Question

The strength of a beam varies inversely with the square of its length. If a 10-foot beam can support 500 pounds how many pounds can a 13 foot beam support? Round the answer to the nearest pound.

Answer 1

The beam varies inversely with the square of it's length. Let's call S the strength and L the length.

Then we can write:

$S=\frac{k}{L^2}$

For a constant k.

Then, we know that if L = 10ft then S = 500 pounds

We write:

$\begin{gathered} 500=\frac{k}{(10)^2} \\ \end{gathered}$

And solve for k:

$k=500\cdot10^2=500\cdot100=50,000$

Then the inverse relation equation is:

$S=\frac{50,000}{L^2}$

Then, for L = 13ft, the strength is:

$S=\frac{50,000}{13^2}=\frac{50,000}{169}=295.857$

To the nearest pound, a beam of 13ft can support 296 pounds.