information, we can determine the value of k by substituting the values of L, w, h, and l. Using the formula, we find k = (L * l) / (w * h^2). Once we have the value of k, we can substitute the given values of w, h, and l into the equation to find the load for the new beam.

For the beam with the dimensions 6 inches wide, 9 inches high, and 192 inches long, we substitute w = 6, h = 9, l = 192, and the value of k we previously found. Solving the equation, we find the load is approximately 320 pounds. Therefore, the load a beam of the same material and with the given dimensions can support is 320 pounds, which is closest to the option (a) 240 pounds.