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

`360kg`

Step-by-step 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 }*(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{ = }(k*0.1*0.06)/(6) \\ \\ k\text{ = 360,000 }(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{ = }(360,000*0.2*0.08)/(16)\text{ = 360 }kg`