Question

The maximum load of a horizontal beam that is supported at both ends varies jointly as the width and the height and inversely as the length between the supports. A beam 6m long, 0.1m wide, and 0.06 m high supports a load of 360kg. What is the maximum load supported by a beam 16m long, 0.2m wide, and 0.08 m high?

Answer 1

Answer:

$360kg$

Explanation:

Here, we want to get the maximum load supported

From the first part of the question, we have it that:

The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports

Mathematically, we have that as:

$g\text{ = k }\times\frac{wh}{l}$

where k is the proportionality constant

Now, let us get the value of k

We substitute the first set of values as follows:

$\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}$

Now, using this value of k, we want to get the value of g

Mathematically, we have that as:

$g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg$