Posted by deel on Thursday, August 9, 2012 at 2:13am.
The stiffness S of a rectangular beam is proportional to its width (w) times the cube of its depth/height (h). find the dimensions (i.e.: w and h) of stiffest beam that can be cut from a log which has a circular crosssection with diameter of 12in.

math  MathMate, Thursday, August 9, 2012 at 8:52am
You would use the relation of the circular crosssection of (w/2)²+(h/2)²=(12/2)² to relate h and w.
After multiplying by 4 on both sides and rearranging, we have w=√(12²h²).
Now the stiffness has been defined as
S=k(w)(h³) where k is a constant.
If you substitute w from above then S is now a function of h only.
Can you take it from here?

math  deel, Thursday, August 9, 2012 at 11:08am
h^3=s/kw
h^3=s/k(12h)
sorry, I'm still confused how to get the function of h. please help me to complete the assignment. thank you

math  MathMate, Thursday, August 9, 2012 at 11:32am
You need to use the relation
w=√12²h²) to eliminate w from the function S.
S(h)=k w h³
=k √12²h²) h³
To find the maximum/minimum stiffness, you will proceed normally to equate
S'(h) = 0
to solve for h.

math  deel, Thursday, August 9, 2012 at 7:46pm
yes i understand now, thanks for your help

math :)  MathMate, Thursday, August 9, 2012 at 8:46pm
You're welcome!
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