Question

The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam one third 1/3 foot​ wide, one half 1/2 foot​ high, and 15 feet long can support 30 ​tons, find how much a similar beam can support if the beam is one half 1/2 foot​ wide, one third 1/3 foot​ high, and 15 feet long?

Answer 1

Answer:13.33 tons

Explanation:

Given

Weight of a material varies as

$W\propto b$  (width)

$W\propto h^2$  (height)

$W\propto \frac{1}{L}$  (length)

$W=k\frac{bh^2}{L}$

Dimension of first beam

$b=\frac{1}{3}$ foot

$h=\frac{1}{2}$ foot

$L=15$ foot

Weight supported $W=20 tons$

Second beam

$b=\frac{1}{2} foot$

$h=\frac{1}{3} foot$

$h=15 feet$

let weight of second beam be $W_2$

taking both beams at the same time

$\frac{20}{W_2}=\frac{\frac{1}{3}\times (\frac{1}{2})^2}{15}\times \frac{15}{\frac{1}{2}\times (\frac{1}{3})^2}$

$\frac{20}{W_2}=\frac{3}{2}$

$W_2=\frac{40}{3} \approx 13.33 tons$