SOLUTION: Use the fact that the load a beam with a rectangular cross section can support is jointly proportional to the beam's width and the square of its depth and inversely proportional to

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Question 1205455: Use the fact that the load a beam with a rectangular cross section can support is jointly proportional to the beam's width and the square of its depth and inversely proportional to its length.
A beam 3 cm wide and 5 cm deep can support a load of 630 kg. What load can it support when turned on its side?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given information gives us the following equation:

load=%28%28k%29%28width%29%28depth%5E2%29%29%2Flength

where k is a constant of proportionality.

We are given the load that can be supported for a given width and depth. But we are not given the length, so we can't determine the constant of proportionality.

But to solve the problem we don't have to know the value of k. k is some constant, and in this problem the length is a constant. So the difference in the load that can be supported is due to putting the bean on its side -- i.e., switching the width and depth.

For the load of 630kg, %28width%29%28depth%5E2%29=%283%29%285%5E2%29=75.

When the beam is turned on its side, %28width%29%28depth%5E2%29=%285%29%283%5E2%29=45.

So the load that can be supported when the beam is turned on its side is 45/75 = 3/5 of the load it can support in the given configuration.

630*(3/5)=378

ANSWER: 378kg