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 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.

Answer 1

we know that

L=KW(h^2)/l

we have that

W=5 in

h=8 in

l=216 in

L=7670 pounds

step 1

Find the value of K (constant of proportionality)

substitute the given values in the equation

7670=K(5)(8^2)/216

7670=k(1.4815)

k=5,177.25

step 2

we have the equation

L=(5,177.25)W(h^2)/l

for

W=3 in

h=5 in

l=240 in

substitute in the equation and solve for L

L=(5,177.25)(3)(5^2)/240

L=1,617.89 pounds

Round your answer to the nearest integer

so

L=1,618 pounds