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

Step-by-step explanation:

Given

Weight of a material varies as

`W\propto b` (width)

`W\propto h^2` (height)

`W\propto (1)/(L)` (length)

`W=k(bh^2)/(L)`

Dimension of first beam

`b=(1)/(3)` foot

`h=(1)/(2)` foot

`L=15` foot

Weight supported
`W=20 tons`

Second beam

`b=(1)/(2) foot`

`h=(1)/(3) foot`

`h=15 feet`

let weight of second beam be
`W_2`

taking both beams at the same time

`(20)/(W_2)=((1)/(3)* ((1)/(2))^2)/(15)* (15)/((1)/(2)* ((1)/(3))^2)`

`(20)/(W_2)=(3)/(2)`

`W_2=(40)/(3) \approx 13.33 tons`