Solving the Problem

Question

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length. If a beam that is 6 inches​ wide, 8 inches​ deep, and 4 feet long can support a weight of 768 ​pounds, how much weight could the same type of beam that is 4 inches​ wide, 6 inches​ deep, and 8 feet long​ support?

Answer 1

S = k w d^2 / L; strength S, width w, depth d, and length L

768 = k * 6 * 8^2 / 48 <--- 4ft=48 in

768 = k*384/48

k=96

S = 96 w d^2 / L

S = 96*4*6^2/ 96 <--- 8 ft = 96 in

= 144