Question 1106811
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The information tells us that the mass m that can be supported by a beam of length l, width w, and height (thickness) h is<br>
{{{m = k((w)(h^2)/l)}}}<br>
where k is a constant.<br>
The value of the constant can be determined from the given information: When the length is 6m, the width is 0.1m, and the height is 0.06m, the maximum load is 360kg. So<br>
{{{360 = k((0.1)(0.06^2)/6)}}}
{{{360 = k(.00036/6) = k(.00006)}}}
{{{k = 6000000}}}<br>
Then using this constant with the new beam measurements,
{{{m = 6000000((0.2)(0.08^2))/16}}}
{{{m = 6000000(.00128/16) = 480}}}<br>
That is a general method for solving problems like this.  But if the numbers are fairly simple, as in this case, I find it easier just to modify the given mass according to each changed dimension of the beam.<br>
The length of the beam changes from 6m to 16m; since the mass varies inversely as the length, the maximum load decreases by a factor of 6/16 = 3/8.
The width doubles from 0.1m to 0.2m; since the mass varies directly with the width, the maximum load increases by a factor of 2.
The height changes from 0.06m to 0.08m; since the mass varies directly with the square of the height, the maximum load increases by a factor of (0.08/0.06)^2 = (4/3)^2 = 16/9.<br>
Then the new maximum load is
{{{360*(3/8)*(2)*(16/9) = 360*(4/3) = 480}}}